*Volatility* is the standard deviation of the change in value of a financial instrument and is considered a proxy for risk.

- Wikipedia: Volatility
- riskglossary.com: Volatility
- define:volatility
- Wikipedia: Implied volatility
- Wikipedia: Volatility clustering
- Wikipedia: Volatility Smile
- Publications
- Recent Publications

- GALÍ, Jordi and Tommaso MONACELLI, 2005. Monetary Policy and Exchange Rate Volatility in a Small Open Economy.
*Review of Economic Studies*, Vol. 72, No. 3, pp. 707-734. [Cited by 229] (273.77/year)

Abstract: "We lay out a*small open economy*version of the Calvo sticky price model, and show how the equilibrium dynamics can be reduced to a simple representation in domestic inflation and the output gap. We use the resulting framework to analyse the macroeconomic implications of three alternative rule-based policy regimes for the small open economy: domestic inflation and CPI-based Taylor rules, and an exchange rate peg. We show that a key difference among these regimes lies in the relative amount of exchange rate volatility that they entail. We also discuss a special case for which domestic inflation targeting constitutes the optimal policy, and where a simple second order approximation to the utility of the representative consumer can be derived and used to evaluate the welfare losses associated with the suboptimal rules."

- DING, Z., C.W.J. GRANGER and R.F. ENGLE, 1993. A long memory property of stock market returns and a new model,
*Journal of Empirical Finance*1, 83-106. [Cited by 536] (109.72/year)

Abstract: "A ‘long memory’ property of stock market returns is investigated in this paper. It is found that not only there is substantially more correlation between absolute returns than returns themselves, but the power transformation of the absolute return ¦*r*_{t}¦^{d}also has quite high autocorrelation for long lags. It is possible to characterize ¦*r*_{t}¦^{d}to be ‘long memory’ and this property is strongest when*d*is around 1. This result appears to argue against ARCH type specifications based upon squared returns. But our Monte-Carlo study shows that both ARCH type models based on squared returns and those based on absolute return can produce this property. A new general class of models is proposed which allows the power δ of the heteroskedasticity equation to be estimated from the data."

- MANTEGNA, R.N. and H.E. STANLEY, 1999. Introduction to Econophysics: Correlations and Complexity in Finance. books.google.com. [Cited by 730] (106.74/year)

"The autocorrelation function of price changes has exponential decay with small characteristic times - a few trading minutes for the S&P500 index (Fig. 7.3). However, pairwise independence does not directly imply that the price changes are independent random variables. Several studies performed by economists and physicists have shown that the autocorrelation function of nonlinear functions of price changes has a much longer time memory. Indeed nonlinear functions such as the absolute value or the square are long-range correlated for stock market indices and for foreign exchange currency rates.

The presence of long-range correlation in the square value of price changes suggests that there might be some other fundamental stochastic process in addition to the price change itself. This process is often referred to as volatility. The volatility is often estimated by calculating the standard deviation of the price changes in an appropriate time window. One can also use other ways of estimating it, for example by averaging the absolute values of the price changes, by maximum likelihood methods or by Bayesian methods (see [129] for a review). There are several motivations for considering the statistical properties of volatility itself. (i) Volatility can be directly to the amount of information arriving in the market at a given time. For example, if there is large amount of information arriving in the market, then the traders would act accordingly - resulting in a large number of trades, and, in general, in large volatility. (ii) Volatility can be directly used in the modeling of the stochastic process governing the price changes, as for example in ARCH/GARCH models, to be discussed in Chapter 10. (iii) From a practical point of view, volatility is a key parameter in the measure of the risk of a financial investment.

The autocorrelation function of the volatility, estimated either as a local average of the absolute value of price changes or by the local standard deviation, is well described by a power-law decay [31, 36, 41, 95, 137]. Figure 7.5 shows the autocorrelation function for the absolute values of 1 min S&P 500 price changes using the same data as plotted in Fig. 7.3. In this case, a power-law decay with an exponent γ ≈ 0.3 [96] is a good fit to the autocorrelation function.

Long-range correlations in the absolute value of price changes can also be investigated by considering the power spectrum. Figure 7.6 shows the power spectrum of absolute value of price changes of the S&P 500 index - measured in a one-hour interval. The power spectrum results are consistent with the autocorrelation function results, namely a 1/*f*^{η}behavior with η = 1 - γ ≈ 0.7 [95, 96, 114].

Studies on the distribution of volatility report a log-normal distribution for the volatility near the center of the distribution [31, 96, 133], while another work suggests that the asymptotic behavior displays power-law behavior [96]. Before concluding, we note that the existence of volatility correlation does not contradict the observation of pairwise independence of price changes because the autocorrelation of price changes depends on the second-order conditional probability density, while the volatility autocorrelation is affected by higher-order conditional probability densities."

Mantegna and Stanley (2000) page 57

Can we describe price changes in terms of a stationary process? Empirical analyses of financial data show that price changes cannot be described by a strict-sense stationary stochastic process, since the standard deviation of price changes, namely the volatility, is time-dependent in real markets. Hence, the form of stationarity that is present in financial markets is at best asymptotic stationarity

. Mantegna and Stanley (2000) page 58

- BERAN, J., 1994. Statistics for Long-Memory Processes. books.google.com. [Cited by 1158] (97.43/year)

- HESTON, Steven L., 1993. A Closed-Form Solution for Options with Stochastic Volatility with Applications to Bond and Currency Options,
*The Review of Financial Studies*, Vol. 6, No. 2. (1993), pp. 327-343. [Cited by 1014] (78.00/year)

Abstract: "I use a new technique to derive a closed-form solution for the price of a European call option on an asset with stochastic volatility. The model allows arbitrary correlation between volatility and spot-asset returns. I introduce stochastic interest rates and show how to apply the model to bond options and foreign currency options. Simulations show that correlation between volatility and the spot asset's price is important for explaining return skewness and strike-price biases in the Black-Scholes (1973) model. The solution technique is based on characteristic functions and can be applied to other problems."

- GLOSTEN, L.R., R. JAGANATHAN and D.E. RUNKLE, 1993. On the Relation between the Expected Value and the Volatility of the Nominal Excess Return on Stocks,
*The Journal of Finance*, Vol. 48, No. 5 (Dec., 1993) , pp. 1779-1801. [Cited by 990] (77.12/year)

Abstract: "We find support for a negative relation between conditional expected monthly return and conditional variance of monthly return, using a GARCH-M model modified by allowing (1) seasonal patterns in volatility, (2) positive and negative innovations to returns having different impacts on conditional volatility, and (3) nominal interest rates to predict conditional variance. Using the modified GARCH-M model, we also show that monthly conditional volatility may not be as persistent as was thought. Positive unanticipated returns appear to result in a downward revision of the conditional volatility whereas negative unanticipated returns result in an upward revision of conditional volatility."

Glosten, Jagannathan and Runkle (1993)

- BOLLERSLEV, T., R.Y. CHOU and K.F. KRONER, 1992. ARCH Modeling in Finance: A Review of the Theory and Empirical Evidence,
*Journal of Econometrics*, 52, 5. [Cited by 968] (69.71/year)

Abstract: "Although volatility clustering has a long history as a salient empirical regularity characterizing high-frequency speculative prices, it was not until recently that applied researchers in finance have recognized the importance of explicitly modeling time-varying second-order moments. Instrumental in most of these empirical studies has been the Autoregressive Conditional Heteroskedasticity (ARCH) model introduced by Engle (1982). This paper contains an overview of some of the developments in the formulation of ARCH models and a survey of the numerous empirical applications using financial data. Several suggestions for future research, including the implementation and tests of competing asset pricing theories, market microstructure models, information transmission mechanisms, dynamic hedging strategies, and the pricing of derivative assets, are also discussed."

- CAMPBELL, J.Y.,
*et al.*, 2001. Have Individual Stocks Become More Volatile? An Empirical Exploration of Idiosyncratic Risk,*The Journal of Finance.*[Cited by 291] (59.54/year)
Abstract: "This paper uses a disaggregated approach to study the volatility of common stocks at the market, industry, and firm levels. Over the period from 1962 to 1997 there has been a noticeable increase in firm-level volatility relative to market volatility. Accordingly, correlations among individual stocks and the explanatory power of the market model for a typical stock have declined, whereas the number of stocks needed to achieve a given level of diversification has increased. All the volatility measures move together countercyclically and help to predict GDP growth. Market volatility tends to lead the other volatility series. Factors that may be responsible for these findings are suggested."
- ANDERSEN, Torben G.,
*et al.*, 2003. Modeling and Forecasting Realized Volatility,*Econometrica*, Vol. 71, No. 2. (Mar., 2003), pp. 579-625. [Cited by 268] (55.38/year)

Abstract: "We provide a framework for integration of high-frequency intraday data into the measurement, modeling, and forecasting of daily and lower frequency return volatilities and return distributions. Building on the theory of continuous-time arbitrage-free price processes and the theory of quadratic variation, we develop formal links between realized volatility and the conditional covariance matrix. Next, using continuously recorded observations for the Deutschemark/Dollar and Yen/Dollar spot exchange rates, we find that forecasts from a simple long-memory Gaussian vector autoregression for the logarithmic daily realized volatilities perform admirably. Moreover, the vector autoregressive volatility forecast, coupled with a parametric lognormal-normal mixture distribution produces well-calibrated density forecasts of future returns, and correspondingly accurate quantile predictions. Our results hold promise for practical modeling and forecasting of the large covariance matrices relevant in asset pricing, asset allocation, and financial risk management applications."

- ENGLE, R.F. and V.K. NG, 1993. Measuring and Testing the Impact of News on Volatility.
*The Journal of Finance*, Vol. 48, No. 5. (Dec., 1993), pp. 1749-1778. [Cited by 706] (55.00/year)

Abstract: "This paper defines the news impact curve which measures how new information is incorporated into volatility estimates. Various new and existing ARCH models including a partially nonparametric one are compared and estimated with daily Japanese stock return data. New diagnostic tests are presented which emphasize the asymmetry of the volatility response to news. Our results suggest that the model by Glosten, Jagannathan, and Runkle is the best parametric model. The EGARCH also can capture most of the asymmetry; however, there is evidence that the variability of the conditional variance implied by the EGARCH is too high."

- ERAKER, B., M. JOHANNES and N. POLSON, 2003. The Impact of Jumps in Volatility and Returns.
*The Journal of Finance.*[Cited by 156] (55.00/year)

Abstract: "This paper examines continuous-time stochastic volatility models incorporating jumps in returns and volatility.We develop a likelihood-based estimation strategy and provide estimates of parameters, spot volatility, jump times, and jump sizes using S&P 500 and Nasdaq 100 index returns. Estimates of jump times, jump sizes, and volatility are particularly useful for identifying the effects of these factors during periods of market stress, such as those in 1987, 1997, and 1998.Using formal and informal diagnostics,we ¢nd strong evidence for jumps in volatility and jumps in returns. Finally, we study how these factors and estimation risk impact option pricing."

- BARNDORFF-NIELSEN, O.E. and N. SHEPHARD, 2002. Econometric analysis of realized volatility and its use in estimating stochastic volatility models.
*ingentaconnect.com.*[Cited by 206] (51.50/year)

Abstract: "Summary.

The availability of intraday data on the prices of speculative assets means that we can use quadratic variation-like measures of activity in financial markets, called realized volatility, to study the stochastic properties of returns. Here, under the assumption of a rather general stochastic volatility model, we derive the moments and the asymptotic distribution of the realized volatility error—the difference between realized volatility and the discretized integrated volatility (which we call actual volatility). These properties can be used to allow us to estimate the parameters of stochastic volatility models without recourse to the use of simulation-intensive methods."

- KIM, Sangjoon, Neil SHEPHARD and Siddhartha CHIB, 1998. Stochastic Volatility: Likelihood Inference and Comparison with ARCH Models,
*The Review of Economic Studies*, Vol. 65, No. 3. (Jul., 1998), pp. 361-393. [Cited by 377] (48.11/year)

Abstract: "In this paper, Markov chain Monte Carlo sampling methods are exploited to provide a unified, practical likelihood-based framework for the analysis of stochastic volatility models. A highly effective method is developed that samples all the unobserved volatilities at once using an approximating offset mixture model, followed by an importance reweighting procedure. This approach is compared with several alternative methods using real data. The paper also develops simulation-based methods for filtering, likelihood evaluation and model failure diagnostics. The issue of model choice using non-nested likelihood ratios and Bayes factors is also investigated. These methods are used to compare the fit of stochastic volatility and GARCH models. All the procedures are illustrated in detail."

- ANDERSEN, T.G.,
*et al.*, 2000. The Distribution of Stock Return Volatility. [Cited by 280] (47.60/year)

published as below: - ANDERSEN, Torben G.,
*et al.*, 2001. The distribution of realized stock return volatility,*Journal of Financial Economics*, Volume 61, Issue 1, July 2001, Pages 43-76. [Cited by 2] (0.41/year)

Abstract: "We examine "realized" daily equity return volatilities and correlations obtained from high-frequency intraday transaction prices on individual stocks in the Dow Jones Industrial Average. We find that the unconditional distributions of realized variances and covariances are highly right-skewed, while the realized logarithmic standard deviations and correlations are approximately Gaussian, as are the distributions of the returns scaled by realized standard deviations. Realized volatilities and correlations show strong temporal dependence and appear to be well described by long-memory processes. Finally, there is strong evidence that realized volatilities and correlations move together in a manner broadly consistent with latent factor structure."

Conclusions: "We exploit direct model-free measures of realized daily volatility and correlation obtained from high-frequency intraday stockprices to confirm, solidify and extend existing characterizations. Our findings are remarkably consistent with existing worksuch as ABDL (2001a, b) and Ebens (1999a). This is true of the right-skewed distributions of the variances and covariances, the normal distributions of the logarithmic standard deviations and correlations, the normal distributions of daily returns standardized by realized standard deviations, and the strongly persistent dynamics of the realized volatilities and correlations, well-described by a stationary fractionally integrated process and conforming to scaling laws under temporal aggregation. The striking congruence of all findings across asset classes (equity vs. foreign exchange) and underlying method of price recording (transaction prices vs. averages of logarithmic bid and askquotes) suggests that the results reflect fundamental attributes of speculative returns.

Our analysis is noteworthy not only for confirming and checking the robustness of existing results, but also for achieving significant extensions, facilitated throughout by the model-free measurement of realized volatility and correlation afforded by high-frequency data, and the simplicity of our methods, which enable straightforward high-dimensional correlation estimation. We shed new light on some distinct properties of equity return dynamics and illustrate them, for example, via the news impact curve. We confirm the existence of an asymmetric relation between returns and volatility, with negative returns being associated with higher volatility innovations than positive returns of the same magnitude. However, the effect is much weaker at the individual stocklevel than at the aggregate market level, thus lending support to a volatility risk premium feedback explanation rather than a financial leverage effect. Finally, we find a pronounced volatility-in-correlation effect. The volatility-in-correlation effect, the strong positive relations between individual stockvolat ilities, and the corresponding strong positive relations between contemporaneous stock correlations should motivate additional work on the development of parsimonious factor models for the covariance structure of stock returns.

We envision several applications of the approach adopted in this paper. For example, the direct measurement of volatilities and correlations should alleviate the errors-in-variables problem that plagues much workon the implementation and testing of the CAPM, because realized betas can be constructed directly from the corresponding realized covariances and standard deviations. Multifactor models based on factor-replicating portfolios are similarly amenable to direct analysis. As a second example, the effective observability of volatilities and correlations facilitates direct time-series modeling of portfolio choice and riskmanage ment problems under realistic and testable distributional assumptions. Worka long those lines is pursued in Andersen et al. (2000). Finally, our methods will also facilitate direct comparisons of volatility forecasts generated by alternative models and procedures. Such explorations are underway in Ebens (1999b) and Ebens and de Lima (1999)."

- BOLLERSLEV, T., R.F. ENGLE and D.B. NELSON, 1994. ARCH Models,
*Handbook of Econometrics.*[Cited by 14] (46.17/year) - BERNANKE, B.S. and M. GERTLER, 2000. Monetary Policy and Asset Price Volatility. [Cited by 272] (46.60/year)

Abstract: "We explore the implications of asset price volatility for the management of monetary policy. We show that it is desirable for central banks to focus on underlying inflationary pressures. Asset prices become relevant only to the extent they may signal potential inflationary or deflationary forces. Rules that directly target asset prices appear to have undesirable side effects. We base our conclusions on (i) simulation of different policy rules in a small scale macro model and (ii) a comparative analysis of recent U.S. and Japanese monetary policy."

