A Kind Of Martingale Method About Barrier Options Pricing

Barrier option is a kind of limited options. The final income of the kind of options not only depends on the original asset price in the option expire but whether the original asset price attains prescriptive price in term of option validity is related. So its pricing is more complicated than European option. But the investment of Barrier option is low-risk and low- cost. And it is favored by market. The pricing of the Barrier option is one of the most important questions in financial statistics.In this paper, we research background of option pricing theory, Based on the concepts, contents and methods of option, general option pricing method and B-S option pricing function are discussed to illuminate hedge thoughts.Martingale analysis is applied to option pricing. Based on the fundamental concepts and theories, developments in recent years of martingale, Barrier option pricing is discussed by martingale analysis. It is pricing Barrier option by solving partial differential equation with boundary conditions in Mathematics model and method of option pricing. That process is complicated. But discussing discounted stock price by equivalent martingale measure and pricing Barrier option with martingale analysis and stochastic process simplified the pricing process. On the basis of the research of the former, The pricing of Barrier option added abnormal fluctuation is discussed. Finally, we make a contrast between traditional lognomality model and fluctuating sources model through empirical analysis, it shows that fluctuating sources model can describe the real stock market more practically and accurately than the traditional lognomality model, so the pricing of option in fluctuating sources model has guiding action .we obtain formulation of option pricing by martingale analysis, which is not only valuable to rich application of martingale theory, but also practical to financial statistics.