Gamma Expansion of the Heston Stochastic Volatility Model
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Date: 02-02-2009
Start Time:
6:00pm
End Time: 7:30pm
Speaker: Paul Glasserman, Business School: Columbia University
Location: 412 Schapiro CEPSR, Davis Auditorium
ABSTRACT
The Heston stochastic volatility model is among the most important models in both the theory and practice of financial engineering. After some background on the model and on the problem of simulating diffusions, we present an explicit representation of the transitions of the Heston stochastic volatility model and use it for fast and accurate simulation.
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.
This is joint work with Kyoung-Kuk Kim of Barclays Capital.