- ANDERSEN, T.G. and T. BOLLERSLEV, 1998. Answering the Skeptics: Yes, Standard Volatility Models do Provide Accurate Forecasts.
*International Economic Review*, Vol. 39, No. 4, Symposium on Forecasting and Empirical Methods in Macroeconomics and Finance. (Nov., 1998), pp. 885-905. [Cited by 351] (44.79/year)

Abstract: "A voluminous literature has emerged for modeling the temporal dependencies in financial market volatility using ARCH and stochastic volatility models. While most of these studies have documented highly significant in-sample parameter estimates and pronounced intertemporal volatility persistence, traditional ex-post forecast evaluation criteria suggest that the models provide seemingly poor volatility forecasts. Contrary to this contention, we show that volatility models produce strikingly accurate interdaily forecasts for the latent volatility factor that would be of interest in most financial applications. New methods for improved ex-post interdaily volatility measurements based on high-frequency intradaily data are also discussed."

in text:

"Volatility permeates finance."

"It is also a well-established fact, dating back to Mandelbrot (1963) and Fama (1965), that financial returns display pronounced volatility clustering."

"The existence of volatility clustering in speculative returns is ubiquitous."

- ANDERSEN, T.G.,
*et al.*, 2001. The Distribution of Realized Exchange Rate Volatility,*Journal of the American Statistical Association*, Vol. 96, No. 453, March 2001 pp.42-55. [Cited by 215] (44.45/year)

Abstract: "Using high-frequency data on deutschemark and yen returns against the dollar, we construct model-free estimates of daily exchange rate volatility and correlation that cover an entire decade. Our estimates, termed realized volatilities and correlations, are not only model-free, but also approximately free of measurement error under general conditions, which we discuss in detail. Hence, for practical purposes, we may treat the exchange rate volatilities and correlations as observed rather than latent. We do so, and we characterize their joint distribution, both unconditionally and conditionally. Noteworthy results include a simple normality-inducing volatility transformation, high contemporaneous correlation across volatilities, high correlation between correlation and volatilities, pronounced and persistent dynamics in volatilities and correlations, evidence of long-memory dynamics in volatilities and correlations, and remarkably precise scaling laws under temporal aggregation."

"Finally, we confirm the wealth of existing evidence of strong volatility clustering effects in daily returns. However, in contrast to earlier work, which often indicates that volatility persistence decreases quickly with the horizon, we find that even monthly realized volatilities remain highly persistent. Nonetheless, realized volatilities do not have unit roots; instead, they appear fractionally integrated and therefore very slowly mean-reverting. This finding is strengthened by our analysis of temporally aggregated volatility series, whose properties adhere closely to the scaling laws implied by the structure of fractional integration."

"Financial market volatility is central to the theory and practice of asset pricing, asset allocation, and risk management."

Andersen,*et al.*, 2001b

- FAMA, E.F., 1970. Efficient Capital Markets: A Review of Theory and Empirical Work.
*The Journal of Finance.*[Cited by 1524] (42.47/year)

- DUMAS, Bernard, Jeff FLEMING and Robert E. WHALEY, 1998. Implied Volatility Functions: Empirical Tests.
*The Journal of Finance*, Vol. 53, No. 6. (Dec., 1998), pp. 2059-2106. [Cited by 327] (41.73/year)

Abstract: "Derman and Kani (1994), Dupire (1994), and Rubinstein (1994) hypothesize that asset return volatility is a deterministic function of asset price and time, and develop a deterministic volatility function (DVF) option valuation model that has the potential of fitting the observed cross section of option prices exactly. Using S&P 500 options from June 1988 through December 1993, we examine the predictive and hedging performance of the DVF option valuation model and find it is no better than an ad hoc procedure that merely smooths Black-Scholes (1973) implied volatilities across exercise prices and times to expiration."

- LIU, Yanhui,
*et al.*, 1999. Statistical properties of the volatility of price fluctuations,*Physical Review E*, Volume 60, Issue 2, Pages 1390-1400, August 1999. [Cited by 286] (41.52/year)
Abstract: "We study the statistical properties of volatility, measured by locally averaging over a time window - SCHWERT, G. William, 1990. Why Does Stock Market Volatility Change Over Time?,
*The Journal of Finance*, Vol. 44, No. 5. (Dec., 1989), pp. 1115-1153. [Cited by 642] (40.54/year)

Abstract: "This paper analyzes the relation of stock volatility with real and nominal macroeconomic volatility, economic activity, financial leverage, and stock trading activity using monthly data from 1857 to 1987. An important fact, previously noted by Officer (1973), is that stock return variability was unusually high during the 1929-1939 Great Depression. While aggregate leverage is significantly correlated with volatility, it explains a relatively small part of the movements in stock volatility. The amplitude of the fluctuations in aggregate stock volatility is difficult to explain using simple models of stock valuation, especially during the Great Depression."

- ACEMOGLU, D.,
*et al.*, 2002. Institutional Causes, Macroeconomic Symptoms: Volatility, Crises and Growth. [Cited by 154] (40.14/year)

Abstract: "Countries that have pursued distortionary macroeconomic policies, including high inflation, large budget deficits and misaligned exchange rates, appear to have suffered more macroeconomic volatility and also grown more slowly during the postwar period. Does this reflect the causal effect of these macroeconomic policies on economic outcomes? One reason to suspect that the answer may be no is that countries pursuing poor macroeconomic policies also have weak 'institutions,' including political institutions that do not constrain politicians and political elites, ineffective enforcement of property rights for investors, widespread corruption, and a high degree of political instability. This paper documents that countries that inherited more 'extractive' instit utions from their colonial past were more likely to experience high volatility a nd economic crises during the postwar period. More specifically, societies where European colonists faced high mortality rates more than 100 years ago are much more volatile and prone to crises. Based on our previous work, we interpret this relationship as due to the causal effect of institutions on economic outcomes: Europeans did not settle and were more likely to set up extractive institutions in areas where they faced high mortality. Once we control for the effect of institutions, macroeconomic policies appear to have only a minor impact on volatility and crises. This suggests that distortionary macroeconomic policies are more likely to be symptoms of underlying institutional problems rather than the main causes of economic volatility, and also that the effects of institutional differences on volatility do not appear to be primarily mediated by any of the standard macroeconomic variables. Instead, it appears that weak institutions cause volatility through a number of microeconomic, as well as macroeconomic, channels."

- BEKAERT, G. and C.R. HARVEY, 1997. Emerging Equity Market Volatility,
*Journal of Financial Economics*, Volume 43, Issue 1, Pages 1-149 (January 1997). [Cited by 351] (39.72/year)

Abstract: "Understanding volatility in emerging capital markets is important for determining the cost of capital and for evaluating direct investment and asset allocation decisions. We provide an approach that allows the relative importance of world and local information to change through time in both the expected returns and conditional variance processes. Our time-series and cross-sectional models analyze the reasons that volatility is different across emerging markets, particularly with respect to the timing of capital market reforms. We find that capital market liberalizations often increase the correlation between local market returns and the world market but do not drive up local market volatility."

- BATES, David S., Review of Financial Studies. Jumps and stochastic volatility: exchange rate processes implicit in deutsche mark options,
*The Review of Financial Studies*, Vol. 9, No. 1. (Spring, 1996), pp. 69-107. [Cited by 391] (39.10/year)

Abstract: "An efficient method is developed for pricing American options on stochastic volatility/jump-diffusion processes under systematic jump and volatility risk. The parameters implicit in deutsche mark (DM) options of the model and various submodels are estimated over the period 1984 to 1991 via nonlinear generalized least squares, and are tested for consistency with /DM futures prices and the implicit volatility sample path. The stochastic volatility submodel cannot explain the "volatility smile" evidence of implicit excess kurtosis, except under parameters implausible given the time series properties of implicit volatilities. Jump fears can explain the smile, and are consistent with one 8 percent DM appreciation öutlier" observed over the period 1984 to 1991."

- FRENCH, K.R., G.W. SCHWERT and R.F. STAMBAUGH, 1987. Expected stock returns and volatility.
*Journal of Financial Economics*, Volume 19, Issue 1 , September 1987, Pages 3-29. [Cited by 709] (37.64/year)

Abstract: "This paper examines the relation between stock returns and stock market volatility. We find evidence that the expected market risk premium (the expected return on a stock portfolio minus the Treasury bill yield) is positively related to the predictable volatility of stock returns. There is also evidence that unexpected stock market returns are negatively related to the unexpected change in the volatility of stock returns. This negative relation provides indirect evidence of a positive relation between expected risk premiums and volatility."

French, Schwert and Stambaugh (1987)

- GHYSELS, E., A.C. HARVEY and É. RENAULT, 1995. Stochastic volatility. depot.erudit.org. [Cited by 406] (37.47/year)

- BLANCHARD, O. and J. SIMON, 2001. The Long and Large Decline in US Output Volatility,
*Brookings Papers on Economic Activity.*[Cited by 176] (36.39/year)

The last two U.S. expansions have been unusually long. One view is that this is the result of luck, of an absence of major adverse shocks over the last twenty years. We argue that more is at work, namely a large underlying decline in output volatility. This decline is not a recent development, but rather a steady one, visible already in the 1950s and the 1960s, interrupted in the 1970s and early 1980s, with a return to trend in the late 1980s and the 1990s. The standard deviation of quarterly output growth has declined by a factor of 3 over the period. This is more than enough to account for the increased length of expansions.

We reach two other conclusions. First, the trend decrease can be traced to a number of proximate causes, from a decrease in the volatility in government spending early on, to a decrease in consumption and investment volatility throughout the period, to a change in the sign of the correlation between inventory investment and sales in the last decade. Second, there is a strong relation between movements in output volatility and inflation volatility. This association accounts for the interruption of the trend decline in output volatility in the 1970s and early 1980s.

- ALIZADEH, Sassan, Michael W. BRANDT and Francis X. DIEBOLD, 2002. Range-Based Estimation of Stochastic Volatility Models.
*The Journal of Finance.*[Cited by 139] (36.23/year)

Abstract: "We propose using the price range in the estimation of stochastic volatility models. We show theoretically, numerically, and empirically that range-based volatility proxies are not only highly efficient, but also approximately Gaussian and robust to microstructure noise. Hence range-based Gaussian quasi-maximum likelihood estimation produces highly efficient estimates of stochastic volatility models and extractions of latent volatility. We use our method to examine the dynamics of daily exchange rate volatility and find the evidence points strongly toward two-factor models with one highly persistent factor and one quickly mean-reverting factor."

- BEKAERT, G. and G. WU, 2000. Asymmetric volatility and risk in equity markets,
*Review of Financial Studies*[Cited by 212] (35.33/year)

Abstract: "It appears that volatility in equity markets is asymmetric: returns and conditional volatility are negatively correlated. We provide a unified framework to simultaneously investigate asymmetric volatility at the firm and the market level and to examine two potential explanations of the asymmetry: leverage effects and volatility feedback. Our empirical application uses the market portfolio and portfolios with different leverage constructed from Nikkei 225 stocks. We reject the pure leverage model of Christie (1982) and find support for a volatility feedback story. Volatility feedback at the firm level is enhanced by strong asymmetries in conditional covariances. Conditional betas do not show significant asymmetries. We document the risk premium implications of these findings."

- RAMEY, G. and V.A. RAMEY, 1994. Cross-Country Evidence on the Link Between Volatility and Growth,
*The American Economic Review*, Vol. 85, No. 5. (Dec., 1995), pp. 1138-1151. [Cited by 400] (33.79/year)

Abstract: "This paper presents empirical evidence against the standard dichotomy in macroeconomics that separates growth from the volatility of economic fluctuations. In a sample of 92 countries as well as a sample of OECD countries, we find that countries with higher volatility have lower growth. The addition of standard control variables strengthens the negative relationship. We also find that government spending-induced volatility is negatively associated with growth even after controlling for both time- and country-fixed effects."

- FOUQUE, J.P., G. PAPANICOLAOU and K.R. SIRCAR, 2000. Derivatives in Financial Markets with Stochastic Volatility. books.google.com. [Cited by 193] (33.07/year)

- ANDERSEN, T.G. and T. BOLLERSLEV, 1998. Deutsche Mark-Dollar Volatility: Intraday Activity Patterns, Macroeconomic Announcements, and Longer Run Dependencies.
*The Journal of Finance.*[Cited by 257] (32.80/year)

Abstract: "This paper provides a detailed characterization of the volatility in the deutsche mark–dollar foreign exchange market using an annual sample of five-minute returns. The approach captures the intraday activity patterns, the macroeconomic announcements, and the volatility persistence (ARCH) known from daily returns. The different features are separately quantified and shown to account for a substantial fraction of return variability, both at the intraday and daily level. The implications of the results for the interpretation of the fundamental "driving forces" behind the volatility process is also discussed."

Concluding Remarks: "The volatility process of the DM–$ spot exchange rate market is involved, with entirely new phenomena becoming visible as one proceeds from daily returns to high-frequency intraday returns. Nonetheless, it is possible to identify three general sets of characteristics that govern the systematic features of the process. At the high-frequency level, the pronounced intraday volatility pattern is dominant, accounting for an average variation in absolute returns of more than 250 percent across the 24-hour trading cycle (after exclusion of the Tokyo lunch period). At the intraday level, the magnitude of this effect overwhelms the predictable changes in volatility captured by, e.g., ARCH models, which rarely move by more than 25 percent over any 24-hour period. Additionally, strong but short-lived announcement effects are prevalent at the highest frequencies. [...]"

- ODEAN, T., 1998. Volume, Volatility, Price, and Profit When All Traders Are Above Average.
*The Journal of Finance.*[Cited by 244] (31.14/year)

Abstract: "People are overconfident. Overconfidence affects financial markets. How depends on who in the market is overconfident and on how information is distributed. This paper examines markets in which price-taking traders, a strategic-trading insider, and risk-averse marketmakers are overconfident. Overconfidence increases expected trading volume, increases market depth, and decreases the expected utility of overconfident traders. Its effect on volatility and price quality depend on who is overconfident. Overconfident traders can cause markets to underreact to the information of rational traders. Markets also underreact to abstract, statistical, and highly relevant information, and they overreact to salient, anecdotal, and less relevant information."

- SHEPHARD, N., 1995. Statistical Aspects of ARCH and Stochastic Volatility. Nuffield College Oxford. [Cited by 321] (29.62/year)

- GOPIKRISHNAN, P.,
*et al.*, 1999. Scaling of the distribution of fluctuations of financial market indices.*Physical Review E.*[Cited by 199] (28.93/year)

Abstract: "We study the distribution of fluctuations of the S&P 500 index over a time scale Δ*t*by analyzing three distinct databases. Database (i) contains approximately 1 200 000 records, sampled at 1-min intervals, for the 13-year period 1984–1996, database (ii) contains 8686 daily records for the 35-year period 1962–1996, and database (iii) contains 852 monthly records for the 71-year period 1926–1996. We compute the probability distributions of returns over a time scale Δ*t*, where Δ*t*varies approximately over a factor of 10^{4}—from 1 min up to more than one month. We find that the distributions for Δ*t*≤ 4 d (1560 min) are consistent with a power-law asymptotic behavior, characterized by an exponent α≈3, well outside the stable Lévy regime 0<α<2. To test the robustness of the S&P result, we perform a parallel analysis on two other financial market indices. Database (iv) contains 3560 daily records of the NIKKEI index for the 14-year period 1984–1997, and database (v) contains 4649 daily records of the Hang-Seng index for the 18-year period 1980–1997. We find estimates of a consistent with those describing the distribution of S&P 500 daily returns. One possible reason for the scaling of these distributions is the long persistence of the autocorrelation function of the volatility. For time scales longer than (Δ*t*)_{×}≈ 4 d, our results are consistent with a slow convergence to Gaussian behavior."

in text: "Indeed, the amplitude of the returns, referred to in economics as the*volatility*[56], shows long-range time correlations that persist up to several months [14,33,53-63], and are characterized by an asymptotic power-law decay."

in text: "Recent studies [59] show that the distribution of volatility is consistent with an asymptotic power-law behavior with exponent 3, just as observed for the distribution of returns."

