Efficient, Almost Exact Simulation of the Heston Stochastic Volatility Model

International Journal of Theoretical and Applied Finance (IJTAF), 2010

Posted: 7 Jun 2010

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: February 1, 2010

Abstract

We deal with discretization schemes for the simulation of the Heston stochastic volatility model. These simulation methods yield a popular and flexible pricing alternative for pricing and managing a book of exotic derivatives which cannot be valued using closed-form expressions. For the Heston dynamics an exact simulation method was developed by Broadie and Kaya (2006), however we argue why its practical use is limited. Instead we focus on efficient approximations of the exact scheme, aimed to resolve the disadvantages of this method; one of the main bottlenecks in the exact scheme is the simulation of the Non-central Chi-squared distributed variance process, for which we suggest an efficient caching technique. At first sight the creation of a cache containing the inverses of this distribution might seem straightforward, however as the parameter space of the inverse Non-central Chi-squared distribution is three-dimensional, the design of such a direct cache is rather complicated, as pointed out by Broadie and Andersen. Nonetheless, for the case of the Heston model we are able to tackle this dimensionality problem and show that the three-dimensional inverse of the non-central chi-squared distribution can effectively be reduced to a one dimensional cache. The performed analysis hence leads to the development of three new efficient simulation methods (the NCI, NCI-QE and BK-DI scheme). Finally, we conclude with a comprehensive numerical study of these new schemes and the exact scheme of Broadie and Kaya, the almost exact scheme of Smith, the Kahl-J├Ąckel scheme, the FT scheme of Lord et al. and the QE-M scheme of Andersen. From these results, we find that the QE-M scheme is the most efficient, followed closely by the NCI-M, NCI-QE-M and BK-DI-M schemes, whilst we observe that all other considered schemes perform a factor 6 to 70 times less efficient than the latter four methods.

Keywords: Stochastic volatility, simulation, Heston, non-central chi-squared inversion, control variate

Suggested Citation

van Haastrecht, Alexander and Pelsser, Antoon A. J., Efficient, Almost Exact Simulation of the Heston Stochastic Volatility Model (February 1, 2010). International Journal of Theoretical and Applied Finance (IJTAF), 2010 . Available at SSRN: https://ssrn.com/abstract=1621544

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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