Mispricing of S&P 500 Index Options

Abstract

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.