- ANDERSEN, T.G.,
*et al.*, 1999. The Distribution of Exchange Rate Volatility. [Cited by 191] (27.94/year)

Abstract: "Using high-frequency data on Deutschemark and Yen returns against the dollar, we construct model-free estimates of daily exchange rate volatility and correlation, covering an entire decade. In addition to being model-free, our estimates are also approximately free of measurement error under general conditions, which we delineate. Hence, for all practical purposes, we can treat the exchange rate volatilities and correlations as observed rather than latent. We do so, and we characterize their joint distribution, both unconditionally and conditionally. Noteworthy results include a simple normality-inducing volatility transformation, high contemporaneous correlation across volatilities, high correlation between correlation and volatilities, pronounced and highly persistent temporal variation in both volatilities and correlation, clear evidence of long-memory dynamics in both volatilities and correlation, and remarkably precise scaling laws under temporal aggregation."

- ANDERSEN, Torben G. and Tim BOLLERSLEV, 1997. Intraday periodicity and volatility persistence in financial markets,
*Journal of Empirical Finance*, Volume 4, Issues 2-3, Pages 69-293 (June 1997). [Cited by 234] (26.48/year)

Abstract: "The pervasive intraday periodicity in the return volatility in foreign exchange and equity markets is shown to have a strong impact on the dynamic properties of high frequency returns. Only by taking account of this strong intraday periodicity is it possible to uncover the complex intraday volatility dynamics that exists both within and across different financial markets. The explicit periodic modeling procedure developed here provides such a framework and thus sets the stage for a formal integration of standard volatility models with market microstructure variables to allow for a more comprehensive empirical investigation of the fundamental determinants behind the volatility clustering phenomenon."

Concluding remarks: "Our analysis of the intraday volatility patterns in the DM-$ foreign exchange and S&P 500 equity markets documents how traditional time series methods applied to raw high frequency returns may give rise to erroneous inference about the return volatility dynamics. Explicit allowance for the influence of the strong periodicity, as exemplified by our flexible Fourier form, is a necessary requirement for discovery of the salient intraday volatility features. Moreover, adjusting for the pronounced periodic structure appears critical in uncovering the complex link between the short- and long-run return components, which may help to explain the apparent conflict between the long-memory volatility characteristics observed in interday data and the rapid short-run decay associated with news arrivals in intraday data. More directly, however, our findings have immediate and important implications for a large range of issues in the rapidly growing literature using very high frequency financial data. Examples include investigations into the lead-lag relationship among returns and volatility both within and across different markets, the effect of cross listings of securities, the fundamental determinants behind the volatility clustering phenomenon, the development of real time trading and investment strategies and the evaluation of continuous option valuation and hedging decisions. Only future research will reveal the extent of the biases induced into these studies by the neglect of intraday periodic components."

- MANDELBROT, Benoit, 1963. The Variation of Certain Speculative Prices,
*The Journal of Business*, Vol. 36, No. 4. (Oct., 1963), pp. 394-419. [Cited by 1120] (26.14/year)

". . . large changes tend to be followed by large changes, of either sign, and small changes tend to be followed by small changes . . . ."

- SHILLER, R.J., 1989. Market volatility. cowles.econ.yale.edu. [Cited by 438] (26.01/year)

blurb: "The origins of price movements are poorly known in all speculative markets: markets for corporate stocks, bonds, homes, land, commercial structures, commodities, collectables, and foreign exchange. Why do stock prices often change up or down 20% in a year's time? Why do long term bond prices sometimes change up or down as much? Why do we sometimes find "hot" markets for homes, with prices sometimes jumping or more 20% in a year, after years of stable prices? The book presents basic research on the ultimate causes of price volatility in speculative markets, on the causes that make good economic sense and on the causes that are psychological or sociological in origin. The research, conducted over the last dozen years, includes both my own work and joint research with John Y. Campbell, Karl E. Case, Sanford J. Grossman, and Jeremy J. Siegel. About two thirds of the book consists of previously published articles. [464 pages]"

- CONT, R., 2001. Empirical properties of asset returns: stylized facts and statistical issues.
*Quantitative Finance.*[Cited by 123] (25.15/year) - BREIDT, F. Jay, Nuno CRATO and Pedro de LIMA, 1998. The detection and estimation of long memory in stochastic volatility.
*Journal of Econometrics*, Volume 83, Issues 1-2 , March-April 1998, Pages 325-348. [Cited by 195] (24.88/year)

Abstract: "We propose a new time series representation of persistence in conditional variance called a long memory stochastic volatility (LMSV) model. The LMSV model is constructed by incorporating an ARFIMA process in a standard stochastic volatility scheme. Strongly consistent estimators of the parameters of the model are obtained by maximizing the spectral approximation to the Gaussian likelihood. The finite sample properties of the spectral likelihood estimator are analyzed by means of a Monte Carlo study. An empirical example with a long time series of stock prices demonstrates the superiority of the LMSV model over existing (short-memory) volatility models."

- CHRISTENSEN, B.J. and N.R. PRABHALA, 1998. The relation between implied and realized volatility.
*Journal of Financial Economics*, v50 (2,Nov), 125-150. [Cited by 194] (24.76/year)

Abstract: "Previous research finds the volatility implied by S&P 100 index option prices to be a biased and inefficient forecast of future volatility and to contain little or no incremental information beyond that in past realized volatility. In contrast, we find that implied volatility outperforms past volatility in forecasting future volatility and even subsumes the information content of past volatility in some of our specifications. Our results differ from previous studies because we use longer time series and nonoverlapping data. A regime shift around the October 1987 crash explains why implied volatility is more biased in previous work."

- GALLANT, A.R., P.E. ROSSI and G. TAUCHEN, Stock prices and volume, Review of Financial Studies 5, 199. [Cited by 346] (24.71/year)

Abstract: "We undertake a comprehensive investigation of price and volume co-movement using daily New York Stock Exchange data from 1928 to 1987. We adjust the data to take into account well-known calendar effects and long-run trends. To describe the process, we use a seminonparametric estimate of the joint density of current price change and volume conditional on past price changes and volume. Four empirical regularities are found: (i) positive correlation between conditional volatility and volume; (ii) large price movements are followed by high volume; (iii) conditioning on lagged volume substantially attenuates the "leverage" effect; and (iv) after conditioning on lagged volume, there is a positive risk-return relation."

- PLEROU, V.,
*et al.*, 1999. Scaling of the distribution of price fluctuations of individual companies.*Physical Review E.*[Cited by 161] (23.41/year)

Abstract: "We present a phenomenological study of stock price fluctuations of individual companies. We systematically analyze two different databases covering securities from the three major U.S. stock markets: (a) the New York Stock Exchange, (b) the American Stock Exchange, and (c) the National Association of Securities Dealers Automated Quotation stock market. Specifically, we consider (i) the trades and quotes database, for which we analyze 40 million records for 1000 U.S. companies for the 2-yr period 1994–95; and (ii) the Center for Research and Security Prices database, for which we analyze 35 million daily records for approximately 16 000 companies in the 35-yr period 1962–96. We study the probability distribution of returns over varying time scales Δ*t*, where Δ*t*varies by a factor of ≈10^{5}, from 5 min up to ≈ 4 yr. For time scales from 5 min up to approximately 16 days, we find that the tails of the distributions can be well described by a power-law decay, characterized by an exponent 2.5<∝<4, well outside the stable Lévy regime 0<α<2. For time scales Δ*t*>> (Δ*t*)_{×}≈ 16 days, we observe results consistent with a slow convergence to Gaussian behavior. We also analyze the role of cross correlations between the returns of different companies and relate these correlations to the distribution of returns for market indices."

- ANDERSEN, T.G. and T. BOLLERSLEV, 1997. Heterogeneous Information Arrivals and Return Volatility Dynamics: Uncovering the Long-Run in High Frequency Returns
.
*The Journal of Finance.*[Cited by 204] (23.09/year)

Abstract: "Recent empirical evidence suggests that the long-run dependence in financial market volatility is best characterized by a slowly mean-reverting fractionally integrated process. At the same time, much shorter-lived volatility dependencies are typically observed with high-frequency intradaily returns. This paper draws on the information arrival, or mixture-of-distributions hypothesis interpretation of the latent volatility process in rationalizing this behavior. By interpreting the overall volatility as the manifestation of numerous heterogeneous information arrivals, sudden bursts of volatility typically will have both short-run and long-run components. Over intradaily frequencies, the short-run decay stands out most clearly, while the impact of the highly persistent processes will be dominant over longer horizons. These ideas are confirmed by our empirical analysis of a one-year time series of intradaily five-minute Deutschemark - U.S. Dollar returns. Whereas traditional time series based measures for the temporal dependencies in the absolute returns give rise to very conflicting results across different intradaily sampling frequencies, the corresponding semiparametric estimates for the order of fractional integration remain remarkably stable. Similarly, the autocorrelogram for the low-pass filtered absolute returns, obtained by annihilating periods in excess of one day, exhibit a striking hyperbolic rate of decay."

Conclusion: "The temporal dependence in the volatility of speculative returns is of the utmost importance for the pricing and hedging of financial of financial contracts. Yet, the empirical analysis of low frequency interdaily and high frequency intradaily returns have hitherto given rise to very different conclusions regarding the degree of volatility persistence for any particular asset. The mixture-of-distributions hypothesis developed here provides a justification for these conflicting empirical findings by interpreting the volatility as resulting from the aggregation of numerous consistent component processes; some with very short-run decay rates and others possessing much longer-run dependencies. When analyzing intradaily returns the short-run components will tend to dominate the estimates obtained with traditional time series models, whereas for daily or longer-run return intervals the estimates will be driven by the more persistent components. Nonetheless, under suitable conditions the aggregation of these multiple components implies, that the process for the volatility should exhibit the identical form of long-memory dependence irrespective of the sampling intervals. [...]"

- BOLLERSLEV, Tim and Hans Ole MIKKELSEN, 1996. Modeling and pricing long memory in stock market volatility,
*Journal of Econometrics*, Volume 73, Issue 1 , July 1996, Pages 151-184. [Cited by 220] (22.37/year)

Abstract: "A new class of fractionally integrated GARCH and EGARCH models for characterizing financial market volatility is discussed. Monte Carlo simulations illustrate the reliability of quasi maximum likelihood estimation methods, standard model selection criteria, and residual-based portmanteau diagnostic tests in this context. New empirical evidence suggests that the apparent long-run dependence in U.S. stock market volatility is best described by a mean-reverting fractionally integrated process, so that a shock to the optimal forecast of the future conditional variance dissipate at a slow hyperbolic rate. The asset pricing implications of this finding is illustrated via the implementation of various option pricing formula."

Conclusion: "A new class of more flexible fractionally integrated EGARCH models for characterizing the long-run dependencies in U.S. stock market volatility was proposed. Strong evidence was uncovered that the conditional variance for the Standard and Poor’s 500 composite index is best modeled as a mean-reverting fractionally integrated process. [...]"

Bollerslev and Mikkelsen (1996)

- JACQUIER, E., N.G. POLSON and P.E. ROSSI, 1994. Bayesian Analysis of Stochastic Volatility Models.
*Journal of Business & Economic Statistics.*[Cited by 268] (22.54/year)
Abstract: "New techniques for the analysis of stochastic volatility models in which the logarithm of conditional variance follows an autoregressive model are developed. A cyclic Metropolis algorithm is used to construct a Markov-chain simulation tool. Simulations from this Markov chain converge in distribution to draws from the posterior distribution enabling exact finite-sample inference. The exact solution to the filtering/smoothing problem of inferring about the unobserved variance states is a by-product of our Markov-chain method. In addition, multistep-ahead predictive densities can be constructed that reflect both inherent model variability and parameter uncertainty. We illustrate our method by analyzing both daily and weekly data on stock returns and exchange rates. Sampling experiments are conducted to compare the performance of Bayes estimators to method of moments and quasi-maximum likelihood estimators proposed in the literature. In both parameter estimation and filtering, the Bayes estimators outperform these other approaches." - ANDERSEN, T.G., 1996. Return Volatility and Trading Volume: An Information Flow Interpretation of Stochastic Volatility,
*The Journal of Finance*51:169-204. [Cited by 217] (22.06/year)

Abstract: "This paper develops an empirical return volatility-trading volume model from a microstructure framework in which informational asymmetries and liquidity needs motivate trade in response to information arrivals. The resulting system modifies the so-called 'mixture of distribution hypothesis' (MDH). The dynamic features are governed by the information flow, modeled as a stochastic volatility process, and generalize standard autoregressive conditional heteroskedasticity specifications. Specification tests support the modified MDH representation and show that it vastly outperforms the standard MDH. The findings suggest that the model may be useful for analysis of the economic factors behind the observed volatility clustering in returns."

- ANDERSEN, T.G. and J. LUND, 1997. Estimating continuous-time stochastic volatility models of the short-term interest rate,
*Journal of Econometrics.*[Cited by 192] (21.73/year)

Abstract: "We obtain consistent parameter estimates of continuous-time stochastic volatility diffusions for the U.S. risk-free short-term interest rate, sampled weekly over 1954–1995, using the Efficient Method of Moments procedure of Gallant and Tauchen. The preferred model displays mean reversion and incorporates ‘level effects’ and stochastic volatility in the diffusion function. Extensive diagnostics indicate that the Cox-Ingersoll-Ross model with an added stochastic volatility factor provides a good characterization of the short rate process. Further, they suggest that recently proposed GARCH models fail to approximate the discrete-time short rate dynamics, while ‘Level-EGARCH’ models perform reasonably well."

- DING, Zhuanxin and Clive W. J. GRANGER, 1996. Modeling volatility persistence of speculative returns: A new approach,
*Journal of Econometrics*, Volume 73, Number 1, July 1996, pp. 185-215(31). [Cited by 211] (21.45/year)

Abstract: "This paper extends the work by Ding, Granger, and Engle (1993) and further examines the long memory property for various speculative returns. The long memory property found for S&P 500 returns is also found to exist for four other different speculative returns. One significant difference is that for foreign exchange rate returns, this property is strongest when instead of at*d*= 1 for stock returns. The theoretical autocorrelation functions for various GARCH(1, 1) models are also derived and found to be exponential decreasing, which is rather different from the sample autocorrelation function for the real data. A general class of long memory models that has no memory in returns themselves but long memory in absolute returns and their power transformations is proposed. The issue of estimation and simulation for this class of model is discussed. The Monte Carlo simulation shows that the theoretical model can mimic the stylized empirical facts strikingly well."

- BLAIR, B.J., S.H. POON and S.J. TAYLOR, 2001. Forecasting S&P 100 volatility: The Incremental Information Content of Implied Volatilities and High Frequency Index Returns .
*Journal of Econometrics.*[Cited by 101] (20.88/year)

Abstract: "The information content of implied volatilities and intra-day returns is compared, in the context of forecasting index volatility over horizons from one to twenty days. Forecasts of two measures of realised volatility are obtained after estimating ARCH models using daily index returns, daily observations of the VIX index of implied volatility and sums of squares of five minute index returns. The in-sample estimates show that all relevant information is provided by the VIX index and hence there is no incremental information in high-frequency index returns. For out-of-sample forecasting, the VIX index and information from five minute returns provide forecasts that have similar accuracy."

- CAMPBELL, J.Y. and L. HENTSCHEL, 1991. No News is Good News: An Asymmetric Model of Changing Volatility in Stock Returns, Volume 31, Issue 3 , June 1992, Pages 281-318. [Cited by 309] (20.83/year)

Abstract: "It seems plausible that an increase in stock market volatility raises required stock returns, and thus lowers stock prices. We develop a formal model of this volatility feedback effect using a simple model of changing variance (a quadratic generalized autoregressive conditionally heteroskedastic, or QGARCH, model). Our model is asymmetric and helps to explain the negative skewness and excess kurtosis of U.S. monthly and daily stock returns over the period 1926–1988. We find that volatility feedback normally has little effect on returns, but it can be important during periods of high volatility."

- STEIN, Elias M. and Jeremy C. STEIN, 1991. Stock price distributions with stochastic volatility: an analytic approach,
*The Review of Financial Studies*, Vol. 4, No. 4. (1991), pp. 727-752. [Cited by 308] (20.53/year)

Abstract: "We study the stock price distributions that arise when prices follow a diffusion process with a stochastically varying volatility parameter. We use analytic techniques to derive an explicit closed-form solution for the case where volatility is driven by an arithmetic Ornstein-Uhlenbeck (or AR1) process. We then apply our results to two related problems in the finance literature: (i) options pricing in a world of stochastic volatility, and (ii) the relationship between stochastic volatility and the nature of "fat tails" in stock price distributions."

