European Power Option Pricing Model Under Bi-Fractional Ornstein-Uhlenbeck Process

Option pricing is one of the core problems in financial mathematics.In recent years,with the rapid rise of the financial market,exotic options have become one of the hot issues in research options pricing.Power option,as a kind of exotic option,its value on the expiration date is not simply a comparison between the price of stock and exercise price,but the compared with an exponential function the price of stock and exercise price.In contrast to traditional standard options,power options have the effect of amplifying the risk of the option,and more flexibility to adapt to the needs of investors in different risk preferences.Thus,the power option is a kind of option exotic options of low cost and simple structure,get the favour of the broad masses of investors in the financial market.In this paper,the mathematical model of financial market under the process of bifraction(o-u)was established,using the nature of the bi-fractional Brownian motion and the actuarial approach,the research on the pricing of power options was conducted.The main research results are as follows:(1)The related pricing problems of power options under bi-fractional o-u process were studied.Assuming the interest rate is constant,the corresponding mathematical model is established under the bi-fractional o-u process,and the pricing formula of the power option under the bi-fractional o-u process is solved by using the actuarial approach.(2)Discusses power option pricing problem under.the bi-fractional O-U jump diffusion process,Assumes that the price of stock follow driven bi-fractional O-U jump diffusion process stochastic differential equation,the use of bi-fractional O U jump diffusion process stochastic analysis theory,establish the corresponding mathematical model of financial markets.Based on the actuarial theory of insurance,the formula of power option pricing is derived.