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Free boundary and American options in a jump-diffusion model

Published online by Cambridge University Press:  21 October 2005

YANG CHENGRONG ,
JIANG LISHANG  and
BIAN BAOJUN
YANG CHENGRONG
Affiliation:
Institute of Mathematics, Jilin University, Changchun, 130012, China email: wytr@email.jlu.edu.cn Business School of Jilin University, Changchun, 130012, China
JIANG LISHANG
Affiliation:
Department of Applied Mathematics, Tongji University, Shanghai, 200092, China email: jianglsk@online.sh.cn, bianbj@yahoo.com.cn
BIAN BAOJUN
Affiliation:
Department of Applied Mathematics, Tongji University, Shanghai, 200092, China email: jianglsk@online.sh.cn, bianbj@yahoo.com.cn
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Abstract

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The purpose of this paper is to give a pricing analysis for the American option in a jump-diffusion model by PDE arguments. Existence and uniqueness of the solution to the obstacle problem for the associated model is shown in suitable spaces. We also prove the unique existence of the solution of the corresponding free boundary problem. Furthermore, smoothness and monotonicity of the free boundary which is the optimal exercise boundary of the option are deduced.

Type
Papers
Information
European Journal of Applied Mathematics , Volume 17 , Issue 1 , February 2006 , pp. 95 - 127
Copyright
2005 Cambridge University Press