A Fast Numerical Method for American Call Options under Jump-Diffusion Processes: An Artificial Boundary Approach
کد مقاله : 1167-FEMATH
1سیدمحمدمهدی کاظمی *، 2علی فروش باستانی، 3مهدی دهقان
1دانشجو/دانشگاه صنعتی امیرکبیر تهران
2عضو هیات علمی
3عضو هیات علمی/دانشگاه صنعتی امیرکبیر تهران
چکیده مقاله:
In this paper, we propose a new method to approximate the price of an American call option written on a dividend-paying risky underlying following a jump-diffusion process. We extend the methodology proposed in [H. Han and X. Wu, A fast numerical method for the Black-Scholes equation of American options, SIAM J. Numer. Anal. 41 (6) (2003) 2081-2095] to the case of parabolic partial integro-differential equations (PIDEs). The integral term in the PIDE arising from this model can also be considered as a driving term, then the integro-differential equation can be viewed as a parabolic PDE. Using this approach, we introduce an exact non-local boundary condition on a suitably defined artificial (transparent) boundary introduced to reduce the infinite physical'' domain into a finite computational'' one. We then develop a Crank-Nicolson scheme to solve the PIDE along with the artificialnboundary condition. Our results show that the proposed approach is efficient and gives a betternaccuracy than other alternatives from the literature.
کلیدواژه ها:
American call option; Free boundary value problem; Artificial boundary conditions; Jump-diffusion processes
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