CHINESE JOURNAL OF APPLIED PROBABILITY AND STATIST 2014, 30(5) 510-526 DOI:      ISSN: 1001-4268 CN: 31-1256

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Pricing of Extension of European Exchange Option under Esscher Transforms

Liu Guoxiang, Zhu Quanxin, Zhang Xiangqiang

School of Mathematical Sciences and Institute of Finance and Statistics, Nanjing Normal University

Abstract��

This paper studies the price of extension of the European
exchange option (including generalized exchange option; compound exchange option;
barrier exchange option; traffic-light option) with the geometric Brownian motion.
Firstly, the reflection principle and property of the Browian motion with drift
are given; Secondly, the definitions and properties of the Esscher transform of
multidimensional processes with stationary and independent increments and
two-dimensional Browian motion with drift are given by borrowing from the idea of
Gerber and Shiu (1994); Finally, using related theory of Esscher transform, pricing
formulas of extension of several European exchange options are obtained when the
price of the underlying asset follows the geometric Brownian motion.

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