Year: 2014
Author: Haiming Song, Ran Zhang, Wenyi Tian
Journal of Mathematical Study, Vol. 47 (2014), Iss. 1 : pp. 47–64
Abstract
In this paper, we devote ourselves to the research of numerical methods for American option pricing problems under the Black-Scholes model. The optimal exercise boundary which satisfies a nonlinear Volterra integral equation is resolved by a high-order collocation method based on graded meshes. For the other spatial domain boundary, an artificial boundary condition is applied to the pricing problem for the effective truncation of the semi-infinite domain. Then, the front-fixing and stretching transformations are employed to change the truncated problem in an irregular domain into a one-dimensional parabolic problem in [−1,1]. The Chebyshev spectral method coupled with fourth-order Runge-Kutta method is proposed for the resulting parabolic problem related to the options. The stability of the semi-discrete numerical method is established for the parabolic problem transformed from the original model. Numerical experiments are conducted to verify the performance of the proposed methods and compare them with some existing methods.
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Journal Article Details
Publisher Name: Global Science Press
Language: English
DOI: https://doi.org/10.4208/jms.v47n1.14.03
Journal of Mathematical Study, Vol. 47 (2014), Iss. 1 : pp. 47–64
Published online: 2014-01
AMS Subject Headings:
Copyright: COPYRIGHT: © Global Science Press
Pages: 18
Keywords: American option pricing Black-Scholes model optimal exercise boundary front-fixing Chebyshev spectral method Runge-Kutta method.