Application Of Martingale Analysis To Pricing Of Geometric Average Asian Options

In recent years, as an effective method to avoid risk or speculation have rapid development. The option pricing is the core issue in the trade of option.Asian option is an average price option. It can enormously decrease the possibility of price manipulation and short-term unusual fluctuation of the stock price. So the Asian option has been widely used. Because of the property of path-dependent, there exists distinguishes difference between Asian option pricing model and standard options, so Asian options pricing to be more complex than other options.Based on the hypothesis that market is non-arbitrage, we should understand Black-ScholesOption Pricing Model fully concludes to our research. The pricing on Asian geometric average options with fixed strike price at any valid time are studied in this paper. Using the method of martingale, we draw the price formula of the Asian geometric average options at any valid time. Furthermore, the analytical expression of the Asian geometric average options pricing and call-put parity relation are derived. It main content is as follows.Firstly explored several current method of pricing option at present, and overview some historical documents which is related to strongly path-dependent options-Asian options.Then we prove in detail the pricing model of Asian geometric average options with fixed strike price. First, we prove that the geometric average options of stocks have the Gauss distributions with constant and floating rate. Finally, we draw the price formula of the Asian geometric average options at any valid time.Secondly we prove in detail the pricing model of Asian geometric average options with floating strike price. It is difficult to draw the joint distribution of the geometric average value and the maturity value of stocks, so we use price of stock as numerical and probability measure changes, the geometric average value and the maturity value of stocks changes to a random variable, then we draw it's distribution.Finally, we draw the price formula of Asian geometric average options at any valid time, as well as call and put options pricing formula respectively.Thirdly theoretically to European call options and call the geometric average Asian options when investing in the relationship between income and risk, and from Shanghai and Shenzhen Stock Exchange were randomly selected 10 stocks closing price data for empirical analysis, thereby Asian options come to more than the design of European options must be reasonable.