The Pricing Research Of Several Types Of Barrier Options

This paper focuses on the study of the barrier option price.The pricing formulaes of different types of barrier options are given when the underlying asset price satisfies the exponential O-U process model.The mainly innovative work is such:Firstly,we get partial differential equation and the pricing formula of the European power-type knock down out put option.Secondly,the pricing formula and the derivation method of different type of double obstacles option are given.In the second chapter,the joint distribution of the final value and the minimum value of Brownian motion with drift in the limited time [0,T] is given by reflection principle of Brownian motion , Girsanov theorem and appropriate transformation of measure.And then we get the pricing formula of European power-type put option.In the third chapter,we discuss the exponential O-U process model based on the above theory. And We get the pricing formula of the European power-type knock down out put option. In the fourth chapter, we discuss the pricing method of double barieres options. We get the pricing formula of double obstacles options which becomes effective when it touches the above obstacle or the following obstacle through the risk-neutral pricing formula and transition probability desity. And then we get the pricing method of the other types of double barieres options by the appropriate transformations of set.