We show that the compensation for rare events accounts for a large fraction of the average equity and variance risk premia. Exploiting the special structure of the jump tails and the pricing thereof, we identify and estimate a new Investor Fears index. The index reveals large time‐varying compensation for fears of disasters. Our empirical investigations involve new extreme value theory approximations and high‐frequency intraday data for estimating the expected jump tails under the statistical probability measure, and short maturity out‐of‐the‐money options and new model‐free implied variation measures for estimating the corresponding risk‐neutral expectations.

We derive tight pricing kernel restrictions from options with same‐day expiration (“0DTEs”). These restrictions concern the volatility of small and frequent asset price moves that the equity and options markets must agree on in a frictionless economy. Their violation leads to pseudo‐arbitrage opportunities, characterized by nontrivial reward‐to‐risk ratios over arbitrarily short horizons and achieved by a combined position in 0DTEs and the underlying asset. Empirically, we find no evidence of feasible pseudo‐arbitrage opportunities, as transaction costs, estimation risk, and short‐term volatility risk prevent investors from taking advantage of small and infrequent disagreements about volatility between equity and options markets.

We study short‐maturity (“weekly”) S&P 500 index options, which provide a direct way to analyze volatility and jump risks. Unlike longer‐dated options, they are largely insensitive to the risk of intertemporal shifts in the economic environment. Adopting a novel seminonparametric approach, we uncover variation in the negative jump tail risk, which is not spanned by market volatility and helps predict future equity returns. As such, our approach allows for easy identification of periods of heightened concerns about negative tail events that are not always “signaled” by the level of market volatility and elude standard asset pricing models.