Pricing Of European Exotic Option Of Fractional Brownian Motion Environment

With the continuous development and the growth of the financial markets, the pricing of financial derivatives, especially, the exotic option pricing problem is a main research content in the field of finance, especially, in the field of financial mathematics. The classical B-S option pricing model assumes the underlying asset follows a geometric Brownian motion, but a large number of experiments show that has the same characteristics with fractional Brownian motion. Therefore this article mainly introducing the fractional Brownian motion, assume that following fractional Brownian motion process, researching two exotic option pricing model.This thesis mainly includes the following contents:Part Ⅰ:using the idea of timeline transform, establishing fraction European power type option pricing model, Including a fraction European call options with the bonus, also get a parity relationship of fraction European type power call options and put options.Part Ⅱ:setting diffusion process driven by the fractional Brownian motion and jump process for counting process, using fractional stochastic analysis theory of the martingale pricing method and risk neutral pricing theory, and we get the fractional jump-diffusion European power option pricing.Part Ⅲ:using the portfolio and△hedge principle, obtaining the partial differential equations of Asian options which are in the fractional Brownian motion environment. By conversion deformation, the equations are converted into the one-dimensional partial differential equations of the Cauchy problem, establishing a model of fraction geometric average Asian call option pricing with a fixed exercise price.