Gamma expansion of the Heston stochastic volatility model

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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.
Publisher
SPRINGER HEIDELBERG
Issue Date
2011-06
Language
English
Article Type
Article
Keywords

BESSEL DISTRIBUTION; AMERICAN OPTIONS; MONTE-CARLO; SIMULATION; SCHEMES; TERM

Citation

FINANCE AND STOCHASTICS, v.15, no.2, pp.267 - 296

ISSN
0949-2984
URI
http://hdl.handle.net/10203/97951
Appears in Collection
IE-Journal Papers(저널논문)
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