The Pricing Of Compound Option Under Stochastic Interest Rate In A Fractional Brown Motion Environment

Options is known to us as an important financial derivates product, which occurred from USA in the middle of1970s. Since then, the study of options pricing theory and its application have developed rapidly and achieved rich achievements. With the devel-opment of financial market, a lot of new options emerge as the times,such as Asia option,Barrier option,compound option and so on.Thus, how to price these new options is one of most important problems urgently needing to be solved by financial and mathematics people.This paper mainly discuss the pricing of call option and compound option, through-ing mathematical tools such as stochastic process and stochastic analysis. In the con-dition that the stochastic rate obeys Vasicek stochastic process or fractional Vasicek stochastic process and the stock price follows fractional diffusion model or obeys frac-tional jump-diffusion model, we deduce compound option pricing formulas.In chapter two, we discuss the pricing of compound option and deduce the pricing formulas, underlying the assumptions that the stochastic rate is Vasicek rate and the stock price follows Fractional geometry Brownian Motion.In chapter three, we price the compound option under the condition of Vasicek rate with a fractional jump-diffusion model and deduce the pricing formulas.In chapter four, we price the formula of compound option underlying the assump-tions that the stochastic rate is fractional Vasicek model and stock price follow Fractional geometry Brownian Motion.In chapter five, we discuss the pricing formulas of compound option, under the condition that the stochastic rate follows the fractional Vasicek model and stock price obeys fractional jump-diffusion model.In chapter six, we give some problems that need further effort.