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Closed-Form Analytic Pricing and Hedging of Arithmetic Asian Options using a Reciprocal Gamma Distribution

17 Pages Posted: 6 Jun 1997  

Moshe A. Milevsky

York University - Schulich School of Business

Steven E. Posner

Morgan Stanley - United Kingdom Office

Date Written: May 27, 1997

Abstract

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

Milevsky, Moshe A. and Posner, Steven E., Closed-Form Analytic Pricing and Hedging of Arithmetic Asian Options using a Reciprocal Gamma Distribution (May 27, 1997). Available at SSRN: https://ssrn.com/abstract=37676 or http://dx.doi.org/10.2139/ssrn.37676

Moshe Arye Milevsky (Contact Author)

York University - Schulich School of Business ( email )

4700 Keele Street
Toronto, Ontario M3J 1P3
Canada

Steven Eli Posner

Morgan Stanley - United Kingdom Office

Cabot Square, Canary Whart
London, E14 4QW
United Kingdom

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