In this chapter we introduce Heston’s stochastic volatility model for asset price movement. Heston (1993) proposed an option pricing method under the assumption that volatility is stochastic. It is more realistic than the Black–Scholes–Merton model, and is most widely used. There are two sources of randomness in the Heston stochastic volatility model: two Brownian motions for the asset price and volatility. The Heston model is not complete, i.e., we cannot replicate every contingent claim since there is only one traded asset except the risk-free asset. For more information on a complete market consult (Bjork, 2009).