Quanto Option Pricing In Bi-fractional Brownian Motion Environment

Since the model of the Black-Scholes came out,option pricing theory has developed rapidly,provide technical guidance for investors investment,it becomes more and more important.Quanto option pricing is not only related to the foreign stock price,but also related to the exchange rate.At first,the researchers studied in Brownian motion.In recent years,many scholars have found that the bi-fractional Brownian motion is a more general Guassian process.The bi-fractional Brownian motion can be described more general financial phenomena.In this thesis,the quanto option pricing problem in bi-fractional Brownian motion environment.The main research results are as follows:(1)The stock price and exchange obey the stochastic differential equation driven by bi-fractional Brownian motion,the financial market model in bi-fractional Brownian motion environment is built,applying the actuarial approach for bi-fractional Brownian motion,the pricing formula of quanto option in bi-fractional Brownian motion environment is obtained.(2)Assume that stock price follow the stochastic differential equation driven by the bi-fractional Brownian motion and jump process,the financial mathematical model in bi-fractional jump-diffusion process is built.The quanto option is discussed using the actuarial approach,and the quanto option pricing formula is obtained.(3)Assume tha the stock price and exchange 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 quanto option in bi-fractional Vasicek rate environment is obtained.