In this article we propose an efficient Monte Carlo scheme for simulating the stochastic volatility model of Heston (1993) enhanced by a non-parametric local volatility component. This hybrid model combines the main advantages of the Heston model and the local volatility model introduced by Dupire (1994) and Derman & Kani (1998). In particular, the additional local volatility component acts as a "compensator" that bridges the mismatch between the non-perfectly calibrated Heston model and the market quotes for European-type options. By means of numerical experiments we show that our scheme enables a consistent and fast pricing of products that are sensitive to the forward volatility skew. Detailed error analysis is also provided.
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World Scientific
International Journal of Theoretical and Applied Finance
Accurate pricing and calibration of models with stochastic volatility
Scientific Computing

van der Stoep, A., Grzelak, L. A., & Oosterlee, K. (2014). The Heston Stochastic-Local Volatility Model: Efficient Monte Carlo Simulation. International Journal of Theoretical and Applied Finance, 17(7), 1450045:1–1450045:30. doi:10.1142/S0219024914500459