This article investigates crash risk premiums in individual stocks using skewness swaps. These swaps involve buying a stock’s risk-neutral skewness and receiving the realized skewness as a payoff. The strategy’s returns, which measure the skewness risk premium, are found to be consistently large and positive. This suggests investors are concerned about potential crashes in individual stocks and require substantial compensation for bearing this risk. Notably, significant results are mainly observed after the 2007/2009 financial crisis, indicating changes in post-crisis option market dynamics. Cross-sectional determinants of skewness swap returns include measures of systematic crash risk and stock overvaluation.

Using a fast numerical technique, we investigate a large database of investors’ suboptimal nonexercise of short-maturity American call options on dividend-paying stocks listed on the Dow Jones. The correct modeling of the discrete dividend is essential for a correct calculation of the early exercise boundary, as confirmed by theoretical insights. Pricing with stochastic volatility and jumps instead of the Black–Scholes–Merton benchmark cuts the amount lost by investors through suboptimal exercise by one-quarter. The remaining three-quarters are largely unexplained by transaction fees and may be interpreted as an opportunity cost for the investors to monitor optimal exercise.