The Pricing Of Discrete Arithmetic Average Asian Options

Asian option is a path-dependent option,it has the following advantages:It usually can be used to hedge the thinly traded assets within a certain period of time; Compared with the hedging portfolio of standard option,asian option’s price is cheaper; Its earnings depend on the average price of a certain period before the date of maturity,so its price is less affected by the execution day’s price,it also reduces the loss of companies by the insider trading.So asian option is one of the most active exotic option in financial markets,its pricing has became a hot issue in the pricing of financial derivatives.Many literatures have studied the pricing of Asian option, but the author generally choose Asian option in a row as the object in most of the research literatures. In the real market of options, however, trading of Asian option is in discrete state, so the research about the pricing of discrete Asian option has important theoretical significance and widespread practical significance.This paper introduces the origin and development of options, and respectively gives the pricing method of European and American options.On the basis of these,we come up with the concept and the classification of Asian option. Asian option has many kinds of classification,the main research object is Asian option of fixed price and discrete arithmetic average price in this paper.Under the assumption that the underlying stocks follows geometric Brownian motion,we get a approximate pricing formula of European-style Asian option by combining the risk neutral pricing theory and the second-order Taylor expansion.Then we compare the results of the approximate pricing formula with the results of the monte carlo simulation method.In addition, this paper uses binary tree model to study the pricing problem of the Asian option,due to the complexity of binary tree method, we find that it’s not suitable for the pricing of American Asian option.Finally, we use the control variable method, the paper puts forward a way to improve the pricing efficiency of the American Asian option.