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Componentwise splitting methods for pricing American options under stochastic volatility (2007)
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| Venue: | Int. J. Theor. Appl. Finance |
| Citations: | 12 - 1 self |
BibTeX
@ARTICLE{Toivanen07componentwisesplitting,
author = {Jari Toivanen},
title = {Componentwise splitting methods for pricing American options under stochastic volatility},
journal = {Int. J. Theor. Appl. Finance},
year = {2007},
pages = {331--361}
}
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Abstract
Abstract A linear complementarity problem (LCP) is formulated for the price of American options under the Bates model which combines the Heston stochastic volatility model and the Merton jump-diffusion model. A finite difference discretization is described for the partial derivatives and a simple quadrature is used for the integral term due to jumps. A componentwise splitting method is generalized for the Bates model. It is leads to solution of sequence of one-dimensional LCPs which can be solved very efficiently using the Brennan and Schwartz algorithm. The numerical experiments demonstrate the componentwise splitting method to be essentially as accurate as the PSOR method, but order of magnitude faster. Furthermore, pricing under the Bates model is less than twice more expensive computationally than under the Heston model in the experiments. 1
Keyphrases
componentwise splitting method american option bates model stochastic volatility psor method simple quadrature partial derivative heston stochastic volatility model integral term schwartz algorithm one-dimensional lcps merton jump-diffusion model finite difference discretization linear complementarity problem numerical experiment heston model