- KRONER, K.E. and V.K. NG, 1998. Review of Financial Studies. Modeling asymmetric comovements of asset returns. [Cited by 161] (20.12/year) Abstract: "Existing time-varying covariance models usually impose strong restrictions on how past shocks affect the forecasted covariance matrix. In this article we compare the restrictions imposed by the four most popular multivariate GARCH models, and introduce a set of robust conditional moment tests to detect misspecification. We demonstrate that the choice of a multivariate volatility model can lead to substantially different conclusions in any application that involves forecasting dynamic covariance matrices (like estimating the optimal hedge ratio or deriving the risk minimizing portfolio). We therefore introduce a general model which nests these four models and their natural "asymmetric" extensions. The new model is applied to study the dynamic relation between large and small firm returns."
- EASTERLY, W. and A. KRAAY, 2000. Small States, Small Problems? Income, Growth, and Volatility in Small States.
*World Development.*[Cited by 115] (19.70/year)

"**Summary:**Small states have attracted a large amount of research. In this paper we test whether small states are any different from other states in terms of their income, growth, and volatility outcomes. We find that, controlling for location, small states have higher per capita GDP than other states. This income advantage is largely due to a productivity advantage, constituting evidence against the idea that small states suffer from an inability to exploit increasing returns to scale. Small states also do not have different per capita growth rates than other states. Small states do have greater volatility of annual growth rates, which is in part due to their greater volatility of terms of trade shocks. This terms of trade-based volatility is in turn due to small states’ greater openness. However, their greater openness on balance has a positive net payoff for growth. The one differential policy measure that might be relevant for small states is to further open up to international capital markets in order to better diversify risk, but the benefits of even that are still unresolved in the literature. We conclude that small states are no different from large states, and so should receive the same policy advice that large states do."

- KING, Mervyn A. and Sushil WADHWANI, 1990. Transmission of volatility between stock markets,
*The Review of Financial Studies*, Vol. 3, No. 1, National Bureau of Economic Research Conference: Stock Market Volatility and the Crash, Dorado Beach, March 16-18, 1989. (1990), pp. 5-33. [Cited by 315] (19.69/year)

Abstract: "This article investigates why, in October 1987, almost all stock markets fell together despite widely differing economic circumstances. We construct a model in which "contagion" between markets occurs as a result of attempts by rational agents to infer information from price changes in other markets. This provides a channel through which a "mistake" in one market can be transmitted to other markets. We offer supporting evidence for contagion effects using two different sources of data."

- PAGAN, A. and G.W. SCHWERT, 1990. Alternative Models For Conditional Stock Volatility,
*Journal of Econometrics*, Vol. 45, pp. 267-290. [Cited by 309] (19.51/year)

Abstract: "This paper compares several statistical models for monthly stock return volatility. The focus is on U.S. data from 1834-1925 because the post-1926 data have been analyzed in more detail by others. Also, the Great Depression had levels of stock volatility that are inconsistent with stationary models for conditional heteroskedasticity. We show the importance of nonlinearities in stock return behavior that are not captured by conventional ARCH or GARCH models. We also show the nonstationarity of stock volatility."

Pagan and Schwert (1990)

- HAMAO, Yasushi, Ronald W. MASULIS and Victor NG, 1990. Correlations in price changes and volatility across international stock markets,
*The Review of Financial Studies*, Vol. 3, No. 2. (1990), pp. 281-307. [Cited by 312] (19.50/year)

Abstract: "The short-run interdependence of prices and price volatility across three major international stock markets is studied. Daily opening and closing prices of major stock indexes for the Tokyo, London, and New York stock markets are examined. The analysis utilizes the autoregressive conditionally heteroskedastic (ARCH) family of statistical models to explore these pricing relationships. Evidence of price volatility spillovers from New York to Tokyo, London to Tokyo, and New York to London is observed, but no price volatility spillover effects in other directions are found for the pre-October 1987 period."

- JORION, P., 1995. Predicting Volatility in the Foreign Exchange Market.
*The Journal of Finance.*[Cited by 206] (19.01/year)

Abstract: "Measures of volatility implied in option prices are widely believed to be the best available volatility forecasts. In this article, we examine the information content and predictive power of implied standard deviations (ISDs) derived from Chicago Mercantile Exchange options on foreign currency futures. The article finds that statistical time-series models, even when given the advantage of 'ex post' parameter estimates, are outperformed by ISDs. ISDs, however, also appear to be biased volatility forecasts. Using simulations to investigate the robustness of these results, the article finds that measurement errors and statistical problems can substantially distort inferences. Even accounting for these, however, ISDs appear to be too variable relative to future volatility."

- LONGSTAFF, F.A. and E.S. SCHWARTZ, 1992. Interest Rate Volatility and the Term Structure: A Two-Factor General Equilibrium Model.
*The Journal of Finance.*[Cited by 252] (18.21/year)

Abstract: "The authors develop a two-factor general equilibrium model of the term structure. The factors are the short-term interest rate and the volatility of the short-term interest rate. The authors derive closed-form expressions for discount bonds and study the properties of the term structure implied by the model. The dependence of yields on volatility allows the model to capture many observed properties of the term structure. The authors also derive closed-form expressions for discount bond options. The authors use Hansen's generalized method of moments framework to test the cross-sectional restrictions imposed by the model. The tests support the two-factor model."

- TAYLOR, S.J., 1994. Modeling Stochastic Volatility: A Review and Comparative Study,
*Mathematical Finance*4, 183--204. [Cited by 215] (18.16/year)

- ENGLE, R.F., 2001. What good is a volatility model?.
*Quantitative Finance.*[Cited by 86] (17.58/year)
Abstract: "A volatility model must be able to forecast volatility; this is the central requirement in almost all financial applications. In this paper we outline some stylized facts about volatility that should be incorporated in a model: pronounced persistence and mean-reversion, asymmetry such that the sign of an innovation also affects volatility and the possibility of exogenous or pre-determined variables influencing volatility. We use data on the Dow Jones Industrial Index to illustrate these stylized facts, and the ability of GARCH-type models to capture these features. We conclude with some challenges for future research in this area."
- CANINA, L. and S. FIGLEWSKI, 1993. The informational content of implied volatility,
*Review of Financial Studies*[Cited by 216] (16.62/year)

Abstract: "Implied volatility is widely believed to be informationally superior to historical volatility, because it is the 'market's' forecast of future volatility. But for S&P 1 00 index options, the most actively traded contract in the United States, we find implied volatility to be a poor forecast of subsequent realized volatility. In aggregate and across subsamples separated by maturity and strike price, implied volatility has virtually no correlation with future volatility, and it does not incorporate the information contained in recent observed volatility."

- ENGLE, R.F. and G.G.J. LEE, 1999. A Permanent and Transitory Component Model of Stock Return Volatility.
*Cointegration, Causality, and Forecasting: A Festschrift in ….*[Cited by 110] (16.09/year)

Abstract: "In this paper, we develop a statistical unobserved component model for stock market volatility. The volatility, which is measured by the conditional variance of stock returns, is decomposed into a permanent or long-run and a transitory or short-run component. The transitory component is mean- reverting towards the trend component. Analysis of US and Japanese stock data supports the decomposition and reinforce the common finding in the literature of persistent stock return volatility. The component model is successful in describing the effect of the "October 87 Crash" on stock volatility changes. We hypothesize that the leverage effect as discussed in Black (1976) and Christie (1982) is a short- run phenomenon in the stock market and there is no asymmetric structure of volatility in the long run. The data strongly supports this hypothesis for US and Japanese stock indices."

- DOMINGUEZ, K.M., 1998. Central bank intervention and exchange rate volatility.
*Journal of International Money and Finance.*[Cited by 126] (16.08/year)

Abstract: "This paper explores the effects of foreign exchange intervention by central banks on the behavior of exchange rates. The G-3 central banks have undertaken an unprecedented number of both coordinated and unilateral intervention operations in the last 10 years. Existing empirical evidence on the effectiveness of intervention is mixed: studies using data from the 1970s suggest that intervention operations that do not affect the monetary base have, at most, a short-lived influence on exchange rates, but more recent studies indicate that the intervention operations that followed the Plaza Agreement influenced both the level and variance of exchange rates. This paper examines the effects of US, German and Japanese monetary and intervention policies on dollar-mark and dollar-yen exchange rate volatility over the 1977]1994 period. The results indicate that intervention operations generally increase exchange rate volatility. This is particularly true of secret interventions, which are those undertaken by central banks without notification of the public. Overt interventions in the mid-1980s appear to have reduced exchange rate volatility, but in other periods, and for the 1977]1994 period as a whole, central bank intervention is associated with greater exchange rate volatility."

- EDERINGTON, L.H. and J.H. LEE, 1993. How Markets Process Information: News Releases and Volatility.
*The Journal of Finance.*[Cited by 201] (15.66/year)

Abstract: "The authors examine the impact of scheduled macroeconomic news announcements on interest rate and foreign exchange futures markets. They find these announcements are responsible for most of the observed time-of-day and day-of-the-week volatility patterns in these markets. While the bulk of the price adjustment to a major announcement occurs within the first minute, volatility remains substantially higher than normal for roughly fifteen minutes and slightly elevated for several hours. Nonetheless, these subsequent price adjustments are basically independent of the first minute's return. The authors identify those announcements with the greatest impact on these markets."

- TAUCHEN, G.E. and M. PITTS, 1983. The Price Variability-Volume Relationship on Speculative Markets,
*Econometrica*51:485-505. [Cited by 355] (15.51/year)

Abstract: "This paper concerns the relationship between the variability of the daily price change and the daily volume of trading on the speculative markets. Our work extends the theory of speculative markets in two ways. First, we derive from economic theory the joint probability distribution of the price change and the trading volume over any interval of time within the trading day. And second, we determine how this joint distribution changes as more traders enter (or exit from) the market. The model's parameters are estimated by FIML using daily data from the 90-day T-bills futures market. The results of the estimation can reconcile a conflict between the price variability-volume elationship for this market and the relationship obtained by previous investigators for other speculative markets."

- WIGGINS, J.B., 1987. Options Values Under Stochastic Volatility: Theory and Empirical Evidence,
*Journal of Financial Economics*, 19, pp. 351-372. [Cited by 291] (15.45/year)

Abstract: "This paper numerically solves the call option valuation problem given a fairly general continuous stochastic process for return volatility. Statistical estimators for volatility process parameters are derived, and parameter estimates are calculated for several individual stocks and indices. The resulting estimated option values do not differ dramatically from Black-Scholes values in most cases, although there is some evidence that for longer-maturity index options, Black-Scholes overvalues out-of-the-money calls in relation to in-the-money calls."

- LAMOUREUX, C.G. and W.D. LASTRAPES, 1990. Heteroskedasticity in Stock Return Data: Volume versus GARCH Effects.
*The Journal of Finance.*[Cited by 244] (15.36/year)
Abstract: "This paper provides empirical support for the notion that Autoregressive Conditional Heteroskedasticity (ARCH) in daily stock return data reflects time dependence in the process generating information flow to the market. Daily trading volume, used as a proxy for information arrival time, is shown to have significant explanatory power regarding the variance of daily returns, which is an implication of the assumption that daily returns are subordinated to intraday equilibrium returns. Furthermore, ARCH effects tend to disappear when volume is included in the variance equation."
- HENTSCHEL, L., 1995. All in the Family: Nesting Symmetric and Asymmetric GARCH Models.
*Journal of Financial Economics.*[Cited by 166] (15.25/year)
Abstract: "This paper develops a parametric family of models of generalized autoregressive heteroskedasticity (GARCH). The family nests the most popular symmetric and asymmetric GARCH models, thereby highlighting the relation between the models and their treatment of asymmetry. Furthermore, the structure permits nested tests of different types of asymmetry and functional forms. Daily U.S. stock return data reject all standard GARCH models in favor of a model in which, roughly speaking, the conditional standard deviation depends on the shifted absolute value of the shocks raised to the power three halves and past standard deviations."
- BLACK, F., 1976. Studies of stock price volatility changes.
*Proceedings of the 1976 Meetings of the Business and ….*[Cited by 452] (15.15/year)

- GALLANT, A.R., D. HSIEH and G. TAUCHEN, 1997. Estimation of stochastic volatility models with diagnostics.
*Journal of Econometrics.*[Cited by 128] (14.49/year)

Abstract: "Efficient method of moments (EMM) is used to fit the standard stochastic volatility model of various extensions to several daily financial time series. EMM matches to the score of the model determined by data analysis called the score generator. Discrepancies reveal characteristics of data that stochastic volatility models cannot approximate. The two score generators employed here are ‘semiparametric ARCH’ and ‘nonlinear nonparametric’. With the first, the standard model is rejected, although some extensions are accepted. With the second, all versions are rejected. The extensions required for an adequate fit are so elaborate that nonparametric specifications are probably more convenient."

- JOHNSON, N.F.,
*et al.*, 2003. Financial Market Complexity: What Physics Can Tell Us about Market Behaviour. books.google.com. [Cited by 40] (14.09/year)

"volatility clustering"

Johnson, Jefferies and Hui (2003), page 69

- ENGLE, R.F., T. ITO and W.L. LIN, 1990. Meteor Showers or Heat Waves? Heteroskedastic Intra-Daily Volatility in the Foreign Exchange Market.
*Econometrica*, Vol. 58, No. 3. (May, 1990), pp. 525-542. [Cited by 221] (13.96/year)

Abstract: "This paper seeks to explain the causes of volatility clustering in exchange rates. Careful examination of intra-daily exchange rates provides a test of two hypotheses--heat waves and meteor showers. The heat wave hypothesis is that the volatility has only country-specific autocorrelation. Alternatively, the meteor shower is a phenomenon of intra-daily volatility spillovers from one market to the next. Using the GARCH model to specify the heteroskedasticity across intra-daily market segments, we find that the empirical evidence is generally against the null hypothesis of the heat wave. Using a volatility type of vector autoregression we examine the impact of news in one market on the time path of per-hour volatility in other markets."

- MUZY, J.F.L., J.L. DELOUR and E.L. BACRY, 2000. Modelling fluctuations of financial time series: from cascade process to stochastic volatility model.
*The European Physical Journal B-Condensed Matter.*[Cited by 82] (13.95/year)

Abstract: "In this paper, we provide a simple, "generic'' interpretation of multifractal scaling laws and multiplicative cascade process paradigms in terms of volatility correlations. We show that in this context 1/*f*power spectra, as recently observed in reference [23], naturally emerge. We then propose a simple solvable "stochastic volatility'' model for return fluctuations. This model is able to reproduce most of recent empirical findings concerning financial time series: no correlation between price variations, long-range volatility correlations and multifractal statistics. Moreover, its extension to a multivariate context, in order to model portfolio behavior, is very natural. Comparisons to real data and other models proposed elsewhere are provided."

- SCHWERT, G.W., 1990. Stock volatility and the crash of'87,
*Review of Financial Studies*[Cited by 219] (13.69/year)

Abstract: "This article analyzes the behavior of stock return volatility using daily data from 1885 through 1988. The October 1987 stock market crash was unusual in many ways. October 19 was the largest percentage change in market value in over 29,000 days. Stock volatility jumped dramatically during and after the crash. Nevertheless, it returned to lower, more normal levels more quickly than past experience predicted. I use data on implied volatilities from call option prices and estimates of volatility from futures contracts on stock indexes to confirm this result."

- RAMCHAND, L. and R. SUSMEL, 1998. Volatility and cross correlation across major stock markets.
*Journal of Empirical Finance.*[Cited by 107] (13.65/year)

Abstract: "Several papers have documented the fact that correlations across major stock markets are higher when markets are more volatile - this is done by comparing unconditional correlations over sub-periods or by using conditional correlations that are time varying. In this paper we examine the relation between correlation and variance in a conditional time and state varying framework. We use a switching ARCH (SWARCH) technique that does two things. One, it enables us to model variance as state varying. Two, a bivariate SWARCH model allows us to go from conditional variance to state varying covariances and correlations and hence test for differences in correlations across variance regimes. We find that the correlations between the U.S. and other world markets are on average 2 to 3.5 times higher when the U.S. market is in a high variance state as compared to a low variance regime. We also find that, compared to a GARCH framework, the portfolio choices resulting from our SWARCH model lead to higher Sharpe ratios."

