Volume 7, Issue 2
Finite Volume Method for Pricing European and American Options under Jump-Diffusion Models

East Asian J. Appl. Math., 7 (2017), pp. 227-247.

Published online: 2018-02

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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 method, option pricing, jump-diffusion models, linear complementarity problems, GMRES method, modulus-based successive overrelaxation method.

65M08, 65M12, 65M60, 65N40

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@Article{EAJAM-7-227, author = {}, title = {Finite Volume Method for Pricing European and American Options under Jump-Diffusion Models}, journal = {East Asian Journal on Applied Mathematics}, year = {2018}, volume = {7}, number = {2}, pages = {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.

}, issn = {2079-7370}, doi = {https://doi.org/10.4208/eajam.260316.061016a}, url = {http://global-sci.org/intro/article_detail/eajam/10747.html} }
TY - JOUR T1 - Finite Volume Method for Pricing European and American Options under Jump-Diffusion Models JO - East Asian Journal on Applied Mathematics VL - 2 SP - 227 EP - 247 PY - 2018 DA - 2018/02 SN - 7 DO - http://doi.org/10.4208/eajam.260316.061016a UR - https://global-sci.org/intro/article_detail/eajam/10747.html KW - Finite volume method, option pricing, jump-diffusion models, linear complementarity problems, GMRES method, modulus-based successive overrelaxation method. AB -

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.

Xiao-Ting Gan, Jun-Feng Yin & Yun-Xiang Guo. (2020). Finite Volume Method for Pricing European and American Options under Jump-Diffusion Models. East Asian Journal on Applied Mathematics. 7 (2). 227-247. doi:10.4208/eajam.260316.061016a
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