The Pricing Of Geometric Average Asian Options

In recent years, along with the improvement of demand on the complexity in money market, it is difficult to satisfy the special needs of customers by only using the standard option. In order to satisfying the demand of markets and customers, many financial companies not only designed European options and American options but also devised a great deal of new breeds which derive from standard options and exchange out of the counter commonly. We call it exotic options. Most of exotic options possess the feature of path-dependent, that is to say, the option price not only depends on the option price at maturity; but also depends on varying of the underlying assets price. Asian options are just one of the typical products, and it is a kind of exotic options which is the most active one in financial derivative markets. Because of the property of path-dependent, there exists distinguished difference between Asian option pricing model and standard options.The main goal of this paper is to study Asian options. It is a typical representative of strongly path-dependent options, Asian option is different from standard option obviously. It is innovation of European options. So it connects with the standard European options nearly. Black-Scholes Option Pricing Model is just one of the most effective means to solve main content of the article. Therefore we should understand Black-Scholes Option Pricing Model fully which concludes to our research.This paper gives the uniform Black-Scholes Model of strong path-dependent options.Because of the unique character of path-dependent options, we import a path-factor, then deduce the uniform B-S Model of strong path-dependent option using Ito theory and no-arbitrage principle. For different path-factor, with a concrete path function, initial condition and boundary condition we can get the pricing formula on solving the equation. In addition, we get the price of geometric average Asian option with fixed strike price and floating strike price, making use of the uniform B-S Model of strong path-dependent option and the pricing formula of geometric average Asian options under no risk-neutral world.