American Fell Failure Of The Physical Barrier Option Pricing Method

In the first chapter, the paper first introduced the definition of option, call option, American option ,Europe option and then introduce the definition of barrier option. The price of barrier option is much more cheaper than the normal option, but it can still take good effect in the investment of commodity and financial product. In addition, the barrier option can satisfy the personal necissary of investmentor, give off the rights of investing some items by the investment customs. We elaborate the development of the theory of pricing methods of barrir option, simply introduce some numerical methods of barrier option. We then introduce the defect of the numerical methods and the reason that people select the methods.In the second chapter, the paper introduce the model of geometric Brownian motion that the product of investing items satisfied when the bonus rate is not zero. In addition, this chapter introduce the pricing model of barrier investment option.In the third chapter, the paper introduce three pricing methods of barrier option : contigent claims method, variational inequality method and backward stochastic differential equation method. Karatzas introduced the pricing method of finantial barrier option on Black-Scholes model when the bonus rate is zero. We consider the investing tragity from this point and it demands that the bonus rate is not zero. When the bonus rate is not zero,it is much more difficult to prove the uniqueness and existence of Black-Scholes pricing model, and this step is the base of non-numerical methods. In addition, We introduce the BSDE method to price the real barrier option.In the fourth chapter, the paper analyze the influences of different parameters to barrier option price by concrete numerical value and figue, including different h value , diferent δ value and different σ value, then analyze on the economical aspect.