The Lognormal Characteristic Function in Several Dimensions, with Application to Asian Options

摘要

Many attempts have been made to derive a simple expression for the characteristic function of the lognormal distribution. This would be useful for computing the sum of lognormal variables, either with each other, or with other statistical variables. In this paper , we provide a simple formula for the characteristic function, which is exact, closed and computable. An extension to the sum of correlated lognormals, used in the pricing of Asian options, is a consequence of this approach.