The Pricing Of Contingent Claims Under Fractal Market Hypothesis

The pricing theory of the contingent claims has been the core contents of financial mathematic. This Master's thesis considered the contingent claims pricing theories under fractal market assumption.This Master's thesis is divided into three parts.In chapter one, we mainly introduce the background of the research topic.In chapter two, we discuss the contingent claims pricing under the fractal market assumption. Firstly, we introduce the definition, properties and integral theory of fractional Brownian motion. In section 2, we obtain the European contingent claims pricing formula from the price of underlying asset dividends payments. In section 3, we obtain the pricing formulas of European option at arbitrary time before maturity when the stock pays the bonus. In section 4, we obtain pricing formulas of two kinds of singular options. In section 5, we discuss the pricing model of contingent claims under different financial market assumption.In chapter three, we analyze real option characteristic and the optimal investment regulations of the electric power investment item. Firstly we introduce the optimize investment regulations under the single time. Then according to the characteristic of large investment item we analyze the optimal investment rule and make comparison between the NPV regular and real option regular.