The Application Of Martingale Analysis In American Option

The pricing of the American option is one of the most important questions in financial statistics. It is more difficult than the pricing of the European option, because American option may be carried out, However, because of the practical importance of American option, their accurate pricing is vital to option market participants.In this paper, we begin with research background of option pricing theory, Based on the concept, content and method of option, general option pricing method and B-S option pricing function are discussed to illuminate hedge thoughts.In this paper, martingale theory is applied to option pricing. American option pricing is discussed by using martingale analysis. On the basis of the research of the former, a perpetual mixed American option with default-risk is constructed by using hedge thoughts. It is discussed by optimal stopping theory of martingale, we obtain formulation of optimal asset price in American call option and American put option.In this paper, 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.