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Do S&P 500 index options violate the martingale restriction?
Author(s) -
Strong Norman,
Xu Xinzhong
Publication year - 1999
Publication title -
journal of futures markets
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.88
H-Index - 55
eISSN - 1096-9934
pISSN - 0270-7314
DOI - 10.1002/(sici)1096-9934(199908)19:5<499::aid-fut1>3.0.co;2-o
Subject(s) - economics , martingale (probability theory) , index (typography) , econometrics , mathematical economics , financial economics , mathematics , statistics , computer science , world wide web
The study tests Longstaff's martingale restriction on S&P 500 index options over the period 1990–1994. Assuming the S&P index follows a lognormal distribution results in systematic violations of the martingale restriction, the implied index value from options consistently overestimating the market value. Adopting a generalized distribution, allowing for nonnormal third and fourth moments, produces economically insignificant rejections of the martingale restriction. A simulation analysis supports the empirical results from the lognormal model in the presence of nonnormal skewness and kurtosis. Overall, the results support the conclusion that the no‐arbitrage assumption coupled with the generalized distribution offers a good working model for S&P index options over the period studied. © 1999 John Wiley & Sons, Inc. Jrl Fut Mark 19: 499–521, 1999