Convertible Bond Pricing Model In Bi-fractional Ornstein-uhlenback Process

With the development of financial derivatives,there are more and more advanced financial derivatives and convertible bond is one of them.Convertible bond is a hybrid financial instrument that can be converted into stock at a fixed price,it is very important to price the convertible bond.The bi-fractional Brownian motion is a more general Gaussian process,which can accurately describe random phenomena.The Ornstein-Uhlenback process is an important type of moving average process.This thesis considers the financial market model under the bi-fractional Ornstein-Uhlenback process and discusses the convertible bond pricing.The content of the thesis is as follows:(1)Assuming that the asset price is subject to the bi-fractional Ornstein-Uhlenback process,we discuss convertible bond pricing problem and the actuarial price of the convertible bond is obtained.(2)Considering the impact of sudden events,the financial market model of the bi-fractional jump-diffusion Ornstein-Uhlenback process is established,and the actuarial method is used to get the pricing formula of convertible bonds.(3)Assuming that the interest rate obeys the Vasicek model,the stock price obeys the bi-fractional Ornstein-Uhlenback process.The mathematic model based on the Ornstein-Uhlenback process and stochastic interest rate is established,and the insurance actuarial method is used to get the pricing formula of convertible bond.