Mispricing of S&P 500 index options

We document widespread violations of stochastic dominance in the one-month S&P 500 index options market over the period 1986-2002. These violations imply that a trader can improve her expected utility by engaging in a zero-net-cost trade. We allow the market to be incomplete and also imperfect by introducing transactions costs and bid-ask spreads. There is higher incidence of violations by OTM than by ITM calls, contradicting the common inference drawn from the observed implied volatility smile that the problem lies with the left-hand tail of the index return distribution. Even though pre-crash option prices conform to the BSM model reasonably well, they are incorrectly priced. Over 1997-2002, many options, particularly OTM calls, are overpriced irrespective of which time period is used to determine the index return distribution. These results do not support the hypothesis that the options market is becoming more rational over time. Finally, our results dispel another common misconception, that the observed smile is too steep after the crash: most of the violations by post-crash options are due to the options being either underpriced over 1988-1995, or overpriced over 1997-2002.