Financial models with long-tailed distributions and volatility clustering
Financial models with long-tailed distributions and volatility clustering have been introduced to overcome problems with the realism of classical financial models. These classical models of financial time series typically assume homoskedasticity and normality cannot explain stylized phenomena such as skewness, heavy tails, and volatility clustering of the empirical asset returns in finance. In 1963, Benoit Mandelbrot first used the stable distribution to model the empirical distributions which have the skewness and heavy-tail property. Since -stable distributions have infinite -th moments for all , the tempered stable processes have been proposed for overcoming this limitation of the stable distribution.