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

Part of: Partial differential equations, initial value and time-dependent initial-boundary value problems Partial differential equations, boundary value problems

Published online by Cambridge University Press:  02 May 2017

Xiao-Ting Gan ,
Jun-Feng Yin  and
Yun-Xiang Guo
Xiao-Ting Gan*
Affiliation:
School of Mathematical Science, Tongji University, Shanghai 200092, PR China School of Mathematics and Statistics, Chuxiong Normal University, Chuxiong 675000, Yunnan Province, PR China
Jun-Feng Yin*
Affiliation:
School of Mathematical Science, Tongji University, Shanghai 200092, PR China
Yun-Xiang Guo*
Affiliation:
School of Mathematical Science, Tongji University, Shanghai 200092, PR China
*
*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)
*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)
*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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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.

Keywords

Finite volume methodoption pricingjump-diffusion modelslinear complementarity problemsGMRES methodmodulus-based successive overrelaxation method

MSC classification

Secondary: 65M08: Finite volume methods 65M12: Stability and convergence of numerical methods 65M60: Finite elements, Rayleigh-Ritz and Galerkin methods, finite methods 65N40: Method of lines
Type
Research Article
Information
East Asian Journal on Applied Mathematics , Volume 7 , Issue 2 , May 2017 , pp. 227 - 247
Copyright
Copyright © Global-Science Press 2017 

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