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

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Applied and Numerical Partial Differential Equations

Part of the book series: Computational Methods in Applied Sciences ((COMPUTMETHODS,volume 15))

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.

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Authors and Affiliations

  1. Institute for Computational and Mathematical Engineering, Stanford University, Stanford, CA, 94305, USA

    Jari Toivanen

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  1. Jari Toivanen
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Correspondence to Jari Toivanen .

Editor information

Editors and Affiliations

  1. Dept. Mathematics, University of Houston, Calhoun Road 4800, Houston, 77204-3008, U.S.A.

    W. Fitzgibbon

  2. Dept. Mathematics, University of Houston, Calhoun Road 4800, Houston, 77204-3008, U.S.A.

    Y.A. Kuznetsov

  3. Dept. Mathematical Information , University of Jyväsklyklä, Jyväskylä, 40351, Finland

    Pekka Neittaanmäki

  4. Numèrics en Enginyeria (CIMNE), Centre Internacional de Mètodes, C/ Gran Capitan s/n, Barcelona, 08034, Spain

    Jacques Périaux

  5. Dept. Mathematique, Université de Paris VI, place Jussieu 4 , Paris CX 05, 75252, France

    Olivier Pironneau

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Toivanen, J. (2010). A Componentwise Splitting Method for Pricing American Options Under the Bates Model. In: Fitzgibbon, W., Kuznetsov, Y., Neittaanmäki, P., Périaux, J., Pironneau, O. (eds) Applied and Numerical Partial Differential Equations. Computational Methods in Applied Sciences, vol 15. Springer, Dordrecht. https://doi.org/10.1007/978-90-481-3239-3_16

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  • DOI: https://doi.org/10.1007/978-90-481-3239-3_16

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  • Publisher Name: Springer, Dordrecht

  • Print ISBN: 978-90-481-3238-6

  • Online ISBN: 978-90-481-3239-3

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