The Exchange Option Pricing In Bi-fractional Brownian Motion Environment

Option pricing is one of the hot issues of financial mathematic research.In order to better meet the development of the financial market,the so-called exotic options are spawned,exchange option is one of them.Many scholar discuss option pricing under the fractional Brownian motion environment.The Bi-fractional Brownian motion not only has the various properties of fractional Brownian motion,also has the non stationary increment.Therefore,in this thesis,the exchange option pricing problem is discussed in bi-fractional Brownian motion environment.The main research results are as follows:Firstly,assume that stock price follows the stochastic differential equation driven by bi-fractional Brownian motion,the financial mathematical model under bi-fractionalprocess is built by the stochastic analysis theory of the bi-fractional Brownian motion.The exchange option pricing is discussed using the actuarial approach,and the exchange option pricing formula is obtained.Secondly,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 exchange option pricing is discussed using the actuarial approach,and the exchange option pricing formula is obtained.