Pricing Geometric Average Asian Options

In recent years, along with the improvement of demand on the complexityin money market, it is difficult to satisfy the special needs of customers by onlyusing the standard option. In order to satisfying the demand of markets andcustomers, to avoiding the risk of the inverters, many financial companies notonly designed European options and American options but also devised a greatdeal of new breeds which derive from standard options and exchange out of thecounter commonly. We call it exotic options. Most of exotic options possess thefeature of path-dependent, that is to say, the option price not only depends onthe option price at maturity; but also depends on varying of the underlyingassets price. Asian options are just one of the typical products, and it isa kind of exotic options which is the most active one in financial derivativemarket. Because of the property of path-dependent, there exists distinguisheddifference between Asian option pricing model and standard options.The main goal of this paper is to study Asian options. It is a typicalrepresentative of strongly path-dependent options, Asian option is differentfrom standard option obviously. It is innovation of European options. So itconnects with the standard European options nearly. Black-Scholes OptionPricing Model is just one of the most effective means to solve main contentof the article. Therefore we should understand Black-Scholes Option PricingModel fully which concludes to our research. Its main content is as follows:Chapter One is introduction of the article. It reviews the conception ofoption briefly and several current method of pricing option at present, further, it summarizes some historical documents which is related to Strongly path-dependent options-Asian options. In the end, the main content and idea inthis article is given.Chapter Two proves in detail the pricing model of Asian geometric averageoptions with fixed strike price. First, we prove that the geometric averageprice of stocks has the Gauss distributions with constant and floating rate.Finally, we draw the price formula of the Asian geometric average options at any valid time.Chapter Three proves in detail the pricing model of Asian geometric aver-age options with floating strike price. It is difficult to draw the joint distributionof the geometric average value and the maturity value of stocks, so we use priceof stock as numeraire and probability measure changes, the geometric averagevalue and the maturity value of stocks changes to a random variable, then wedraw it's distribution. Finally, we draw the price formula of the Asian geomet-ric average options at any valid time, as well as call and put options pricingformula respectively.Chapter Four elaborates Asian options is playing an very important rolein financial market, and summarizes this article.