Option pricing in practice - Heston's stochastic volatility model

Options are an important building block of modern financial markets. The theory underlying their valuation is one of the showpieces of modern financial mathematics. It includes the Nobel Prize-winning Black-Scholes formula, the most famous result of financial mathematics. However, the log-normal stock price model on which the Black-Scholes formula is based provides only a very rough description of the behavior of real stock price movements. Thus, modern theory includes many proposals for improving the modeling of stock price dynamics. Heston's stochastic volatility model is a compromise that exhibits theoretically desirable properties on the one hand and numerical tractability on the other. For this reason, it is widely accepted by practitioners. In this chapter, we present and discuss the properties of the Heston model and describe its industrial implementation.