This paper studies the "overpriced puts puzzle" — the finding that historical prices of the S&P 500 put options have been too high and incompatible with the canonical asset-pricing models. To investigate whether put returns could be rationalized by another, possibly non-standard equilibrium model, we implement the model-free methodology of Bondarenko [2003a, Statistical Arbitrage and Securities Prices, Review of Financial Studies 16, 875–919]. The methodology requires no parametric assumptions on investors' preferences. Furthermore, it can be applied even when the sample is affected by certain selection biases (such as the Peso problem) and when investors' beliefs are incorrect. The main finding of the paper is that no model within a studied class of models can possibly explain the put anomaly.

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The notion of model-free implied volatility (MFIV), constituting the basis for the highly publicized VIX volatility index, can be hard to measure with accuracy due to the lack of precise prices for options with strikes in the tails of the return distribution. This is reflected in practice as the VIX index is computed through a tail-truncation which renders it more compatible with the related concept of corridor implied volatility (CIV). We provide a comprehensive derivation of the CIV measure and relate it to MFIV under general assumptions. In addition, we price the various volatility contracts, and hence estimate the corresponding volatility measures, under the standard Black-Scholes model. Finally, we undertake the first empirical exploration of the CIV measures in the literature. Our results indicate that the measure can help us refine and systematize the information embedded in the derivatives markets. As such, the CIV measure may serve as a tool to facilitate empirical analysis of both volatility forecasting and volatility risk pricing across distinct future states of the world for diverse asset categories and time horizons.