Pricing Of Two Kinds Of Power Option Under Fractional Brownian Motion、Stochastic Rate And Jump-Diffusion Models

Option pricing is one of the important elements of financial mathematics and economics,the research and development of option pricing have far-reaching impact on finance and capital markets.The maximum of stochastic process is often encountered in the pricing of exotic options,especially when the stochastic process is a jump-diffusion process,the problem get more complicated because the distribution of the maximum is difficult to derive.There is no doubt that we should use jump-diffusion process to describe the changing behaviors of financial markets,instead of diffusion process,but the pricing process is more complex.Market quotations.trade practices and information dissemination are three important factors which effect trade speed and transaction volume.a reasonable pricing is the premise which active exchange market.In recent years,with the exception of European and American options,a large number of new financial derivatives are derived in the international financial derivative market.Among them,the power options is one of the new typical options.The research of the power options has the significance meaning on both theoretical and practical.compared with the traditional efficient market theory,use the fractal market theory to describe the movement of the actual market is more appropriate and accuracy.Pricing options with stochastic interest rate under jump-diffusion models is a important problem in recent years,this paper intend the traditional jump-diffusion models into jump-diffusion model under fractional Brown motion,The purpose of this extending is to make the option pricing in the actual market more accuracy.In this paper,under the assumption of the exchange rate obey the expanding Vasicek models,we obtained the pricing formulas of two kinds of power options under fractional jump-diffusion models.