- ANDERSEN, T.G., H.J. CHUNG and B.E. SORENSEN, 1999. Efficient method of moments estimation of a stochastic volatility model: A Monte Carlo study.
*Journal of Econometrics.*[Cited by 93] (13.60/year)

Abstract: "We perform an extensive Monte Carlo study of efficient method of moments (EMM) estimation of a stochastic volatility model. EMM uses the expectation under the structural model of the score from an auxiliary model as moment conditions. We examine the sensitivity to the choice of auxiliary model using ARCH, GARCH, and EGARCH models for the score as well as nonparametric extensions. EMM efficiency approaches that of maximum likelihood for larger sample sizes. Inference is sensitive to the choice of auxiliary model in small samples, but robust in larger samples. Specification tests and ‘*t*-tests’ show little size distortion."

- BARNDORFF-NIELSEN, O.E., 1997. Normal inverse Gaussian distributions and stochastic volatility modelling.
*Scandinavian Journal of Statistics.*[Cited by 119] (13.47/year)

Abstract: "The normal inverse Gaussian distribution is defined as a variance-mean mixture of a normal distribution with the inverse Gaussian as the mixing distribution. The distribution determines an homogeneous Lévy process, and this process is representable through subordination of Brownian motion by the inverse Gaussian process. The canonical, Lévy type, decomposition of the process is determined. As a preparation for developments in the latter part of the paper the connection of the normal inverse Gaussian distribution to the classes of generalized hyperbolic and inverse Gaussian distributions is briefly reviewed. Then a discussion is begun of the potential of the normal inverse Gaussian distribution and Lévy process for modelling and analysing statistical data, with particular reference to extensive sets of observations from turbulence and from finance. These areas of application imply a need for extending the inverse Gaussian Lévy process so as to accommodate certain, frequently observed, temporal dependence structures. Some extensions, of the stochastic volatility type, are constructed via an observation-driven approach to state space modelling. At the end of the paper generalizations to multivariate settings are indicated."

- DAY, T.E. and C.M. LEWIS, 1992. Stock market volatility and the information content of stock index options.
*Journal of Econometrics.*[Cited by 186] (13.44/year)

Abstract: "Previous studies of the information content of the implied volatilities from the prices of call options have used a cross-sectional regression approach. This paper compares the information content of the implied volatilities from call options on the S&P 100 index to GARCH (Generalized Autoregressive Conditional Heteroscedasticity) and Exponential GARCH models of conditional volatility. By adding the implied volatility to GARCH and EGARCH models as an exogenous variable, the within-sample incremental information content of implied volatilities can be examined using a likelihood ratio test of several nested models for conditional volatility. The out-of-sample predictive content of these models is also examined by regressing*ex post*volatility on the implied volatilities and the forecasts from GARCH and EGARCH models."

- FOSTER, F. Douglas and S. VISWANATHAN, 1993. Variations in Trading Volume, Return Volatility, and Trading Costs: Evidence on Recent Price Formation Models.
*The Journal of Finance*, Vol. 48, No. 1. (Mar., 1993), pp. 187-211. [Cited by 172] (13.40/year)

Abstract: "Patterns in stock market trading volume, trading costs, and return volatility are examined using New York Stock Exchange data from 1988. Intraday test results indicate that, for actively traded firms trading volume, adverse selection costs, and return volatility are higher in the first half-hour of the day. This evidence is inconsistent with the Admati and Pfleiderer (1988) model which predicts that trading costs are low when volume and return volatility are high. Interday test results show that, for actively traded firms, trading volume is low and adverse selection costs are high on Monday, which is consistent with the predictions of the Foster and Viswanathan (1900) model."

- HARVEY, A.C., 1998. Long memory in stochastic volatility.
*Forecasting Volatility in Financial Markets.*[Cited by 105] (13.40/year)

- MELINO, Angelo and Stuart M. TURNBULL, 1988. Pricing Foreign Currency Options with Stochastic Volatility, Volume 45, Issues 1-2, July-August 1990, Pages 239-265. [Cited by 239] (13.40/year)

Abstract: "This paper investigates the consequences of stochastic volatility for pricing spot foreign currency options. A diffusion model for exchange rates with stochastic volatility is proposed and estimated. The parameter estimates are then used to price foreign currency options and the predictions are compared to observed market prices. We find that allowing volatility to be stochastic results in a much better fit to the empirical distribution of the Canada-U.S. exchange rate, and that this improvement in fit results in more accurate predictions of observed option prices."

- MCKENZIE, M.D., 1999. The Impact of Exchange Rate Volatility on International Trade Flows.
*Journal of Economic Surveys.*[Cited by 88] (12.87/year)

Abstract: "Despite the best efforts of economists, a basic paradox as to the impact of exchange rate volatility on trade flows remains unresolved at both the theoretical and empirical level. This paper surveys the vast literature in the area in an attempt to identify major issues which have contributed to the development of the debate and examine whether any general direction for consensus may be found."

- HAMILTON, J.D. and G. LIN, 1996. Stock market volatility and the business cycle.
*Journal of Applied Econometrics.*[Cited by 117] (11.89/year)

Abstract: "This paper investigates the joint time series behavior of monthly stock returns and growth in industrial production. We find that stock returns are well characterized by year-long episodes of high volatility, separated by longer quiet periods. Real output growth, on the other hand, is subject to abrupt changes in the mean associated with economic recessions. We study a bivariate model in which these two changes are driven by related unobserved variables, and conclude that economic recessions are the primary factor that drives fluctuations in the volatility of stock returns. This framework proves useful both for forecasting stock volatility and for identifying and forecasting economic turning points."

- LIN, W.L., R.F. ENGLE and T. ITO, 1994. Do bulls and bears move across borders? International transmission of stock returns and volatility,
*Review of Financial Studies*[Cited by 141] (11.75/year)

Abstract: "This article investigates empirically how returns and volatilities of stock indices are correlated between the Tokyo and New York markets. Using intradaily data that define daytime and overnight returns for both markets, we find that Tokyo (New York) daytime returns are correlated with New York (Tokyo) overnight returns. We interpret this result as evidence that information revealed during the trading hours of one market has a global impact on the returns of the other market. In order to extract the global factor from the daytime returns of one market, we propose and estimate a signal extraction model with GARCH processes."

- DACOROGNA, M.M.,
*et al.*, 1993. A Geographical Model for the Daily and Weekly Seasonal Volatility in the Foreign Exchange Market,*Journal of International Money and Finance*, Volume 12, Issue 4 , August 1993, Pages 413-438. [Cited by 147] (11.45/year)

Abstract: "The daily and weekly seasonality of foreign exchange volatility is modelled by introducing an activity variable. This activity is explained by a simple model of the changing and sometimes overlapping market presence of geographical components (East Asia, Europe, and America).

Integrating this activity over time results in the new time scale, characterized by non-seasonal volatility. This scale, applied to dense datastreams of absolute price changes, suceeds in removing most of the seasonal heteroscedasticity in an autocorrelation study. Unexpectedly, the positive autocorrelation is found to decline hyperbolically rather than exponentially as a function of the lag."

- GRANGER, C.W.J. and Z. DING, 1996. Varieties of long memory models,
*Journal of Econometrics*73, 61-77. [Cited by 113] (11.43/year)

Abstract: "Long memory is defined as a series having a slowly declining correlogram or, equivalently, an infinite spectrum at zero frequency. Fractional integrated processes have such properties but here it is pointed out that a number of other processes can also be long memory, including generalized fractionally integrated models arising from aggregation, time-changing coefficient models, and possibly nonlinear models. It seems that there are many classes of processes that deserve further study. The relevance of long memory is illustrated using absolute returns from a daily stock market index."

- ANG, A. and G. BEKAERT, 2002. Short Rate Nonlinearities and Regime Switches.
*Journal of Economic Dynamics and Control.*[Cited by 43] (11.05/year)
Abstract: "Using non-parametric estimation methods, various authors have shown distinct non-linearities in the drift and volatility function of the US short rate, which are inconsistent with standard affine term structure models. We document how a regime-switching model with state dependent transition probabilities between regimes can replicate the patterns found by the non-parametric studies. To do so, we use data from the UK and Germany in addition to US data and include term spreads in some of our models. We also examine the drift and volatility function of the term spread."
- DIEBOLD, F.X. and M. NERLOVE, 1989. The Dynamics of Exchange Rate Volatility: A Multivariate Latent Factor ARCH Model.
*J. APPL. ECON.*[Cited by 185] (10.99/year)

Abstract: "We study temporal volatility patterns in seven nominal dollar spot exchange rates, all of which display strong evidence of autoregressive conditional heteroskedasticity (ARCH). We first formulate and estimate univariate models, the results of which are subsequently used to guide specification of a multivariate model. The key element of our multivariate approach is exploitation of factor structure, which facilitates tractable estimation via a substantial reduction in the number of parameters to be estimated. Such a latent-variable model is shown to provide a good description of multivariate exchange rate movements: the ARCH effects capture volatility clustering, and the factor structure captures commonality in volatility movements across exchange rates."

- BRAUN, P.A., D.B. NELSON and A.M. SUNIER, 1995. Good News, Bad News, Volatility, and Betas.
*The Journal of Finance.*[Cited by 119] (10.98/year)

Abstract: "The authors investigate the conditional covariances of stock returns using bivariate exponential ARCH models. These models allow market volatility, portfolio-specific volatility, and beta to respond asymmetrically to positive and negative market and portfolio returns, i.e., 'leverage' effects. Using monthly data, the authors find strong evidence of conditional heteroscedasticity in both market and nonmarket components of returns, and weaker evidence of time-varying conditional betas. Surprisingly, while leverage effects appear strong in the market component of volatility, they are absent in conditional betas and weak and/or inconsistent in nonmarket sources of risk."

- BESSEMBINDER, H. and P.J. SEGUIN, 1993. Price Volatility, Trading Volume, and Market Depth: Evidence from Futures Markets.
*The Journal of Financial and Quantitative Analysis.*[Cited by 135] (10.52/year)

Abstract: "The relations between volume, volatility, and market depth in eight physical and financial futures markets are examined. Evidence suggests that linking volatility to total volume does not extract all information. When volume is partitioned into expected and unexpected components, the paper finds that unexpected volume shocks have a larger effect on volatility. Further, the relation is asymmetric; the impact of positive unexpected volume shocks on volatility is larger than the impact of negative shocks. Finally, consistent with theories of market depth, the study shows large open interest mitigates volatility."

- KOUTMOS, G. and G.G. BOOTH, 1995. Asymmetric volatility transmission in international stock markets.
*Journal of International Money and Finance.*[Cited by 114] (10.52/year)

Abstract: "The transmission mechanism of price and volatility spillovers across the New York, Tokyo and London stock markets is investigated. The asymmetric impact of good news (market advances) and bad news (market declines) on volatility transmission is described by an extended multivariate Exponential Generalized Autoregressive Conditionally Heteroskedastic (EGARCH) model. Using daily open-to-close returns, we find strong evidence that volatility spillovers in a given market are much more pronounced when the news arriving from the last market to trade is bad. A before and after October 1987 crash analysis reveals that the linkages and interactions among the three markets have increased substantially in the post-crash era, suggesting that national markets have grown more interdependent."

- DANIELSSON, J., 1994. Stochastic volatility in asset prices: Estimation with simulated maximum likelihood.
*Journal of Econometrics.*[Cited by 124] (10.48/year)

Abstract: "The stochastic volatility model is used to estimate daily asset price dynamics. The model is estimated by integrating latent volatility out of the joint density of prices and volatility to obtain the marginal density of prices. Due to high number of dimensions of the integral, no conventional integration technique is applicable. A Monte Carlo method, called simulated maximum likelihood, is used to obtain the marginal density, where the latent variable is simulated conditional on available information. The model is estimated by 2022 observations from the S & P 500 index. For comparison ARCH type models are estimated with the same data."

- ZHOU, B., 1996. High-Frequency Data and Volatility in Foreign-Exchange Rates,
*Journal of Business & Economic Statistics.*[Cited by 101] (10.27/year)

Abstract: "Exchange rates, like many other financial time series, display substantial heteroscedasticity. This poses obstacles in detecting trends and changes. Understanding volatility becomes extremely important in studying financial time series. Unfortunately, estimating volatility from low-frequency data, such as daily, weekly, or monthly observations, is very difficult. The recent availability of ultra-high-frequency observations, such as tick-by-tick data, to large financial institutions creates a new possibility for the analysis of volatile time series. This article uses tick-by-tick foreign-exchange rates to explore this new type of data. Unlike low-frequency data, high-frequency data have extremely high negative first-order autocorrelation in their return. In this article, I propose a model that can explain the negative autocorrelation and a volatility estimator for high-frequency data. The daily and hourly volatility estimates of exchange rate show some interesting patterns."

- RITCHKEN, Peter and L. SANKARASUBRAMANIAN, 1995. Volatility Structures of Forward Rates and the Dynamics of the Term Structure,
*Mathematical Finance.*[Cited by 109] (10.06/year)

Abstract: "For general volatility structures for forward rates, the evolution of interest rates may not be Markovian and the entire path may be necessary to capture the dynamics of the term structure. This chapter identifies conditions on the volatility structure of forward rates that permit the dynamics of the term structure to be represented by a two-dimensional state variable Markov process. The permissible set of volatility structures that accomplishes this goal is shown to be quite large and includes many stochastic structures. In general, analytical characterisation of the terminal distributions of the two state variables is unlikely, and numerical procedures are required to value claims. Efficient simulation algorithms using control variates are developed to price claims against the term structure."

- BARCLAY, M.J. and J.B. WARNER, 1993. Stealth trading and volatility: Which trades move prices.
*Journal of Financial Economics.*[Cited by 129] (10.05/year)

Abstract: "We examine the proportion of a stock's cumulative price change that occurs in each trade-size category, using transactions data for a sample of NYSE firms. Although the majority of trades are small, most of the cumulative stock-price change is due to medium-size trades. This evidence is consistent with the hypothesis that informed trades are concentrated in the medium-size category, and that price movements are due mainly to informed traders' private information."

- CORSI, F.,
*et al.*, 2001. Consistent High-precision Volatility from High-frequency Data.*Economic Notes.*[Cited by 49] (10.05/year)

Abstract: "Estimates of daily volatility are investigated. Realized volatility can be computed from returns observed over time intervals of different sizes. For simple statistical reasons, volatility estimators based on high-frequency returns have been proposed, but such estimators are found to be strongly biased as compared to volatilities of daily returns. This bias originates from microstructure effects in the price formation. For foreign exchange, the relevant microstructure effect is the incoherent price formation, which leads to a strong negative first-order autocorrelation (1)40 per cent for tick-by-tick returns and to the volatility bias. On the basis of a simple theoretical model for foreign exchange data, the incoherent term can be filtered away from the tick-by-tick price series. With filtered prices, the daily volatility can be estimated using the information contained in high-frequency data, providing a high-precision measure of volatility at any time interval."

- ROSS, S.A., 1989. Information and Volatility: The No-Arbitrage Martingale Approach to Timing and Resolution ….
*The Journal of Finance.*[Cited by 165] (9.80/year)

Abstract: "The no-arbitrage martingale analysis is used to study the effect on asset prices of changes in the rate of information flow. The analysis is first used to develop some simple tools for asset pricing in a continuous-time setting. These tools are then applied to determine the effect of information on prices and price volatility, to extend Samuelson's theorem on prices fluctuating randomly, and to study the impact on prices of the resolution of uncertainty. The conditions under which uncertainty resolution is irrelevant for asset pricing are shown to be similar to those which support the MM irrelevance theorems."

- DE, G. and S. IMROHOROGLU, 1997. Stock returns and volatility in emerging financial markets.
*Journal of International Money and Finance.*[Cited by 86] (9.73/year)

Abstract: "This paper studies the dynamics of expected stock returns and volatility in emerging financial markets. We find clustering, predictability and persistence in conditional volatility, as others have documented for mature markets. However, emerging markets exhibit higher conditional volatility and conditional probability of large price changes than mature markets. Exposure to high country-specific risk does not appear to be rewarded with higher expected returns. We detect a risk-reward relation in Latin America but not in Asia when we assume some level of international integration. We do not find support for the claim that market liberalization increases price volatility."

