TITLE:
The Lognormal Characteristic Function in Several Dimensions, with Application to Asian Options
AUTHORS:
Andrew P. Leung
KEYWORDS:
Lognormal, Characteristic Function, Multidimensional, Complex Functions, Asian Options
JOURNAL NAME:
Journal of Mathematical Finance,
Vol.10 No.3,
August
14,
2020
ABSTRACT: 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.