A Quasi-analytical Pricing Formula for Arithmetic Asian Options

Abstract

A quasi-analytical pricing method for arithmetic Asian option is presented based on an approximate relation between the geometric and arithmetic average of the log-normal random variables. With a generalized mean function, we use a Taylor expansion in terms of the geometric average value of the underlying assets to approximate the arithmetic average value. Hence, in pricing the arithmetic average Asian option, the density of the geometric average is used rather than that of the arithmetic average. In this way, the quasi-analytical formula for pricing arithmetic Asian option is derived. The accuracy of the method depends on the number of dates at which the asset prices are averaged when the maturity of the option is given, i.e. on the length of the interval between each two time points. The accuracy is desirable when the number is sufficiently large or the length of interval is sufficiently short.