Recovering Probability Distributions from Option Prices
University of California, Berkeley - Haas School of Business
Jens Carsten Jackwerth
University of Konstanz - Department of Economics
J. OF FINANCE, Vol. 51 No. 5, December 1996
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
Date posted: October 24, 1996