New Options Pricing Under Fractional Vasicek Interest Rate

Since1973,Black and Scholes put forward the Black-Scholes option pricing model for the first time and also obtained its pricing formula, option won the swift and violent development by its unique charm. In order to meet a variety of special requirements of market participants, more complex options than conventional options were spawned on the basis of the standard of European or American option, the so-called new options. The power function options and reset options are typical of the new options.This paper mainly deeply researched the pricing of the two new options on the basis of the traditional power function options and reset options. The dissertation includes five chapters.In chapter one, we introduce the development history and current research of options pricing, the power options and reset options, the basis of selected topic and the main content of this paper.In chapter two, we introduce the relevant knowledge of fractional Brownian motion and Poisson process.In chapter three, we discuss the pricing problems of power function options under the fractional Vasicek model. We suppose that stock price process obeys fractional jump-diffusion process, and interest rate satisfies the fractional Vasicek model, some exotic options including power options, cap options are discussed, and their pricing formulas are obtained by the fractional jump-diffusion process theory and actuarial method. The option pricing model is generalized.In chapter four, we discuss the pricing problems of the innovative reset options under the fractional Vasicek model. We suppose that stock price process obeys fractional jump-diffusion process, and interest rate satisfies the fractional Vasicek model, the innovative reset options are researched and the pricing formulas are obtained by the fractional jump-diffusion process theory and actuarial method.In chapter five, we summarize the main research results of power function options and reset options in this dissertation and point out some issues which need further research.