Chooser Option Pricing Model In Fractional Brownian Motion Environment

Option pricing theory is one of core problems in financial mathematics. In1973, Blackand Scholes put forward the famous Black-Scholes option pricing model and also obtained itspricing formula based on the assumption that the stock price followed the geometricBrownian motion. However, in the actual finance market, many scholars agreed that thefractional Brownian motion is more adapted to the financial market since the fractionalBrownian motion has the long-term dependence and fat tail.In this dissertation, we assume that the stock price obeys the stochastic differentialequation driven by fractional Brownian motion. The financial market model is built infractional Brownian motion environment, using stochastic analysis theory for fractionalBrownian motion and insurance actuary method, we discuss the pricing problem of chooseroption. The thesis includes six chapters.In chapter one, we introduce the history and current research of option pricing, the basisof selected topic and the main content in this dissertation.In chapter two, we introduce the definition and characteristic of fractional Brownianmotion, we also introduce the insurance actuary method for European option pricing.In chapter three, we assume that the stock price obeys the stochastic differential equationdriven by fractional Brownian motion, and interest rate satisfies the Hull-White model, Bymeans of the stochastic analysis theory of fractional Brownian motion and the insuranceactuarial method, we discuss the pricing of problem of chooser option and obtain the pricingformula for the chooser option.In chapter four, we build the fractional jump-diffusion Ornstein-Uhlenbeck model forfinancial market, using fractional jump-diffusion process theory and insurance actuarialmethod, we discuss pricing problem for the chooser option and obtain the explicit pricingformula for chooser option.In chapter five, we present the financial market model in mixed fractionaljump-diffusion environment. By means of insurance actuary method and fractionaljump-diffusion process theory, we obtain the pricing formulae of European option andchooser option. In chapter six, we summarize the main results in this dissertation and point out someissues which need further improvement.