Pricing Of European Average Geometric Asian Options Underlying The Fractional Brownian Motion

Withtheintegrationofthefinancial globalization,standardoptionhas been difficultto satisfy the demand of the market, and exotic option has more flexible and effectivecharacteristicwhichattracts alot ofinvestors thanthestandardoptions.Asianoptionisarepresentative of exotic Options. For it can enormously decrease the possibility of pricemanipulation and short-term unusual fluctuation of the stock, investors prefer to choiceAsian option. Because of the property of path- dependent, there exists distinguishesdifference between Asian option pricing model and standard options, so Asian option ispricedtobemorecomplexthanotheroptions.Considering the fractal characteristics of the capital market, this paper studyingAsian option pricing that the stock price fluctuation follows a fractional Brownianmotion is more realistic and more suitable to solve the financial issues in the real capitalmarket, than studying the option pricing that the stock price fluctuation follows astandardBrownianmotion.In the first chapter of this paper, we review the emergence and development ofAsian option theory, and explore several current methods of pricing option at present;The theoretical basis of this paper is the second chapter which introduces the definitionand nature of the fractional Brownian motion, explores the approximation theory of thefractional Brownianmotioninfinance, andreviewsscholarachievementsofapplyingthefractionalBrownianmotiontooptionpricinginrecent years;Thethirdchapteristhecorecontent of this paper. Firstly we obtain The stochastic differential equation of stockoptions pricing by a se-martingale process based on the approximation of the fractionalBrownian motion that is not a se-martingale process, secondly ,and derive the pricingmodel of European geometric Asian Options when H? (1/3,1/2), finally on the pricingmodel of European geometric Asian Options, we deduce with the fixed price and the float price of European geometryaverage Asian option pricing formula, and then get thecall-and-putofEuropeangeometryaverageAsianoptionpricingformula.