Study Of Numerical Methods For Pricing American Barrier Option

The pricing problem of the American barrier option is currently regarded as one of the hot spot in the option pricing studies. Because the American barrier option may be exercised before the expiration date, its pricing is generally more difficult than that of the European barrier option. The article researches the characters of the American option and the principle of forming its value, deduces the pricing model of the American barrier option, and offers two new, very fast and accurate numerical pricing methods of the American barrier option--- the finite difference method and the laplace method which are based on the free boundary problem.Firstly, the pricing formulae of European barrier option is deduced on the base of the Black-Scholes option pricing model. Secondly, the article introduces the free boundary problem of the American option after researching the characters of the American option and the principle of forming its value at the fourth chapter. Considering the effect of barrier level on option price, the pricing model of the American barrier option is concluded at this chapter. At the former part of the fifth chapter, the singularity in the pricing model of the American barrier option is removed, as a result of which the original model is transformed into the new one without discontinuity solution. At the latter part of the fifth chapter, the article sloves the initial value problem with the three methods, including the two new methods offered and the finite difference method based on the technique for densifying part meshes, and gives a comparison on computational accuracy and speed among the three methods. The analysis show that the finite difference method based on the free boundary problem and the laplace method based on the free boundary problem are two good numerical methods.