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Finite Volume Method for Pricing European and American Options under Jump-Diffusion Models

  • Xiao-Ting Gan (a1) (a2), Jun-Feng Yin (a1) and Yun-Xiang Guo (a1)
Abstract
Abstract

A class of finite volume methods is developed for pricing either European or American options under jump-diffusion models based on a linear finite element space. An easy to implement linear interpolation technique is derived to evaluate the integral term involved, and numerical analyses show that the full discrete system matrices are M-matrices. For European option pricing, the resulting dense linear systems are solved by the generalised minimal residual (GMRES) method; while for American options the resulting linear complementarity problems (LCP) are solved using the modulus-based successive overrelaxation (MSOR) method, where the H +-matrix property of the system matrix guarantees convergence. Numerical results are presented to demonstrate the accuracy, efficiency and robustness of these methods.

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*Corresponding author. Email addresses: 9xtgan@tongji.edu.cn (X.-T. Gan), yinjf@tongji.edu.cn (J.-F. Yin), 103646@tongji.edu.cn (Y.-X. Guo)
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East Asian Journal on Applied Mathematics
  • ISSN: 2079-7362
  • EISSN: 2079-7370
  • URL: /core/journals/east-asian-journal-on-applied-mathematics
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