The Reset Option Pricing Model In Bi-fractional Brownian Motion Environment

Option pricing is one of the hot issues of financial mathematics research.The reset option is put forward by Gray and Whaley for the first time in 1997.Reset option is a kind of weakly path-dependent exotic options,that is,the strike price can be adjusted or reset.Scholars both at home and abroad researched reset option pricing under the Brownian motion and jump-diffusion process.However,they found that the stock prices depended on their history prices through a large number of financial markets empirical analysis,and fractional Brownian motion with long-term dependent characteristics performance better on researching the changeable stock price,then scholars research on reset options under fractional Brownian motion.In recent years,many scholars have found that the bi-fractional Brownian motion,which is widely applied in the financial markets,is a more general Guassian process.The bi-fractional Brownian motion can be described more general financial phenomena.In this thesis,the reset option pricing problem is discussed in bi-fractional Brownian motion environment.The main research results are as follows:(1)The reset option prcing problem in bi-fractional Brownian motion environment is discussed.Assume that the interest rate is a constant,the financial market model under bi-fractional Brownian motion environment,applying the actuarial approach and the stochastic analysis theory for bi-fractional Brownian motion,the pricing formula of reset option in bi-fractional Brownian motion environment is obtained.(2)The reset option prcing problem in bi-fractional jump-diffusion process is studied.Assume 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 reset option is discussed using the actuarial approach,and the reset option pricing formula is obtained.(3)The reset option prcing problem in bi-fractional Vasicek rate environment is discussed.Assume that stock price follows the stochastic differential equation driven by bi-fractional Brownian motion,and interest rate satisfies Vasicek rate model which driven by bi-fractional Brownian motion.The mathematical model of financial markets in the bi-fractional Vasicek rate environment is established.Using the actuarial approach,the pricing formula of reset option in bi-fractional Vasicek rate environment is obtained.