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Frontiers of Mathematics in China

ISSN 1673-3452

ISSN 1673-3576(Online)

CN 11-5739/O1

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Front. Math. China    2014, Vol. 9 Issue (2) : 455-476    https://doi.org/10.1007/s11464-014-0358-6
RESEARCH ARTICLE
Weak Galerkin finite element method for valuation of American options
Ran ZHANG1,*(),Haiming SONG1,Nana LUAN2
1. School of Mathematics, Jilin University, Changchun 130012, China
2. School of Insurance and Economics, University of International Business and Economics, Beijing 100190, China
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Abstract

We introduce a weak Galerkin finite element method for the valuation of American options governed by the Black-Scholes equation. In order to implement, we need to solve the optimal exercise boundary and then introduce an artificial boundary to make the computational domain bounded. For the optimal exercise boundary, which satisfies a nonlinear Volterra integral equation, it is resolved by a higher-order collocation method based on graded meshes. With the computed optimal exercise boundary, the front-fixing technique is employed to transform the free boundary problem to a one-dimensional parabolic problem in a half infinite area. For the other spatial domain boundary, a perfectly matched layer is used to truncate the unbounded domain and carry out the computation. Finally, the resulting initial-boundary value problems are solved by weak Galerkin finite element method, and numerical examples are provided to illustrate the efficiency of the method.
Keywords American option      optimal exercise boundary      weak Galerkin finite element method     
Corresponding Author(s): Ran ZHANG   
Issue Date: 16 May 2014
 Cite this article:   
Ran ZHANG,Haiming SONG,Nana LUAN. Weak Galerkin finite element method for valuation of American options[J]. Front. Math. China, 2014, 9(2): 455-476.
 URL:  
https://academic.hep.com.cn/fmc/EN/10.1007/s11464-014-0358-6
https://academic.hep.com.cn/fmc/EN/Y2014/V9/I2/455
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[2] LIN Jianwei, LIANG Jin. Pricing of perpetual American and Bermudan options by binomial tree method[J]. Front. Math. China, 2007, 2(2): 243-256.
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