- STOLL, H.R. and R.E. WHALEY, 1990. Stock market structure and volatility,
*Review of Financial Studies*[Cited by 154] (9.62/year)

Abstract: "The procedure for opening stocks on the NYSE appears to affect price volatility. An analytical framework for assessing the magnitude of the structurally induced volatility is presented. The ratio of variance of open-to-open returns to close-to-close returns is shown to be consistently greater than one for NYSE common stocks during the period 1982 through 1986. The greater volatility at the open is not attributable to the way in which public information is released since both the open-to-open return and the close-to-close returns span the same period of time. Instead, the greater volatility appears to be attributable to private information revealed in trading and to temporary price deviations induced by specialist and other traders. The implied cost of immediacy at the open is significantly higher than at the close. Other empirical evidence in this article documents the volume of trading at the open, the time delays between the exchange opening and the first transaction in a stock, the difference in daytime volatility versus overnight volatility, and the extent to which volatility is related to trading volume."

- BAILLIE, R.T. and R.P. DEGENNARO, 1990. Stock Returns and Volatility.
*The Journal of Financial and Quantitative Analysis.*[Cited by 152] (9.60/year)

Abstract: "Most asset pricing models postulate a positive relationship between a stock portfolio's expected returns and risk, which is often modeled by the variance of the asset price. This paper uses GARCH in mean models to examine the relationship between mean returns on a stock portfolio and its conditional variance or standard deviation. After estimating a variety of models from daily and monthly portfolio return data, we conclude that any relationship between mean returns and own variance or standard deviation is weak. The results suggest that investors consider some other risk measure to be more important than the variance of portfolio returns."

- TAYLOR, S.J. and X. XU, 1997. The incremental volatility information in one million foreign exchange quotations.
*Journal of Empirical Finance.*[Cited by 83] (9.39/year)

Abstract: "The volatility information found in high-frequency exchange rate quotations and in implied volatilities is compared by estimating ARCH models for DM/$ returns. Reuters quotations are used to calculate five-minute returns and hence hourly and daily estimates of realised volatility that can be included in equations for the conditional variances of hourly and daily returns. The ARCH results show that there is a significant amount of information in five-minute returns that is incremental to options information when estimating hourly variances. The same conclusion is obtained by an out-of-sample comparison of forecasts of hourly realised volatility."

- JONES, C.M., O. LAMONT and R.L. LUMSDAINE, 1998. Macroeconomic news and bond market volatility.
*Journal of Financial Economics.*[Cited by 73] (9.32/year)

Abstract: "We examine the reaction of daily Treasury bond prices to the release of U.S. macroeconomic news. These news releases (of employment and producer price index data) are of interest because they are released on periodic, preannounced dates and because they are associated with substantial bond market volatility. We investigate whether these nonautocorrelated announcements give rise to autocorrelated volatility. We find that announcement-day volatility does not persist at all, consistent with the immediate incorporation of information into prices. We also find a risk premium on these release dates."

- BACCHETTA, P. and E. WINCOOP, 1998. Capital Flows to Emerging Markets: Liberalization, Overshooting, and Volatility. [Cited by 73] (9.32/year)

Abstract: "The paper analyzes the impact of financial liberalizations and reforms in emerging markets on the dynamics of capital flows to these markets, using a simple model of international investors' behavior. We first show that the gradual nature of liberalizations, combined with the cost of absorbing large inflows in emerging economies, leads to rich dynamics of capital flows and often implies an initial period of overshooting as portfolios adjust. Asset prices will overshoot as well. Second, we show that if investors have incomplete information about new emerging markets, and learn over time, there can be high volatility of capital flows as well as contagion. Finally, we provide numerical estimates of long run capital inflows to emerging market economies and compare them to actual inflows. This gives a good indicator of upcoming crisis situations."

- MEDDAHI, N., 2001. An Eigenfunction Approach for Volatility Modeling. sceco.umontreal.ca. [Cited by 44] (9.10/year)

Abstract: "In this paper, we introduce a new approach for volatility modeling in discrete and continuous time. We follow the stochastic volatility literature by assuming that the variance is a function of a state variable. However, instead of assuming that the loading function is ad hoc (e.g., exponential or affine), we assume that it is a linear combination of the eigenfunctions of the conditional expectation (resp. infinitesimal generator) operator associated to the state variable in discrete (resp. continuous) time. Special examples are the popular log-normal and square-root models where the eigenfunctions are the Hermite and Laguerre polynomials respectively. The eigenfunction approach has at least six advantages: i) it is general since any square integrable function may be written as a linear combination of the eigenfunctions; ii) the orthogonality of the eigenfunctions leads to the traditional interpretations of the linear principal components analysis; iii) the implied dynamics of the variance and squared return processes are ARMA and, hence, simple for forecasting and inference purposes; (iv) more importantly, this generates fat tails for the variance and returns processes; v) in contrast to popular models, the variance of the variance is a flexible function of the variance; vi) these models are closed under temporal aggregation."

- LIU, Y.,
*et al.*, 1997. Correlations in Economic Time Series,*Physica A*, Volume 245, Issues 3-4 , 1 November 1997, Pages 437-440. [Cited by 80] (9.05/year)

Abstract: "A financial index of the New York stock exchange, the S&P500, is analyzed at 1 min intervals over the 13 yr period, January 84–December 96. We quantify the correlations of the absolute values of the index increment. We find that these correlations can be described by two different power laws with a crossover time*t*_{x}600 min. Detrended fluctuation analysis gives exponents α_{1}= 0.66 and α_{2}= 0.93 for*t*<*t*_{x}and*t*>*t*_{x}, respectively. Power spectrum analysis gives corresponding exponents β_{1}= 0.31 and β_{2}= 0.90 for*f*>*f*_{x}and*f*<*f*_{x}, respectively."

- ARNEODO, A., J.F. MUZY and D. SORNETTE, 1998. Causal cascade in the stock market from the``infrared''to the``ultraviolet''.
*European Physical Journal*, B 2:277-282, 1998 [Cited by 80] (9.01/year)

Abstract: "We use wavelets to decompose the volatility (standard deviation) of intraday (S&P500) return data across scales. We show that when investigating two-point correlation functions of the volatility logarithms across different time scales, one reveals the existence of a causal information cascade from large scales (*i.e.*small frequencies) to fine scales. We quantify and visualize the information flux across scales. We provide a possible interpretation of our findings in terms of market dynamics."

- BOLLERSLEV, Tim and Hans Ole MIKKELSEN 1999. Long-term equity anticipation securities and stock market volatility dynamics.
*Journal of Econometrics.*[Cited by 61] (8.86/year)
Abstract: "Recent empirical findings suggest that the long-run dependence in U.S. stock market volatility is best described by a slowly mean-reverting fractionally integrated process. The present study complements this existing time-series-based evidence by comparing the risk-neutralized option pricing distributions from various ARCH-type formulations. Utilizing a panel data set consisting of newly created exchange traded long-term equity anticipation securities, or leaps, on the Standard and Poor's 500 stock market index with maturity times ranging up to three years, we find that the degree of mean reversion in the volatility process implicit in these prices is best described by a Fractionally Integrated EGARCH (FIEGARCH) model."
- SUNDARESAN, S.M., 1989. Intertemporally dependent preferences and the volatility of consumption and wealth,
*Review of Financial Studies*[Cited by 141] (8.29/year)

Abstract: "In this article we construct a model in which a consumer's utility depends on the consumption history. We describe a general equilibrium framework similar to Cox, Ingersoll, and Ross (1985a). A simple example is then solved in closed form in this general equilibrium setting to rationalize the observed stickiness of the consumption series relative to the fluctuations in stock market wealth. The sample paths of consumption generated from this model imply lower variability in consumption growth rates compared to those generated by models with separable utility functions. We then present a partial equilibrium model similar to Merton (1969, 1971) and extend Merton's results on optimal consumption and portfolio rules to accommodate nonseparability in preferences. Asset pricing implications of our framework are briefly explored."

- KRAWIECKI, A., J.A. HOLYST and D. HELBING, 2002. Volatility Clustering and Scaling for Financial Time Series due to Attractor Bubbling.
*Physical Review Letters.*[Cited by 32] (8.25/year)

Abstract: "A microscopic model of financial markets is considered, consisting of many interacting agents (spins) with global coupling and discrete-time heat bath dynamics, similar to random Ising systems. The interactions between agents change randomly in time. In the thermodynamic limit, the obtained time series of price returns show chaotic bursts resulting from the emergence of attractor bubbling or on-off intermittency, resembling the empirical financial time series with volatility clustering. For a proper choice of the model parameters, the probability distributions of returns exhibit power-law tails with scaling exponents close to the empirical ones."

- MAHEU, J.M. and T.H. MCCURDY, 2002. Nonlinear Features of Realized FX Volatility.
*Review of Economics and Statistics.*[Cited by 32] (8.22/year)
Abstract: "This paper investigates nonlinear features of FX volatility dynamics using estimates of daily volatility based on the sum of intraday squared returns. Measurement errors associated with using realized volatility to estimate ex post latent volatility imply that standard time series models of the conditional variance become variants of an ARMAX model. We explore nonlinear departures from these linear specifications using a doubly stochastic process under duration-dependent mixing. This process can capture large abrupt changes in the level of volatility, time-varying persistence, and time-varying variance of volatility. The results have implications for forecast precision, hedging, and pricing of derivatives."
- FLEMING, J., B. OSTDIEK and R.E. WHALEY, 1995. Predicting stock market volatility: A new measure,
*The Journal of Futures Markets*, Vol. 15, No. 3, 265-302. [Cited by 89] (8.21/year)

Summary: "The CBOE Market Volatility Index (VIX) offers the market place and academic researchers a new measure of stock market volatility. This study describes how the index is constructed from the implied volatilities of eight S&P 100 index options, and then assesses its behavior over a seven-year period. Univariate time-series properties and seasonalities of the index are documented as well as the temporal relationship between the volatility index and stock market returns. Finally, the performance of VIX as a forecast of future stock market volatility is evaluated. [SNIP 4 more paragraphs]"

- CHAN, K., K.C. CHAN and G.A. KAROLYI, 1991. Intraday volatility in the stock index and stock index futures markets,
*Review of Financial Studies*, 4, 657. [Cited by 94] (7.83/year)

Abstract: "We examine the intraday relationship between returns and returns volatility in the stock index and stock index futures markets. Our results indicate a strong intermarket dependence in the volatility of the cash and futures returns. Price innovations that originate in either the stock or futures markets can predict the future volatility in the other market. We show that this relationship persists even during periods in which the dependence in the returns themselves appears to weaken. The findings are robust to controlling for potential market frictions such as asynchronous trading in the stock index. Our results have implications for understanding the pattern of information flows between the two markets."

- WEST, K.D. and D. CHO, 1994. The Predictive Ability of Several Models of Exchange Rate Volatility. ideas.uqam.ca. [Cited by 92] (7.77/year)

Abstract: "We compare the out-of-sample forecasting performance of univariate homoskedastic, GARCH, autoregressive, and nonparametric models for conditional variances, using five bilateral weekly exchange rates for the dollar, 1973–1989. For a one-week horizon, GARCH models tend to make slightly more accurate forecasts. For longer horizons, it is difficult to find grounds for choosing between the various models. None of the models perform well in a conventional test of forecast efficiency."

- WHITELAW, R.F., 1994. Time Variations and Covariations in the Expectation and Volatility of Stock Market Returns.
*The Journal of Finance.*[Cited by 89] (7.52/year)

Abstract: "This article investigates empirically the comovements of the conditional mean and volatility of stock returns. It extends the results in the literature by demonstrating the role of the commercial paper-Treasury yield spread in predicting time variation in volatility. The conditional mean and volatility exhibit an asymmetric relation, which contrasts with the contemporaneous relation that has been tested previously. The volatility leads the expected return, and this time series relation is documented using offset correlations, short-horizon contemporaneous correlations, and a vector autoregression. These results bring into question the value of modeling expected returns as a constant function of conditional volatility."

- CALVERT, L. and A. FISHER, 2000. Forecasting Multifractal Volatility. finance.commerce.ubc.ca. [Cited by 44] (7.49/year)

Abstract: "This paper develops analytical methods to forecast the distribution of future returns for a new continuous-time process, the Poisson multifractal. The process captures the thick tails, volatility persistence, and moment scaling exhibited by many financial time series. It can be interpreted as a stochastic volatility model with multiple frequencies and a Markov latent state. We assume for simplicity that the forecaster knows the true generating process with certainty but only observes past returns. The challenge in this environment is long memory and the corresponding infinite dimension of the state space. We introduce a discretized version of the model that has a finite state space and an analytical solution to the conditioning problem. As the grid step size goes to zero, the discretized model weakly converges to the continuous-time process, implying the consistency of the density forecasts."

- HULL, J. and A. WHITE, 1987. The pricing of options on assets with stochastic volatility.
*Journal of Finance.*[Cited by 141] (7.49/year)

Abstract: "One option-pricing problem that has hitherto been unsolved is the pricing of a European call on an asset that has a stochastic volatility. This paper examines this problem. The option price is determined in series form for the case in which the stochastic volatility is independent of the stock price. Numerical solutions are also produced for the case in which the volatility is correlated with the stock price. It is found that the Black-Scholes price frequently overprices options and that the degree of overpricing increases with the time to maturity."

- BONSER-NEAL, C. and G. TANNER, 1995. Central Bank Intervention and the Volatility of Foreign Exchange Rates: Evidence from the Options …. ideas.repec.org. [Cited by 78] (7.20/year)

Abstract: "This paper tests the effects of central bank intervention on the ex ante volatility of $/DM and $/yen exchange rates between 1985 and 1991. In contrast to previous research which employed GARCH estimates of conditional volatility, we estimate ex ante volatility using the implied volatilities of currency option prices. We also control for the effects of other macroeconomic announcements. We find little support for the hypothesis that central bank intervention decreases expected exchange rate volatility. Instead, central bank intervention is generally associated with a positive change in ex ante exchange rate volatility, or with no change."

- CôTé, A., 1994. Exchange Rate Volatility and Trade: A Survey. ideas.repec.org. [Cited by 85] (7.18/year)

Abstract: "This paper provides an extensive survey of the literature on exchange rate volatility and trade, examining both the theory that underlies the work in this area and the results of empirical studies published since 1988. Despite the widespread view that an increase in volatility will reduce the level of trade, this review reveals that the effects of volatility are ambiguous. There is no real consensus on either the direction or the size of the exchange rate volatility - trade level relationship. Overall, a larger number of studies find that volatility tends to reduce the level of trade, but when the effect is measured, it is found to be relatively small. Several reasons can explain this tenuous relationship: (i) even for risk-averse businesses, an increase in risk does not necessarily lead to a reduction in the risky activity, (ii) the availability of hedging techniques makes it possible for traders to avoid most of exchange risk at little cost, (iii) exchange rate volatility may actually offset some other forms of business risk, and (iv) exchange rate volatility can create profitable trading and investment opportunities. La presente etude offre un panorama des recherches faites sur les liens qui existent entre la volatilite des taux de change et les echanges internationaux. L'auteure y examine d'une part les fondements theoriques des travaux effectues dans ce domaine et, d'autre part, les resultats des etudes empiriques publiees depuis 1988. Meme si la perception generale est que l'accroissement de la volatilite des taux de change abaisse le niveau des echanges commerciaux, la presente etude montre que les effets de la volatilite sont ambigus. Un veritable consensus ne se degage ni sur le sens ni sur l'importance des liens entre la volatilite des taux de change et les echanges commerciaux. Dans l'ensemble, parmi les etudes consultees, la majorite arrivent a la conclusion que la volatilite du cours de la monnaie tend a abaisser le niveau des echanges, mais lorsque l'effet est mesure, on constate qu'il est relativement mineur. La faiblesse de ce lien peut s'expliquer de plusieurs facons : i) un accroissement du risque n'entraine pas forcement une diminution des activites a risque meme pour les entreprises qui ont une aversion pour le risque; ii) les techniques de couverture permettent aux entreprises de reduire considerablement, a peu de frais, le risque de change; iii) la volatilite des taux de change peut en fait compenser d'autres types de risque; et iv) la volatilite des taux de change peut creer des conditions propices a des echanges commerciaux et a des investissements rentables."

