An Efficient Numerical Method for the Valuation of American Better-of Options Based on the Front-Fixing Transform and the Far Field Truncation
Year: 2020
Author: Xiaowei Pang, Haiming Song, Xiaoshen Wang, Kai Zhang
Advances in Applied Mathematics and Mechanics, Vol. 12 (2020), Iss. 4 : pp. 902–919
Abstract
In this paper, an efficient numerical method is proposed for the valuation of American better-of options based on the Black-Scholes model. Because of the existence of the optimal exercise boundary, the American better-of option satisfies a two dimensional parabolic linear complementarity problem on an unbounded domain. We first transform it into a one dimensional free boundary problem by a standard change of variables. And then the front-fixing transformation and the far field truncation are used to deal with the free boundary and the unbounded domain in succession, which yields a parabolic problem with unknown coefficient (free boundary) on a bounded regular domain. Furthermore, a finite element method is applied to discretize the resulting continuous system. The stability of the semi-discrete solution is also established. Meanwhile, Newton's method is used to solve the discretized system to obtain the free boundary and the option value simultaneously. The nonnegativity of the iteration solutions is also proved. Finally, numerical simulations are carried out to test the performance of the proposed method.
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Journal Article Details
Publisher Name: Global Science Press
Language: English
DOI: https://doi.org/10.4208/aamm.OA-2019-0107
Advances in Applied Mathematics and Mechanics, Vol. 12 (2020), Iss. 4 : pp. 902–919
Published online: 2020-01
AMS Subject Headings: Global Science Press
Copyright: COPYRIGHT: © Global Science Press
Pages: 18
Keywords: American better-of option far field truncation front-fixing transformation finite element method.