The Basket Option Pricing In Bi-fractional Brownian Motion Environment

Option pricing is a core problem in financial mathematics.Today,many exotic options are derived from financial markets,and basket option is one of the exotic options.In recent years,the scholars have found that the bi-fractional Brownian motion can not have stability increment,so it can describe more financial phenomena.In this paper,the problem of basket option pricing is discussed in bi-fractional Brownian motion.The main contents are as follows:(1)Under the condition that the interest rate is contest,assuming the option price of risky assets follows the stochastic differential equations that driven by bi-fractional Brownian motion.the mathematical model of financial markets in the bi-fractional Brownian motion environment is established.The pricing formula for European geometric basket option is obtained by insurance actuary approach.(2)The interest rate satisfies vasicek interest rate model,using the stochastic analysis theory of bi-fractional Brownian motion and the insurance actuary approach to analysis.The pricing formula of basket option under Vasicek interest rate in bi-fractional Brownian motion environment is obtained.(3)Under the condition that the option price of risky assets satisfy the bi-fractional jump-diffusion process.Based on the theory of bi-fractional jump-diffusion process,using the actuarial theory approach,the pricing formula of basket option in bi-fractional jump-diffusion environment is obtained.