- KALISKY, T., Y. ASHKENAZY and S. HAVLIN, 2005. Volatility of linear and nonlinear time series.
*Physical Review E.*[Cited by 6] (6.84/year)

Abstract: "Previous studies indicated that nonlinear properties of Gaussian distributed time series with long-range correlations,*u*_{i}, can be detected and quantified by studying the correlations in the magnitude series |*u*_{i}|, the "volatility." However, the origin for this empirical observation still remains unclear and the exact relation between the correlations in*u*_{i}and the correlations in |*u*_{i}| is still unknown. Here we develop analytical relations between the scaling exponent of linear series*u*_{i}and its magnitude series |*u*_{i}|. Moreover, we find that nonlinear time series exhibit stronger (or the same) correlations in the magnitude time series compared with linear time series with the same two-point correlations. Based on these results we propose a simple model that generates multifractal time series by explicitly inserting long range correlations in the magnitude series; the nonlinear multifractal time series is generated by multiplying a long-range correlated time series (that represents the magnitude series) with uncorrelated time series [that represents the sign series sgn(*u*_{i})]. We apply our techniques on daily deep ocean temperature records from the equatorial Pacific, the region of the El-Ninõ phenomenon, and find: (i) long-range correlations from several days to several years with 1/*f*power spectrum, (ii) significant nonlinear behavior as expressed by long-range correlations of the volatility series, and (iii) broad multifractal spectrum."

- CHALLET, D., M. MARSILI and Y.C. ZHANG, 2001. Stylized facts of financial markets and market crashes in Minority Games.
*Arxiv preprint cond-mat/0101326.*[Cited by 33] (6.82/year)

Volatility clustering is a very well known stylized fact. It is known that the volatility has algebraically decaying auto-correlation, and accordingly that the returns activity is clustered in time, which is an easy pattern to detect with naked eyes.

Challet, Marsili and Zhang (2001)"The volatility auto-correlation is known to be algebraically decaying, typically as t-0.3 in real financial markets [2]. Volatility auto-correlation is known to be related to volume correlation [2]."

Abstract: "We present and study a Minority Game based model of a financial market where adaptive agents—the speculators—interact with deterministic agents—called

Challet, Marsili and Zhang (2001)*producers*. Speculators trade only if they detect predictable patterns which grant them a positive gain. Indeed the average number of active speculators grows with the amount of information that producers inject into the market. Transitions between equilibrium and out of equilibrium behavior are observed when the relative number of speculators to the complexity of information or to the number of producers are changed. When the system is out of equilibrium, stylized facts arise, such as fat tailed distribution of returns and volatility clustering. Without speculators, the price follows a random walk; this implies that stylized facts arise because of the presence of speculators. Furthermore, if speculators abandon price taking behavior, stylized facts disappear."

- CAI, J.,
*et al.*, 2001. ‘Once-in-a-Generation'Yen Volatility in 1998: Fundamentals, Intervention and Order Flow.*Journal of International Money and Finance.*[Cited by 32] (6.56/year)

Abstract: "The yen provided foreign exchange market participants with 'once-in-a-generation' volatility movements in 1998. For instance, after many months of uneven yen depreciation a remarkable period of yen appreciation was experienced where, in one two-day period, the U.S. dollar dropped in value by 20 yen, market-makers were refusing to quote yen/dollar prices for more than $1 million, and funds with short yen positions incurred massive losses. Not since the early 1970s has the yen-dollar exchange rate experienced such shifts. Analysts claimed that the yen reversal was due to order flow driven by changing tastes for risk and hedge-fund herding on unwinding yen ‘carry trade’ positions rather than any fundamentals related to the yen. In this paper, we examine the high-frequency evidence on the yen/dollar exchange rate in 1998 and provide a detailed characterization of the return volatility. Evidence of shifting fundamentals is provided by a comprehensive list of macroeconomic announcements from both the U.S. and Japan. While macroeconomic announcements and intervention are found to have significant effects on volatility, our results lead to the conclusion that order flow played a more important role than news regarding fundamentals. Evidence regarding the independent effect of order flow was provided by spot, forward, and futures positions of major market participants. These position changes are found to be significant determinants of volatility. Since such portfolio shifts are revealed to the market through trading, the results are consistent with order flow playing a significant role in the revelation of private information and the associated exchange rate shifts."

- GAUNERSDORFER, A. and C.H. HOMMES, 1999. A nonlinear structural model for volatility clustering.
*University of Amsterdam preprint (hommes@ fee. uva. nl).*[Cited by 44] (6.39/year)
Abstract: "A simple nonlinear structural model of endogenous belief heterogeneity is proposed. News about fundamentals is an IID random process, but nevertheless volatility clustering occurs as an endogenous phenomenon caused by the interaction between different types of traders, fundamentalists and technical analysts. The belief types are driven by an adaptive, evolutionary dynamics according to the success of the prediction strategies in the recent past conditioned upon price deviations from the rational expectations fundamental price. Asset prices switch irregularly between two different regimes - close to the fundamental price fluctuations with low volatility, and periods of persistent deviations from fundamentals where the market is dominated by technical trading - thus, creating time varying volatility similar to that observed in real financial data."
- GRANGER, C.W.J. and Z. DING, 1997. Some Properties of Absolute Returns: An Alternative Measure of Risk,
*Annales d’Economie et de Statistique*, 40:67--91. [Cited by 82] (6.36/year)

- CONT, R., M. POTTERS and J.P. BOUCHAUD, 1997. Scaling in stock market data: stable laws and beyond.
*Scale invariance and beyond.*[Cited by 56] (6.31/year)

Abstract: "The concepts of scale invariance, self-similarity and scaling have been fruitfully applied to the study of price fluctuations in financial markets. After a brief review of the properties of stable Levy distributions and their applications to market data we indicate the shortcomings of such models and describe the truncated Levy flight as an alternative model for price movements. Furthermore, studying the dependence structure of the price increments shows that while their autocorrelation function decreases rapidly to zero, the correlation of their squares and absolute values shows a slow power law decay, indicating persistence in the scale of fluctuations, a property which can be related to the anomalous scaling of the kurtosis. In the last section we review, in the light of these empirical facts, recent attempts to draw analogies between scaling in financial markets and in turbulent flows."

- CHOU, R.Y., 1988. Volatility Persistence and Stock Valuations: Some Empirical Evidence Using GARCH,
*Journal of Applied Econometrics.*[Cited by 111] (6.22/year)

Abstract: "In this paper issues of volatility persistence and the changing risk premium in the stock market are investigated using the GARCH estimation technique. We get a point estimate of the index of relative risk aversion of 4.5 and confirm the existence of changing equity premiums in the US during 1962-1985. The persistence of shocks to the stock return volatility is so high that the data cannot reject a non-stationary volatility process specification. The results of this paper are consistent with Malkiel and Pindyck's hypothesis that it is the unforseen rise in the investment uncertainty during 1974 that causes the market to plunge."

Chou (1988)

- CIZEAU, Pierre,
*et al.*, 1997. Volatility distribution in the S&P500 Stock Index,*Physica A: Statistical and Theoretical Physics*, Volume 245, Issues 3-4, 1 November 1997, Pages 441-445. [Cited by 55] (6.22/year)

Abstract: "We study the volatility of the S&P500 stock index from 1984 to 1996 and find that the volatility distribution can be very well described by a log-normal function. Further, using detrended fluctuation analysis we show that the volatility is power-law correlated with Hurst exponent α 0.9."

final paragraph: "In summary, we have found that the probability distribution of the S&P volatility can be well described by a log-normal function and that the volatility shows power-law correlations with Hurst exponent α ≅ 0.9. The log-normal shape of the distribution is consistent with a multiplicative process [21] for the volatility [22]. However, a multiplicative behavior would be surprising, because efficient market theories [2] assume that the price changes,*G*(*t*), are caused by incoming new informations about an asset. Since such information-induced price changes are additive in*G*(*t*), they should not give rise to multiplicative behavior of the volatility."

Cizeau,*et al.*(1997)

- SHILLER, R.J., 1979. The Volatility of Long-Term Interest Rates and Expectations Models of the Term Structure.
*The Journal of Political Economy.*[Cited by 164] (6.11/year)

Abstract: "Models which represent long-term interest rates as long averages of expected short-term interest rates imply, because of the smoothing implicit in the averaging, that long rates should not be too volatile. The volatility of actual long-term interest rates, as measured by the variance of short-term holding yields on long-term bonds, appears to exceed limits imposed by the models. Such excess volatility implies a kind of forecastability for long rates. Long rates show a slight tendency to fall when they are high relative to short rates rather than rise as predicted by expectations models."

- GENCAY, R., F. SELCUK and B. WHITCHER, 2001. Scaling properties of foreign exchange volatility.
*Physica A.*[Cited by 28] (5.74/year)

Abstract: "In this paper, we investigate the scaling properties of foreign exchange volatility. Our methodology is based on a wavelet multi-scaling approach which decomposes the variance of a time series and the covariance between two time series on a scale by scale basis through the application of a discrete wavelet transformation. It is shown that foreign exchange rate volatilities follow different scaling laws at different horizons. Particularly, there is a smaller degree of persistence in intra-day volatility as compared to volatility at one day and higher scales. Therefore, a common practice in the risk management industry to convert risk measures calculated at shorter horizons into longer horizons through a global scaling parameter may not be appropriate. This paper also demonstrates that correlation between the foreign exchange volatilities is the lowest at the intra-day scales but exhibits a gradual increase up to a daily scale. The correlation coefficient stabilizes at scales one day and higher. Therefore, the benefit of currency diversification is the greatest at the intra-day scales and diminishes gradually at higher scales (lower frequencies). The wavelet cross-correlation analysis also indicates that the association between two volatilities is stronger at lower frequencies."

Conclusions:

"We have proposed a simple method for identifying the scaling laws in financial time series. The proposed methodology is based on a wavelet multi-scaling approach which decomposes the variance of a time series and the covariance between two time series on scale by scale basis through the application of a non-decimated discrete wavelet transformation. It is simple to calculate and can easily be implemented as it does not depend on a particular model selection criterion and model specific parameter choices. It is shown that exchange rate volatility has different scaling properties at different horizons. The intra-day persistence in volatility is significantly less than the volatility at one day or higher scales. The correlation between two volatility series increases within the day but remains constant at one day or higher scales. The wavelet cross-correlation analysis indicates that the association between two volatilities is stronger at higher scales (low frequencies)."

- KIM, D. and S.J. KON, 1994. Alternative Models for the Conditional Heteroscedasticity of Stock Returns.
*The Journal of Business.*[Cited by 68] (5.72/year)
Abstract: "This article compares econometric model specifications that have been proposed to explain the commonly observed characteristics of the unconditional distribution of daily stock returns. The empirical results indicate that the most likely ranking is (1) intertemporal dependence models, (2) Student t, (3) generalized mixture-of-normal distributions, (4) Poisson jump, and (5) the stationary normal. Among the intertemporal dependence models for conditional heteroscedasticity, those with a leverage (or asymmetry) effect are superior. The Glosten, Jagannathan, and Runkle specification is the most descriptive for individual stocks, while Nelson's exponential model is the most likely for stock indexes."
- HARVEY, C.R. and R.E. WHALEY, 1992. Market volatility prediction and the efficiency of the S&P 100 index option market.
*Journal of Financial Economics.*[Cited by 76] (5.49/year)

Abstract: "Most models of market volatility use either past returns or ex post volatility to forecast volatility. In this paper, the dynamic behavior of market volatility is assessed by forecasting the volatility implied in the transaction prices of Standard & Poor's 100 index options. We test and reject the hypothesis that volatility changes are unpredictable. However, while our statistical model delivers precise forecasts, abnormal returns are not possible in a trading strategy (based on daily out-of-sample volatility projections) which takes transaction costs into account, suggesting that predictable time-varying volatility is consistent with market efficiency."

- BLACK, F., 1976. Studies of Stock Market Volatility Changes.
*Proceedings of the American Statistical Association, ….*[Cited by 162] (5.43/year)

- DUFFEE, G.R., 1995. Stock returns and volatility: A firm-level analysis,
*Journal of Financial Economics.*[Cited by 56] (5.14/year)
Abstract: "It has been previously documented that individual firms' stock return volatility rises after stock prices fall. This paper finds that this statistical relation is largely due to a positive contemporaneous relation between firm stock returns and firm stock return volatility. This positive relation is strongest for both small firms and firms with little financial leverage. At the aggregate level, the sign of this contemporaneous relation is reversed. The reasons for the difference between the aggregate- and firm-level relations are explored."
- CANNING, D.,
*et al.*, 1998. Scaling the volatility of GDP growth rates.*Economics Letters.*[Cited by 40] (5.08/year)

Abstract: "The distribution of shocks to GDP growth rates is found to be exponential rather than normal. Their standard deviation scales with GDP^{β}where*β*=−0.15±0.03. These macroeconomic results place restrictions on the microeconomic structure of interactions between agents."

- KENEN, P.B. and D. RODRIK, 1986. Measuring and Analyzing the Effects of Short-Term Volatility in Real Exchange Rates.
*The Review of Economics and Statistics.*[Cited by 96] (4.84/year)

- LEBARON, B., 1992. Some Relations Between Volatility and Serial Correlations in Stock Market Returns.
*The Journal of Business.*[Cited by 66] (4.75/year)
Abstract: "This article explores the relation between serial correlation and volatility for several different stock return series at daily and weekly frequencies. It is found that serial correlations are changing over time and are related to stock return volatility. An extension to the GARCH model is proposed and estimated, revealing parameters consistent with other findings in this article."
- CHRISTOFFERSEN, P.F., F.X. DIEBOLD and T. SCHUERMANN, 1998. Horizon Problems and Extreme Events in Financial Risk Management.
*Federal Reserve Bank of New York.*[Cited by 34] (4.32/year)

- YANG, L., W. HARDLE and J. NIELSEN, 1999. Nonparametric Autoregression with Multiplicative Volatility and Additive mean.
*Journal of Time Series Analysis.*[Cited by 29] (4.21/year)
Abstract: "For over a decade, nonparametric modelling has been successfully applied to study nonlinear structures in financial time series. It is well known that the usual nonparametric models often have less than satisfactory performance when dealing with more than one lag. When the mean has an additive structure, however, better estimation methods are available which fully exploit such a structure Although in the past such nonparametric applications had been focused more on the estimation of the conditional mean, it is equally if not more important to measure the future risk of the series along with the mean. For the volatility function, i.e., the conditional variance given the past, a multiplicative structure is more appropriate than an additive one, as the volatility is a positive scale function and a multiplicative model provides a better interpretation of each lagged value’s influence on such a function In this paper we consider the joint estimation of both the additive mean and the multiplicative volatility. The technique used is marginally integrated local polynomial estimation. The procedure is applied to the DEMUSD (Deutsche MarkUS Dollar) daily exchange returns."
- FRANSES, Philip Hans and Dick Van DIJK, 1996. Forecasting stock market volatility using (non-linear) Garch models,
*Journal of Forecasting*, Volume 15, Issue 3, April 1996, Pages: 229-235. [Cited by 37] (3.88/year)
Abstract: "In this paper we study the performance of the GARCH model and two of its non-linear modifications to forecast weekly stock market volatility. The models are the Quadratic GARCH (Engle and Ng, 1993) and the Glosten, Jagannathan and Runkle (1992) models which have been proposed to describe, for example, the often observed negative skewness in stock market indices. We find that the QGARCH model is best when the estimation sample does not contain extreme observations such as the 1987 stock market crash and that the GJR model cannot be recommended for forecasting."
- SENAY, Özge, 1998. The Effects of Goods and Financial Market Integration on Macroeconomic Volatility,
*The Manchester School*, Volume 66 Pages 39-61 - Supplement, 1998. [Cited by 28] (3.57/year)

Abstract: "The aim of this work is to determine whether increasing goods and financial market integration raises or lowers macroeconomic volatility. Shocks to money, government expenditure, and labour supply are analysed under different degrees of goods and financial market integration in a dynamic general equilibrium framework. Simulations show that the effects of the different shocks on economic volatility change significantly depending on the presence of incompletely integrated goods and/or financial markets. However, the results suggest that the effect of integration in one market is largely independent of the extent of integration in the other market." - MARTENS, Martin, Dick van DIJK and Michiel de POOTER, 2004. Modeling and Forecasting S&P500 Volatility: Long-Memory, Structural Breaks and Nonlinearity, Tinbergen Institute Discussion Paper, TI 2004-067/4. [Cited by 10] (3.46/year) Abstract: "The sum of squared intraday returns provides an unbiased and almost error-free measure of ex-post volatility. In this paper we develop a nonlinear Autoregressive Fractionally Integrated Moving Average (ARFIMA) model for realized volatility, which accommodates level shifts, day-of-the-week eects, leverage eects and volatility level eects. Applying the model to realized volatilities of the S&P 500 stock index and three exchange rates produces forecasts that clearly improve upon the ones obtained from a linear ARFIMA model and from conventional time-series models based on daily returns, treating volatility as a latent variable."
- PASQUINI, M. and M. SERVA, 1998. Multiscale behaviour of volatility autocorrelations in a financial market.
*Arxiv preprint cond-mat/9810232.*[Cited by 27] (3.43/year)

