On the valuation of Asian options: integral representations

Abstract

This paper derives integral representations for the Black-Scholes price of arithmetic-average Asian options. Their proof is by Laplace inverting the 1992 Laplace transform of Geman-Yor using complex analytic methods. The analysis ultimately rests on the gamma function which in this sense is at the base of Asian options. The results of Geman-Yor are corrected and their validitity is extended.