Asian Option Pricing Model And Its Empirical Research

Options are important derivative securities. They are certain rights that ennable theirholders to buy or sell the underlying assets of certain quality and in certain quantity at afixed time in the future after paying the cost of options. Option theory is one of thegreatest findings in the economics field of the world in the 20th century. Effectivemanagement of risk depends on the right evaluation of derivative securities. It isinstrumental for the existence and development of financial derivative securities toascertain its fair price. Among all the pricing systems of derivative securities, option iseasier to price than other derivative securities. Many securities may be expressed in theform of option combinations, and the pricing principles are same to all sorts of derivativesecurities. Thus, it is possible to induce a pricing theory for all derivative securities byway of a research of the option pricing method. Therefore, the option pricing is alwaysthe core of financial mathematics.In 1973, F.Black and M.Scholes, the scholars from the Chicago University putforward their Black-Scholes Option Pricing Model, which has been hailed as abreakthrough in the research of options pricing theory, has laid the foundation for theestablishment of the theory for pricing the options in various emerging derivativefinancial markets—the stock market, the bond market, the money market, and thecommodity market. However, in recent years, with the increasing complexity of thedemands of the financial markets, it is difficult to satisfy the specific needs of customersto use the standard option alone. In order to satisfy specific needs of customers, and toelude the risks that may befall the investors, many financial companies devised a greatdeal of non-standard derivative securities, the so-called exotic options, which derivedfrom standard options. Being one of the typical non-standard derivative securities, Asianoption is the most active one in financial derivative market.The main goal of this paper is to study the typical representative of stronglypath-dependent option—Asian option. Because of strong path dependence, the pricing ofAsian option is very complicated. Meanwhile, as an innovation of European option, it hasclose relationship with the standard European option. Therefore, the research of thispaper should be based on the sympathetic, critical understanding of Black-ScholesOption Pricing Model.This paper contains two main research works: The first one is to establish a modelfor the pricing of target asset option on the presumption that the fluctuation of their priceis subjected to the geometric Brownian Motion, and to procure, under the Black-Scholesenvironments, a closed form analytic pricing formula of European weighted geometricaverage Asian option. The second one is to discuss the relationship between the profitand the risk of investing by virtue of the European call option and the rising geometricaverage Asian option in terms of the Black-Scholes option pricing theory;and to givefurther analysis of the closing price data of 10 shares of ShangHai stock exchange andShenZhen stock exchange, which were chosen at random. Therefore, it can be concludedthat the risk is less when investment is made by means of geometric average Asian optionthan European call option. This is also in line with the design of geometric average Asianoption.