Pricing Exotic Options In Fractional Brownian Montion Environment

After the empirical study ,we found that the stock price has the property of long-term dependence, this is a certain gap to geometric Brownian motion, and fractionalBrownian motion with a steady incremental continuous zero mean Guassian process,these incremental correlation Hurst parameters H to describe. When fractionalBrownian motion with 12 < H < 1, The properties make long-term dependence onfractional Brownian motion in the research of the options pricing more rational.This paper mainly discusses the environment of fractional Brownian motion to pricethree exotic options which divided into five chapters:The first chapter presents the option pricing theory and the formation of thedevelopment and the main part of this.The second chapter introducing fractional Scholes market and quasi-martingalepricing method from the definition of fractional Brownian motion and the corre-sponding random integral theory,describes option pricing model in the market offractional Black-Scholes , and analyze the in?uence of the parameters in the model.The third chapter discusses the valuation of continuous strike option underfractional Black-Scholes market, use the model of fractional Brownian motion tocalculate option prices to compare the price of European option , and analyze therelationship to Hurst parameter and volatility with option prices.The fourth chapter discusses the valuation of European complex chooser optionunder fractional Black-Scholes market, use the fractional Brownian motion modeland monte-carlo simulation calculation By comparison, illustrates the rationality offractional Brownian motion model, and analyze Hurst parameter and choose datefor the relationship with the option price.The fifth chapter discusses the valuation of VPO under fractional Black-Scholesmarket , use the fractional Brownian motion model and monte-carlo simulation cal-culation By comparison, illustrates the rationality of fractional Brownian motionmodel,and analyze Hurst parameter and volatility for the relationship with the op-tion price, and obtained the sensitivity analysis of VPO.