Esscher变换下扩展的欧式交换期权定价

Pricing of Extension of European Exchange Option under Esscher Transforms

文章研究Esscher变换下标的资产价格服从几何布朗运动的扩展的几种欧式交换期权(包括广义交换期权,复合交换期权,障碍交换期权,红绿灯期权)定价问题.首先,给出了带漂移布朗运动的反射原理和性质;其次,借助Gerber和Shiu(1994)给出了多维独立平稳增量过程和二维带漂移布朗运动的Esscher变换定义及其性质;最后,应用Esscher变换的相关理论给出了标的资产价格服从几何布朗运动的扩展的多种欧式交换期权定价公式.特别,本文所得到的期权定价公式与以往文献中给出的结果是一致的.

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.