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

Center for Mathematics and Computer Science (CWI)

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

Center for Mathematics and Computer Science (CWI) ( email )

P.O. Box 94079
Amsterdam, NL-1090 GB
Netherlands

Register to save articles to
your library

Register

Paper statistics

Downloads
957
rank
22,589
Abstract Views
4,111
PlumX Metrics
!

Under construction: SSRN citations will be offline until July when we will launch a brand new and improved citations service, check here for more details.

For more information