Option Implied Tail Risk

We propose a model-free formula to evaluate the unspanned tails of a risk-neutral distribution. The method leads to the estimation of risk neutral tail probabilities and tail expectations beyond the minimum and maximum strike... [ view full abstract ]

We propose a model-free formula to evaluate the unspanned tails of a risk-neutral distribution. The method leads to the estimation of risk neutral tail probabilities and tail expectations beyond the minimum and maximum strike prices. We extract time series of left and right option implied tail risk measures from S\&P 500 index options. We find the ratio of risk-neutral (RN) left tail conditional expectation to a physical measure of tail risk significantly predicts the equity risk premium. We find that the RN left and right tail conditional expectations significantly predict the variance risk premium.