The Reload Option Pricing In Bi-fractional Brownian Motion Environment

The option pricing is one of the hot topics in financial mathematic theories. With the development of financial markets, the assets could not meet the demand of various financial markets. So many exotic options are derived from the financial markets to satisfy the demand of financial markets, and reload option is a kind of the exotic options.In this thesis, we mainly built the financial market model under Bi-fractional Brownian motion, then the reload option pricing formula in Bi-fractional Brownian motion environment is obtained.The thesis includes five chapters.(1) we introduce the development history and current research of options pricing,the reload options, the relevant knowledge of Bi-fractional Brownian motion.(2) we discuss the reload options pricing in Bi-fractional Brownian motion environment. First, we find out the definition formula of reload option by search literature; suppose the interest rate is a constant, then introduce the process of Bi-fractional Brownian motion and build the financial market model under Bi-fractional Brownian motion environment, using the actuarial approach and then solve the financial market mathematical model by the stochastic analysis for Bi-fractional Brownian motion,the pricing formula of reload option in Bi-fractional Brownian motion environment is obtained.(3) we discuss the reload options pricing under Bi-fractional jump-diffusion Process.First, we suppose that stock price follows the stochastic differential equation driven by the Bi-fractional Brownian motion and jump process, the financial mathematical model under Bi-fractional jump-diffusion process is built by the stochastic analysis theory of the Bi-fractional Brownian motion and jump process. The reload option is discussed using the actuarial approach, and the reload option pricing formula is obtained.