Accessible Unlicensed Requires Authentication Published by De Gruyter September 1, 2015

Simulating from the Heston model: A gamma approximation scheme

Jean-François Bégin, Mylène Bédard and Patrice Gaillardetz

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.

MSC: 62P05

Funding source: National Science and Engineering Research Council of Canada (NSERC)

Received: 2014-6-3
Accepted: 2015-8-20
Published Online: 2015-9-1
Published in Print: 2015-9-1

© 2015 by De Gruyter