Mispricing of S&P 500 Index Options

Widespread violations of stochastic dominance by 1-month S&P 500 index call options over 1986-2006 imply that a trader can improve expected utility by engaging in a zero-net-cost trade net of transaction costs and bid-ask spread. Although precrash option prices conform to the Black-Scholes-Merton model reasonably well, they are incorrectly priced if the distribution of the index return is estimated from time-series data. Substantial violations by postcrash OTM calls contradict the notion that the problem lies primarily with the left-hand tail of the index return distribution and that the smile is too steep. The decrease in violations over the postcrash period of 1988-1995 is followed by a substantial increase over 1997-2006, which may be due to the lower quality of the data but, in any case, does not provide evidence that the options market is becoming more rational over time.