Efficient, Almost Exact Simulation of the Heston Stochastic Volatility Model

35 Pages Posted: 9 May 2008 Last revised: 9 May 2011

See all articles by Alexander van Haastrecht

Alexander van Haastrecht

Delta Lloyd; Vrije Universiteit Amsterdam, School of Business and Economics

Antoon Pelsser

Maastricht University; Netspar

Multiple version iconThere are 2 versions of this paper

Date Written: November 17, 2008

Abstract

We deal with several efficient discretization methods for the simulation of the Heston stochastic volatility model. The resulting schemes can be used to calculate all kind of options and corresponding sensitivities, in particular the exotic options that cannot be valued with closed-form solutions. We focus on to the (computational) efficiency of the simulation schemes: though the Broadie and Kaya (2006) paper provided an exact simulation method for the Heston dynamics, we argue why its practical use might be limited. Instead we consider efficient approximations of the exact scheme, which try to exploit certain distributional features of the underlying variance process. The resulting methods are fast, highly accurate and easy to implement. We conclude by numerically comparing our new schemes to the exact scheme of Broadie and Kaya, the almost exact scheme of Smith, the Kahl-Jackel scheme, the Full Truncation scheme of Lord et al. and the Quadratic Exponential scheme of Andersen.

Keywords: Stochastic volatility, Simulation, Heston, Non-central chi-squared inversion

JEL Classification: C10

Suggested Citation

van Haastrecht, Alexander and Pelsser, Antoon A. J., Efficient, Almost Exact Simulation of the Heston Stochastic Volatility Model (November 17, 2008). International Journal of Theoretical and Applied Finance, Vol. 31, No. 1, 2010. Available at SSRN: https://ssrn.com/abstract=1131137

Alexander Van Haastrecht (Contact Author)

Delta Lloyd ( email )

Spaklerweg 4
Amsterdam, Noord-Holland 1096BA
Netherlands

Vrije Universiteit Amsterdam, School of Business and Economics ( email )

De Boelelaan 1105
Amsterdam, 1081HV
Netherlands

Antoon A. J. Pelsser

Maastricht University ( email )

P.O. Box 616
Maastricht, 6200 MD
Netherlands

HOME PAGE: http://https://sites.google.com/site/apelsseraca/

Netspar ( email )

P.O. Box 90153
Tilburg, 5000 LE
Netherlands

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