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2011

Gamma expansion of the Heston stochastic volatility model

7 years 12 months ago
Gamma expansion of the Heston stochastic volatility model
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 model · Monte Carlo methods Mathematics Subject Classification (2000) 60H35 · 65C05 · 91B70 JEL Classification C63 · G12 · G13
Paul Glasserman, Kyoung-Kuk Kim
Added 28 Aug 2011
Updated 28 Aug 2011
Type Journal
Year 2011
Where FS
Authors Paul Glasserman, Kyoung-Kuk Kim
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