Gamma Expansion of the Heston Stochastic Volatility Model

31 Pages Posted: 7 Oct 2008

See all articles by Paul Glasserman

Paul Glasserman

Columbia Business School

Kyoung-Kuk Kim

Korea Advanced Institute of Science and Technology

Date Written: August 2008

Abstract

We derive an explicit representation of the transitions of the Heston stochastic volatility model and use it for fast and accurate simulation of the model. Of particular interest is the integral of the variance process over an interval, conditional on the level of the variance at the endpoints. We give an explicit representation of this quantity in terms of infinite sums and mixtures of gamma random variables. The increments of the variance process are themselves mixtures of gamma random variables. The representation of the integrated conditional variance applies the Pitman-Yor decomposition of Bessel bridges. We combine this representation with the Broadie-Kaya exact simulation method and use it to circumvent the most time-consuming step in that method.

Keywords: stochastic volatility, Bessel bridge, Monte Carlo simulation

Suggested Citation

Glasserman, Paul and Kim, Kyoung-Kuk, Gamma Expansion of the Heston Stochastic Volatility Model (August 2008). Available at SSRN: https://ssrn.com/abstract=1279850 or http://dx.doi.org/10.2139/ssrn.1279850

Paul Glasserman

Columbia Business School ( email )

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New York, NY 10027
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Kyoung-Kuk Kim (Contact Author)

Korea Advanced Institute of Science and Technology ( email )

Dept of Industrial and Systems Engineering
KAIST
Daejeon, 305-701
Korea, Republic of (South Korea)

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