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

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 diffusion terms are assumed.