New Option Pricing In Fractional Ornstein-Uhlenback Process

Option pricing problem has always been one of the core problems in financial field of applied mathematics, and has also been one of the most complex problems. In the seventies of the 20 th century, Black and Scholes has published a seminal paper on option pricing and also given the famous Black-Scholes pricing formula. In recent years, new options has become one of the hot issues in the study of option pricing in society today. As the application of the new options in the financial market, the pricing of new options has become one of the important contents of financial mathematics.In this dissertation, we establish the financial market mathematical model in fractional Brownian motion environment, and discuss the pricing problem of vulnerable option by the stochastic analysis theory of fractional Brownian motion and the actuarial approach.The dissertation includes five chapters.Firstly, we introduce the development and current research of option pricing, the basis of selected topic and the main content of this dissertation.In chapter two, we introduce the definition and characteristics of fractional Brownian motion and Poisson process, and the actuarial approach for European option pricing.Then, we assume that stock price obeys the fractional jump-diffusion O-U process,the financial market model is built, the pricing formula for power option is obtained by the stochastic analysis theory of fractional Brownian motion and the actuarial approach.we assume that stock price, corporate value obey tthe fractional jump-diffusion O- U process, and the company is the risk of default, the financial market mathematical model is built, the pricing formula for vulnerable option is obtained by the stochastic analysis theory of fractional Brownian motion and the actuarial approach in the chapter four.At last, we summarize the main research results in this dissertation and point out some issues which need further research.