The Heston Stochastic-Local Volatility Model: Efficient Monte Carlo Simulation

25 Pages Posted: 13 Jun 2013 Last revised: 20 May 2018

See all articles by Anthonie van der Stoep

Anthonie van der Stoep

Rabobank

Lech A. Grzelak

Delft University of Technology

Cornelis W. Oosterlee

Utrecht University - Faculty of Science

Date Written: November 19, 2013

Abstract

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.

Keywords: Heston Stochastic-Local Volatility, HSLV, Stochastic Volatility, Local Volatility, Heston, Hybrid Models, Calibration, Monte Carlo

JEL Classification: C63, G12, G13

Suggested Citation

van der Stoep, Anthonie and Grzelak, Lech Aleksander and Oosterlee, Cornelis W., The Heston Stochastic-Local Volatility Model: Efficient Monte Carlo Simulation (November 19, 2013). International Journal of Theoretical and Applied Finance, Vol. 17, No. 7 (2014)., Available at SSRN: https://ssrn.com/abstract=2278122 or http://dx.doi.org/10.2139/ssrn.2278122

Lech Aleksander Grzelak

Delft University of Technology ( email )

Netherlands
00310655731315 (Phone)

Cornelis W. Oosterlee

Utrecht University - Faculty of Science

Vredenburg 138
Utrecht, 3511 BG
Netherlands

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