Chooser Option Pricing In Bi-fractional Brownian Motion Environment

Option pricing is a core problem in financial engineering.All kinds of exotic option has became the key problem of option pricing theories.Chooser option is a exotic option,which can change the yield structure of the option.In recent years,scholars at domestic and abroad found that bi-fractional Brownian motion has a wide range of applications in financial engineering.Based on the bi-fractional Brownian motion environment,the chooser option pricing were discussed.The main contributions of this dissertation are as follows:Firstly,assume that stock price follows the stochastic differential equation driven by bi-fractional Brownian motion,the expected rate of return and the interest rate are time function,volatility rate is constant,the mathematical model of financial markets in the bi-fractional Brownian motion environment is established.The pricing problem of chooser option is discussed using the actuarial approach,and the pricing formula of the chooser option in bi-fractional Brownian motion environment is obtained.We also analysis the sensitivity of chooser option with respect to parameter S,,,,rt T*s,which allows us have a clearly understanding about the influence level of each parameter on option pricing.Secondly,assume that stock price follows the stochastic deferential equation driven by bi-fraction Brownian motion,and interest rate satisfies Vasicek rate model which driven by bi-fraction Brownian motion,the pricing problem of chooser option is discussed.The pricing formula of chooser option in bi-fraction Vasicek rate environment is obtained.Thirdly,assume that the stock price satisfy the stochastic differential equation driven by bi-fractional Brownian and jump process,the expected return rate,interest rate and volatility rate are constant,the financial mathematics model is built,and the pricing problem of the chooser option is discussed by the theory of bi-fractional Brownian and jump process.The pricing formula of the chooser option is obtained by the actuarial approach.