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

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 dist ribution results in systematic violations of the martingale restriction, th e implied index value from options consistently overestimating the market v alue. Adopting a generalized distribution, allowing for nonnormal third and fourth moments, produces economically insignificant rejections of the mart ingale restriction. A simulation analysis supports the empirical results fr om the lognormal model in the presence of nonnormal skewness and kurtosis, Overall, the results support the conclusion that the no-arbitrage assumptio n coupled with the generalized distribution offers a good working model for S&P index options over the period studied. (C) 1999 John Wiley & Sons, Inc .