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Recovering Probability Distributions from Option Prices
Author(s) -
JACKWERTH JENS CARSTEN,
RUBINSTEIN MARK
Publication year - 1996
Publication title -
the journal of finance
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 18.151
H-Index - 299
eISSN - 1540-6261
pISSN - 0022-1082
DOI - 10.1111/j.1540-6261.1996.tb05219.x
Subject(s) - nonparametric statistics , probability distribution , index (typography) , smoothness , econometrics , probability density function , asset (computer security) , crash , standard deviation , mathematics , statistics , economics , computer science , mathematical analysis , computer security , world wide web , programming language
This article derives underlying asset risk‐neutral probability distributions of European options on the S&P 500 index. Nonparametric methods are used to choose probabilities that 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 percent (−46 percent) over a year) is about 10 (100) times more likely than under the assumption of lognormality.