A Componentwise Splitting Method for Pricing American Options Under the Bates Model

  • Jari ToivanenEmail author
Part of the Computational Methods in Applied Sciences book series (COMPUTMETHODS, volume 15)


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.


Option Price Reference Price Linear Complementarity Problem Stochastic Volatility American Option 
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© Springer Science+Business Media B.V. 2010

Authors and Affiliations

  1. 1.Institute for Computational and Mathematical EngineeringStanford UniversityStanfordUSA

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