- CHEUNG, Y.W. and L.K. NG, 1992. Stock Price Dynamics and Firm Size: An Empirical Investigation,
*The Journal of Finance*[Cited by 47] (3.38/year) - TAUCHEN, G., H. ZHANG and M. LIU, 1996. Volume, Volatility, and Leverage: A Dynamic Analysis.
*Journal of Econometrics.*[Cited by 33] (3.34/year) - LEBARON, B.D., 1991. Forecast Improvements Using a Volatility Index. ideas.repec.org. [Cited by 42] (2.82/year) Abstract: "This paper explores the possibility of improved out of sample forecasting for stock returns and foreign exchange rates using observed nonlinearities in the two series. Forecasting is done using nonparametric techniques where important information is obtained from the current level of volatility in the series. For both series forecast improvements are observed, but for stock returns the improvements are only marginal. These results indicate the usefulness and stability of some types of nonlinear modelling for financial markets."
- DE, P.J.F., 1998. Nonlinearities and Nonstationarities in Stock Returns,
*Journal of Business & Economic Statistics*[Cited by 21] (2.66/year)
Abstract: "This article addresses the question of whether recent findings of nonlinearities in high-frequency financial time series have been contaminated by possible shifts in the distribution of the data. It applies a recursive version of the Brock-Dechert-Scheinkman statistic to daily data on two stock-market indexes between January 1980 and December 1990. It is shown that October 1987 is highly influential in the characterization of the stock-market dynamics and appears to correspond to a shift in the distribution of stock returns. Sampling experiments show that simple linear processes with shifts in variance can replicate the behavior of the tests, but autoregressive conditional heteroscedastic filters are unable to do so."
- LUNDIN, M., M.M. DACOROGNA and U.A. MüLLER, 1999. Correlation of High-Frequency Financial Time Series.
*Financial Markets Tick by Tick.*[Cited by 18] (2.61/year)

- RABERTO, M.,
*et al.*, 1999. Volatility in the Italian Stock Market: An Empirical Study.*Physica A*, Volume 269, Issue 1 , 1 July 1999, Pages 148-155. [Cited by 16] (2.34/year)

Abstract: "We study the volatility of the MIB30-stock-index high-frequency data from November 28, 1994 through September 15, 1995. Our aim is to empirically characterize the volatility random walk in the framework of continuous-time finance. To this end, we compute the index volatility by means of the log-return standard deviation. We choose an hourly time window in order to investigate intraday properties of volatility. A periodic component is found for the hourly time window, in agreement with previous observations. Fluctuations are studied by means of detrended fluctuation analysis, and we detect long-range correlations. Volatility values are log-stable distributed. We discuss the implications of these results for stochastic volatility modelling." - LEBARON, B., 1994. Chaos and Nonlinear Forecastability in Economics and Finance.
*Philosophical Transactions: Physical Sciences and ….*[Cited by 26] (2.20/year)

Abstract: "Both academic and applied researchers studying financial markets and other economic series have become interested in the topic of chaotic dynamics. The possibility of chaos in financial markets opens important questions for both economic theorists as well as financial market participants. This paper will clarify the empirical evidence for chaos in financial markets and macroeconomic series. It will also compare these two concepts from a financial market perspective contrasting the objectives of the practitioner with those of economic researchers. Finally, the paper will speculate on the impact of chaos and nonlinear modeling on future economic research.""It turns out that f() is a decreasing function of conditional variance indicating that local predictability in the series is higher during periods of lower volatility."

LeBaron (1994) - HANSEN, B.E., 1995. Regression with Nonstationary Volatility.
*Econometrica.*[Cited by 22] (2.02/year)
Abstract: "A new asymptotic theory of regression is introduced for possibly nonstationary time series. The regressors are assumed to be generated by a linear process with martingale difference innovations. The conditional variances of these martingale differences are specified as autoregressive stochastic volatility processes with autoregressive roots that are local to unity. The author finds conditions under which the least squares estimates are consistent and asymptotically normal. A simple adaptive estimator is proposed which achieves the same asymptotic distribution as the generalized least squares estimator without requiring parameter assumptions for the stochastic volatility process."
- DIEBOLD, F.X.,
*et al.*, 1998. Converting 1-Day Volatility to h-Day Volatility: Scaling by is Worse than You Think.*Risk.*[Cited by 15] (1.90/year)

- PASQUINI, M.U. and M.U. SERVA, 2000. Clustering of volatility as a multiscale phenomenon.
*The European Physical Journal B-Condensed Matter.*[Cited by 10] (1.70/year)

- BOUCHAUD, J.P., 2001. On a universal mechanism for long-range volatility correlations.
*Quantitative Finance.*[Cited by 8] (1.65/year)

A well documented ‘stylized fact’ of financial markets is volatility clustering [1, 2, 3, 4]. Figure 1 compares the time series of the daily returns of the Dow-Jones index since 1900 and that of a Brownian random walk. Two features are immediately obvious to the eye: the volatility does indeed 1 have rather strong intermittent fluctuations, and these fluctuations tend to persist in time. A more quantitative analysis shows that the daily volatility t (defined, for example, as the average squared high frequency returns) has a log-normal distribution [6], and that its temporal correlation function htt+ i can be fitted by an inverse power of the lag , with a rather small exponent in the range 0.1-0.3 [2, 5, 6, 7]. This suggests that there is no characteristic time scale for volatility fluctuations: outbursts of market activity can persist for rather short times (say a few days), but also for much longer times, months or even years. A very interesting observation is that these long ranged volatility correlations are observed on many different financial markets, with qualitatively similar features: stocks, currencies, commodities or interest rates. This suggests that a common mechanism is at the origin of this rather universal phenomenon.

Bouchaud, Giardina and Mézard (2000) - CONT, R., 1997. Scaling and correlation in financial data.
*Arxiv preprint cond-mat/9705075.*[Cited by 13] (1.47/year)

Abstract: "The statistical properties of the increments x(t+T) - x(t) of a financial time series depend on the time resolution T on which the increments are considered. A non-parametric approach is used to study the scale dependence of the empirical distribution of the price increments x(t+T) - x(t) of S&P Index futures, for time scales T, ranging from a few minutes to a few days using high-frequency price data. We show that while the variance increases linearly with the timescale, the kurtosis exhibits anomalous scaling properties, indicating a departure from the iid hypothesis. Study of the dependence structure of the increments shows that although the autocorrelation function decays rapidly to zero in a few minutes, the correlation of their squares exhibits a slow power law decay with exponent 0.37, indicating persistence in the scale of fluctuations. We establish a link between the scaling behavior and the dependence structure of the increments : in particular, the anomalous scaling of kurtosis may be explained by "long memory" properties of the square of the increments." - BOSWIJK, H.P., 2005. Adaptive Testing for a Unit Root with Nonstationary Volatility. [Cited by 1] (1.13/year)
- CAVALIERE, G. and A.M.R. TAYLOR, 2004. Testing for Unit Roots in Time Series Models with Non-stationary Volatility. cide.info. [Cited by 2] (1.06/year)
- DÍAZ, Andrés Fernández, Pilar GRAU-CARLES and Lorenzo Escot MANGAS, 2002. Nonlinearities in the exchange rates returns and volatility,
*Physica A: Statistical Mechanics and its Applications*, Volume 316, Issues 1-4, 15 December 2002, Pages 469-482. [Cited by 4] (1.03/year)

Abstract: "Recent findings of nonlinearities in financial assets can be the product of contamination produced by shifts in the distribution of the data. Using the BDS and Kaplan tests it is shown that, some of the nonlinearities found in foreign exchange rate returns, can be the product of shifts in variance while other do not. Also, the behavior of the volatility is studied, showing that the ARFIMA modeling is able to capture long memory, but, depending on the*proxy*used for the volatility, is not always able to capture all the nonlinearities of the data"

Conclusions: "Recent research has put forward the idea that both financial assets returns, and volatilities are nonlinear processes. This paper investigates the impact of nonstationarities on the testing of nonlinearities. For returns time series nonlinearities are found for the exchange rates DM=$ an d BP=$, but for the JY=$ a possible shift in conditional variance yields to a rejection of nonlinearity for the hole data set. The behavior of volatility is studied through the behavior of the residuals of the ARFIMA estimated model. Two diKerent behavior are found depending on the proxy of volatility used. For the residuals of the squared returns, similar behavior as the returns time series is found, that means that the ARFIMA model is not able to capture the nonlinearities of the time series under study. However for the log-squared returns the residuals of the ARFIMA model seems to be i.i.d. which means that this kind of model is able to capture, both long-memory and nonlinearities of the series under study."

Díaz, Grau-Carles and Mangas (2002) - KUWAHARA, H. and T.A. MARSH, 1992. The Pricing of Japanese Equity Warrants.
*Management Science.*[Cited by 13] (0.94/year) - ENGLE, R.F. and G.G.J. LEE, 1993. Long Run Volatility Forecasting for Individual Stocks in a One Factor Model.
*Manuscript, University of California, San Diego.*[Cited by 12] (0.93/year) - LEBARON, B., 1999. Volatility Persistence and Apparent Scaling Laws in Finance.
*Manuscript, Brandeis University.*[Cited by 6] (0.87/year) - DIEBOLD, F.X.,
*et al.*, 1998. Converting 1-Day Volatility to h-Day Volatility: Scaling by Root-h is Worse than You Think.*Wharton Financial Institutions Center, Philadelphia, PA, ….*[Cited by 6] (0.76/year)

- EBENS, H., 1999. Realized Stock Index Volatility, Working paper No. 420, Department of Economics Johns Hopkins University. [Cited by 5] (0.73/year)

- BREUNIG, R.V. and A.R. PAGAN, 2003. Do Markov-Switching Models Capture Nonlinearities in the Data? Tests using Nonparametric Methods.
*Mathematics and Computers in Simulation. Forthcoming.*[Cited by 2] (0.69/year)
Abstract: "Markov-switching models have become popular alternatives to linear autoregressive models. Many papers which estimate nonlinear models make little attempt to demonstrate whether the non-linearities they capture are of interest or if the models differ substantially from the linear option. By simulating the models and nonparametrically estimating functions of the simulated data, we can evaluate if and how the nonlinear and linear models differ."
- DIEBOLD, F.X.,
*et al.*, 1996. Converting 1-Day volatility to h-Day volatility: scaling byv h is worse that you think.*University of Pennsilvania working paper.*[Cited by 3] (0.30/year)

- DIEBOLD, F.X.A. and A.I. HICKMAN, lip;. T. Schuermann, 1998, Converting 1-Day Volatility to h-Day Volatility: Scaling by Root-h is Worse ….
*Wharton Financial Institutions Center, Working Paper 97-34. &h.*[Cited by 2] (0.25/year)

- POTERBA, J.M. and L.H. SUMMERS, 1986. The Persistence of Volatility and Stock Market Returns'.
*American Economic Review.*[Cited by 5] (0.25/year) - ANDERSEN, T.G.,
*et al.*, PIER Working Paper 01-001.*econ.upenn.edu.*[not cited] (?/year)

"We exploit direct model-free measures of daily equity return volatility and correlation obtained from high-frequency intraday transaction prices on individual stocks in the Dow Jones Industrial Average over a five-year period to confirm, solidify and extend existing characterizations of stock return volatility and correlation. We find that the unconditional distributions of the variances and covariances for all thirty stocks are leptokurtic and highly skewed to the right, while the logarithmic standard deviations and correlations all appear approximately Gaussian. Moreover, the distributions of the returns scaled by the realized standard deviations are also Gaussian. Consistent with our documentation of remarkably precise scaling laws under temporal aggregation, the realized logarithmic standard deviations and correlations all show strong temporal dependence and appear to be well described by long-memory processes. Positive returns have less impact on future variances and correlations than negative returns of the same absolute magnitude, although the economic importance of this asymmetry is minor. Finally, there is strong evidence that equity volatilities and correlations move together, possibly reducing the benefits to portfolio diversification when the market is most volatile. Our findings are broadly consistent with a latent volatility fact or structure, and they set the stage for improved high-dimensional volatility modeling and out-of-sample forecasting, which in turn hold promise for the development of better decision making in practical situations of risk management, portfolio allocation, and asset pricing."

Torben G. Andersen, Tim Bollerslev, Francis X. Diebold, Heiko Ebens (2000) - NAGARAJAN, R., 2006. Surrogate testing of volatility series from long-range correlated noise.
*Arxiv preprint physics/0603126.*[not cited] (0/year)
Abstract: "Detrended fluctuation analysis (DFA) [1] of the volatility series has been found to be useful in dentifying possible nonlinear/multifractal dynamics in the empirical sample [2-4]. Long-range volatile correlation can be an outcome of static as well as dynamical nonlinearity. In order to argue in favor of dynamical nonlinearity, surrogate testing is used in conjunction with volatility analysis [2-4]. In this brief communication, surrogate testing of volatility series from long-range correlated noise and their static, invertible nonlinear transforms is investigated. Long-range correlated monofractal noise is generated using FARIMA (0, d, 0) with Gaussian and non-Gaussian innovations. We show significant deviation in the scaling behavior between the empirical sample and the surrogate counterpart at large time-scales in the case of FARIMA (0, d, 0) with non-Gaussian innovations whereas no such discrepancy was observed in the case of Gaussian innovations. The results encourage cautious interpretation of surrogate testing in the presence of non-Gaussian innovations."
- LIU, J., 2005. An Analysis of Daily Volatility in the Japanese Foreign Exchange Market.
*Services Systems and Services Management, 2005. Proceedings ….*[not cited] (0/year)

"

*Abstract-*we assess the behavior of daily changes in the Japanese foreign exchange market within the framework of conditional volatility and the day of the week effects. Generalized Autoregressive Conditional Heteroscedasticity (GARCH) model is applied to let exchange rate variances change through time with detection of heteroscedastic errors in the model. Empirical results verify that volatility of the Japanese foreign exchange market is persistent, which is compared with other developed countries for the corresponding period. Moreover, the day of the week effects are present in US dollar and British Pound return series for the period January 1, 1999 to July 29, 2004. Seasonality of exchange rates in Japan foreign exchange markets may be exploitable and judged as evidence against informational efficiency of markets. Central bank intervention and interest rates are as potential sources of heteroscedastic errors in the foreign exchange rates."

Liu (2005) - TAYLOR, S.J., 2005. Asset price dynamics, volatility, and prediction. Princeton University Press. [not cited] (0/year)

[intraday returns]

"There are short bursts of high volatility in intraday prices that follow major macroeconomic announcements."

Taylor (2005)[intraday returns]

XI, G., 1993. "An Exploratory Study of Stock Price Behavior and Volatility Estimation Using High Frequency Data," unpublished thesis, Massachusetts Institute of Technology, Sloan School of Management.

"The average level of volatility depends on the time of day, with a significant intraday variation."

Taylor (2005)

"In this study, we find that the probability density function of the volatility for the S&P 500 index seems to be well fit by a log normal distribution in the center part. However, the tail of the distribution is better described by a power law, with exponent 1 + μ ≈ 4, well outside the stable Lévy range. The power law distribution at the tail is confirmed by the study of the volatility distribution of individual companies, for which we find approximately the same exponent. We also find that the distribution of the volatility scales for a range of time intervals."

Liu, et al. (1999)

Concluding Remarks: "In this paper we propose a nonlinear long-memory time series model for realized volatility that incorporates all well-known stylized facts from the (GARCH) volatility literature, in particular level shifts, day-of-the-week eects, leverage eects and volatility level eects. The model, as well as several restricted versions, are estimated for the S&P 500 index and three exchange rates.

The in-sample results show that all nonlinearities are highly signicant and improve the description of the data. The out-of-sample results show that for shorter horizons, up to 10 days, accounting for these nonlinearities signicantly improves the forecast performance compared to a linear ARFI model. Such short-term volatility forecasts are especially useful for short-term risk management, including Value-at- Risk. For longer horizons no benet is obtained from incorporating nonlinearities.

The most important nonlinearities are the leverage eect for the S&P 500 index, and the leverage eect as well as the day-of-the-week eects for the exchange rates. The best way to incorporate the eects of lagged daily returns is to include them as exogenous regressors, i.e. outside the long memory lter. Not important for the forecast performance is allowing the persistence of shocks to depend on the level of volatility, and modeling the level shifts for the S&P 500 index."