In this chapter we investigate the asset price models in which volatility is assumed to be stochastic. In the Black–Scholes–Merton model the log return of the asset is assumed to be normally distributed, which is an idealistic simplification of the real financial market behavior. Analysis of market data shows that the log return of the asset is not normally distributed but has heavy tails and high peaks. The theoretical consequence of the log normality in the Black–Scholes–Merton model is due to the assumption that the volatility is constant. To better describe the behavior of risky assets in the real financial market we assume that volatility of asset price is not constant but stochastic. A stochastic volatility modelStochastic volatilityVolatilitystochastic consists of two stochastic differential equations: one for the asset price \(S_t\) and another for the volatility.