Calibration of the Heston Stochastic Local Volatility Model: A Finite Volume Scheme1

The two most popular equity derivatives pricing models among practitioners are the local volatility model and the Heston model. While the former has the appealing property that it can be calibrated exactly to any given set of arbitrage free European vanilla option prices, the latter delivers a more realistic smile dynamics. In this article we combine both modeling approaches to the Heston stochastic local volatility model. The theoretical framework for this modeling approach was already developed in Ren, Madan, and Qian (2007). We focus on the numerical model calibration which requires special care in the treatment of mixed derivatives and in cases where the Feller condition is not met in the Heston model which leads to a singular transition density at zero volatility. We propose a finite volume scheme to calibrate the model after a suitable transformation of the model equation and demonstrate its accuracy in numerical test cases using real market data. JEL Classification: G13