A front-fixing finite element method for pricing American options under regime-switching jump-diffusion models
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A front-fixing finite element method is applied to solve the partial integro-differential equations (PIDEs) arising in pricing American options under Markov-modulated jump-diffusion models with the free boundaries feature. For this purpose, we used a front-fixing method to transform the pricing problem into a nonlinear parabolic integro-differential equation on a fixed domain. Then the variational form of the resulting problem is solved by a finite element method. Under some appropriate assumptions, we establish the stability of the method and illustrate some numerical results to examine the rate of convergence of the proposed method for the pricing problem and compare its accuracy to some recent works on pricing American options under regime-switching jump-diffusion models.
KeywordsAmerican option Jump-diffusion model Regime-switching model Front-fixing method Finite element method Free boundary problem
Mathematics Subject Classification65M06 65M32 91G60
This research was supported by Shahid Beheshti University and Scientific Computations Research Group. The authors would like to thank Professor Hongtao Yang, Faculty of Mathematical Sciences, University of Nevada, for his valuable help that was greatly useful in writing this manuscript.
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