Pricng Asian Option Under Jump-diffusion Model With Stochastic Interest Rate

Nowdays, as the development of the society and the progress of the ages, Asian options depend on it’s special properties—strong dependency for the total history price—making the problem of set price become one of the hotest problem in financial community durning these years.Because having think of the emergent events, geometry Asian options under jump-diffusion models which gets most of attention by people. Through building jump-diffusion, defining risk neutrality measureFinding the suitable equivalence martingale measure, making use of Girsanov theorem and martingale law, the paper mainly discusses the price of geometry Asian options when the rate is constant and random this two conditions.In former research, the rate of random under the jump-diffusion models not only a important topic but also a difficult point. So most of researcher choose through make use of backward stochastic differential equation to solve the price problem of jump-diffusion models. Then this paper think over from another side, solving this problem by use of martingale law. In the end we through establish the money market model under jump-diffusion models, equivalent martingale, successfully and gets the pricing formula when the interest rate is constant and when it obeys the Vasicek model.