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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)

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.

Corresponding author
*Corresponding author. Email addresses: (X.-T. Gan), (J.-F. Yin), (Y.-X. Guo)
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[2] L. Andersen and J. Andreasen , Jump-diffusion processes: Volatility smile fitting and numerical methods for option pricing, Rev. Deriv. Res. 4, 231262 (2000).

[3] A. Borici and H.J. Luthi , Fast solution of complementarity formulations in American put option pricing, J. Comp. Fin. 9, 6381 (2005).

[5] F. Black and M. Scholes , The pricing of options and corporate liabilities, J. Polit. Econ. 81, 637654 (1973).

[6] C. W. Cryer , The solution of a quadratic programming using systematic overrelaxation, SIAM J. Control 9, 385392 (1971).

[7] P.A. Forsyth and K.R. Vetzal , Quadratic convergence for valuing American options using a penalty method, SIAM J. Sci. Comput. 23, 20952122 (2002).

[10] Y. d’Halluin , P.A. Forsyth and G.A Labahn , A penalty method for American options with jump diffusion processes, Numer. Math. 97, 321352 (2004).

[11] Y. d’Halluin , P.A. Forsyth and K.R. Vetzal , Robust numerical methods for contingent claims under jump diffusion processes, IMA J. Numer. Anal. 25, 87112 (2005).

[12] S. Salmi and J. Toivanen , An iterative method for pricing American options under jump-diffusion model, Appl. Numer. Math. 61, 821831 (2011).

[14] J. Toivanen , A high-order front-tracking finite difference method for pricing American options under jump-diffusion models, J. Comp. Fin. 13, 6179 (2010).

[15] X.L. Zhang , Numerical analysis of American option pricing in a jump diffusion model, Math. Oper. Res. 22, 668690 (1997).

[18] N. Zheng and J.F. Yin , Modulus-based successive overrelaxation method for pricing American options, J. Appl. Math. Informatics 31, 769784 (2013).

[19] K. Zhang , X.Q. Yang and K.L. Teo , Augmented Lagrangian method applied to American option pricing, Automatica 42, 14071416 (2006).

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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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