基于随机利率下跳-扩散过程的复合期权的定价

Pricing compound options under jump-diffusion processes with stochastic interest rates

复合期权是以期权作为标的资产的期权,在公司金融中应用非常广泛,能够得到复合期权的定价解析公式是十分有用的。首先建立随机利率条件下,含有多个跳跃项和多个扩散项的股票价格过程的随机微分方程,然后利用测度变换及鞅方法得到欧式期权及欧式复合期权的定价解析公式。从两方面推广了以前的一些结果:同时考虑了随机利率和跳扩散过程;假定跳扩散过程含有多个扩散源和跳跃源。

Compound options are asset options on options. They are used extensively in company finance. It is very important to obtain the analytic formulas of pricing compound options. First, Stochastic differential equation of stock price which includes many jump sources and many diffusion terms is constructed under stochastic interest rate firstly. Then, by the help of transformation of measure and martingale method, the analytic formulas of European options and European compound options are obtained. This generalized some previous results from the following two aspects, i. e. , stochastic interest rate and jump-diffusion processes. The other is many jump sources and many dif- fusion terms are assumed.