The Volatility Surface
Fat tails and the high central peak are characteristics of mixtures of distributions with different variances. This motivates us to model variance as a random variable. The volatility clustering feature implies that volatility(or variance) is auto-corelated. In the model, this is a consequence of the mean reversion of volatility. * Note that simple jump-diffusion models do not have this property. After a jump, the stock price volatility does not change.