Simulating from the Heston model: A gamma approximation scheme

Bégin Jean-François (), Bédard Mylène () and Gaillardetz Patrice ()
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Bégin Jean-François: Department of Decision Sciences, HEC Montréal, 3000 Côte Sainte Catherine Road, Montréal, Québec, Canada
Bédard Mylène: Department of Mathematics and Statistics, Université de Montréal, 2900 Édouard-Montpetit Blvd., Montréal, Québec, Canada
Gaillardetz Patrice: Department of Mathematics and Statistics, Concordia University, 1455 de Maisonneuve Blvd. West, Montréal, Québec, Canada

Monte Carlo Methods and Applications, 2015, vol. 21, issue 3, 205-231

Abstract: The Heston model is appealing as it possesses a stochastic volatility term as well as semi-closed formulas for pricing European options. Unfortunately, few simulation schemes for this model can handle the violation of the Feller Condition. An algorithm based on the exact scheme of Broadie and Kaya to simulate price paths under the Heston model is introduced. In order to increase the speed of their exact method, we use a gamma approximation. According to Stewart, Strijbosch, Moors and Batenburg, it is possible to approximate a complex gamma convolution (similar to the representation given by Glasserman and Kim) by a simple moment-matched gamma distribution. We also perform a review of popular simulation schemes for the Heston model and validate our approach through a simulation study. The gamma approximation scheme appears to yield small biases on European and Asian option prices when compared to the most popular schemes.

Keywords: Stochastic volatility; Heston model; Simulation schemes; Gamma expansion; Asian options (search for similar items in EconPapers)
Date: 2015
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DOI: 10.1515/mcma-2015-0105

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