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Operator splitting methods for pricing American options with stochastic volatility (2004)
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BibTeX
@TECHREPORT{Ikonen04operatorsplitting,
author = {Samuli Ikonen and Jari Toivanen},
title = {Operator splitting methods for pricing American options with stochastic volatility},
institution = {},
year = {2004}
}
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Abstract
Summary. Pricing American options using partial (integro-)differential equation based methods leads to linear complementarity problems (LCPs). The numerical solution of these problems resulting from the Black-Scholes model, Kou’s jumpdiffusion model, and Heston’s stochastic volatility model are considered. The finite difference discretization is described. The solutions of the discrete LCPs are approximated using an operator splitting method which separates the linear problem and the early exercise constraint to separate fractional steps. The numerical experiments demonstrate that the price of options can be computed in a few milliseconds on a PC. 1
Keyphrases
american option stochastic volatility linear problem numerical solution differential equation numerical experiment fractional step operator splitting method stochastic volatility model jumpdiffusion model finite difference discretization black-scholes model early exercise constraint discrete lcps complementarity problem
