Finance > Stylized Facts


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


The autocorrelation function of the volatility exhibits long-range dependence and is well described by a power-law decay (Bollerslev and Mikkelsen (1996), Liu, et al. (1999), Andersen, et al. (2001a) and Andersen, et al. (2001b)).


Studies show that the distribution of volatility is log-normal (Cizeau, et al. (1997), Andersen, et al. (2001a) and Andersen, et al. (2001b)), although Liu, et al. (1999) found that the tail of the distribution is better described by a power law.


Volatility clustering is ubiquitous in speculative returns and such nonstationarity has been known since Houthakker (1961).


Franses and van Dijk (1996) find that a nonlinear model improves the forecasting of weekly stock market volatilities. Similarly, Díaz, Grau-Carles and Mangas (2002) and Maheu and McCurdy (2002) found evidence of nonlinearity in FX volatility. Whilst Martens, van Dijk and de Pooter (2003) detailed nonlinearities in S&P 500 volatility.


The distribution of the volatility scales for a range of time intervals (Liu, et al. (1999), Andersen, et al. (2001a), Andersen, et al. (2001b) and Gencay, Selcuk and Whitcher (2001)).