The Study On The American Barrier Option Based On Homotopy Analysis Method

With the development of financial markets,there are more and more kinds of options.Now the pricing of American barrier option has well received more attention because of its low prices,flexible trading and hedging risk in the field.However,it is different from the European barrier option.In 1973,European barrier option has got its analytical formula,while American barrier option,similar to American option,is so complicated that it has no analytical formula due to the characteristics of early exercise.Nowadays,some researchers used Homotopy Analysis Method to obtain the analytical pricing formula of American option.Based on his work,this paper tries to further research American barrier option,so I mainly study the characters of the American barrier option and the principle of its optimal exercise boundary.Besides,this paper takes the example of American down-and-out call option,uses the Homotopy Analysis Method and then changes the original nonlinear problem to the series of linear problems.Then combining with the finite difference method,we successfully solve this problem and get the relevant price of American barrier option and the optimal exercise boundary.Finally,by some numerical examples,we compare with other numerical methods and further verify the validity of the proposed method.