Year: 2017
East Asian Journal on Applied Mathematics, Vol. 7 (2017), Iss. 2 : pp. 227–247
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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Journal Article Details
Publisher Name: Global Science Press
Language: English
DOI: https://doi.org/10.4208/eajam.260316.061016a
East Asian Journal on Applied Mathematics, Vol. 7 (2017), Iss. 2 : pp. 227–247
Published online: 2017-01
AMS Subject Headings:
Copyright: COPYRIGHT: © Global Science Press
Pages: 21
Keywords: Finite volume method option pricing jump-diffusion models linear complementarity problems GMRES method modulus-based successive overrelaxation method.
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