Recovering Probability Distributions from Option Prices

J. OF FINANCE, Vol. 51 No. 5, December 1996

Posted: 24 Oct 1996  

Mark Rubinstein

University of California, Berkeley - Haas School of Business

Jens Carsten Jackwerth

University of Konstanz - Department of Economics

Abstract

This paper derives underlying asset risk-neutral probability distributions of European options on the S&P 500 index. Nonparametric methods are used to choose probabilities which minimize an objective function subject to requiring that the probabilities are consistent with observed option and underlying asset prices. Alternative optimization specifications produce approximately the same implied distributions. A new and fast optimization technique for estimating probability distributions based on maximizing the smoothness of the resulting distribution is proposed. Since the crash, the risk-neutral probability of a three (four) standard deviation decline in the index (about-36% (-46%) over a year) is about 10 (100) times more likely than under the assumption of lognormality.

JEL Classification: G1, G13

Suggested Citation

Rubinstein, Mark and Jackwerth, Jens Carsten, Recovering Probability Distributions from Option Prices. J. OF FINANCE, Vol. 51 No. 5, December 1996. Available at SSRN: https://ssrn.com/abstract=7849

Mark E. Rubinstein

University of California, Berkeley - Haas School of Business ( email )

545 Student Services Building, #1900
2220 Piedmont Avenue
Berkeley, CA 94720
United States
510-642-3580 (Phone)
510-643-1420 (Fax)

HOME PAGE: http://www.haas.berkeley.edu/finance/rubinste.html

Jens Carsten Jackwerth (Contact Author)

University of Konstanz - Department of Economics ( email )

Universitaetsstr. 10
Konstanz, 78457
Germany
+497531882196 (Phone)
+497531883120 (Fax)

HOME PAGE: http://cms.uni-konstanz.de/wiwi/jackwerth/

Paper statistics

Abstract Views
3,008