Closed-Form Analytic Pricing and Hedging of Arithmetic Asian Options Using a Reciprocal Gamma Distribution
17 Pages Posted: 6 Jun 1997
Date Written: May 27, 1997
In this paper we develop a better approximation for the price and hedging parameters of an arithmetic Asian option. We demonstrate that the distribution of the sum of a sequence of asset prices can be better approximated by the Reciprocal Gamma (as opposed to Lognormal) density function. In fact, in the limit, the distribution of the sum converges precisely to the Reciprocal Gamma density. Consequently, we are able to obtain a closed-form analytic expression for the price and hedging parameters of an Asian option which is theoretically justified, as well as more accurate, than the widely used lognormal approximation. We compare our results with previously published tables and formulas (that have appeared in RISK) and conclude that, not only is our formula easy-to-use and explain, our method is at least as good as any other algorithm available in the literature.
JEL Classification: G13
Suggested Citation: Suggested Citation