Do S&P 500 index options violate the martingale restriction?

Norman Strong, Xinzhong Xu

Research output: Contribution to journalArticlepeer-review


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.
Original languageEnglish
Pages (from-to)499-521
Number of pages22
JournalJournal of Futures Markets
Issue number5
Publication statusPublished - Aug 1999


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