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Recovering an Asset's Implied PDF from Option Prices: An Application to Crude Oil during the Gulf Crisis

Published online by Cambridge University Press:  06 April 2009

William R. Melick  and
Charles P. Thomas
William R. Melick
Affiliation:
Staff economists in the Division of International Finance, Board of Governors of the Federal Reserve System, Washington, DC 20551.
Charles P. Thomas
Affiliation:
Staff economists in the Division of International Finance, Board of Governors of the Federal Reserve System, Washington, DC 20551.
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Abstract

We develop a general method for estimating the implied, martingale equivalent, probability density function (PDF) for futures prices from American options prices. The early exercise feature of American options precludes expressing the price of the option in terms of the PDF. There exist tight bounds for the price of American options in terms of the PDF. We demonstrate how these bounds, together with observed option prices, can be used to estimate the parameters of the PDF. We estimate the distribution for crude oil during the Persian Gulf crisis and find the distribution differs significantly from that recovered using standard techniques.

Type
Research Article
Information
Journal of Financial and Quantitative Analysis , Volume 32 , Issue 1 , March 1997 , pp. 91 - 115
Copyright
Copyright © School of Business Administration, University of Washington 1997

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