Nonparametric Option Implied Tail Risk and Market Returns

Abstract

We propose a non-parametric method based on a model-free formula to evaluate the tails of a risk-neutral distribution using the full cross-section of option prices at a fixed horizon. The method leads to the joint estimation of risk-neutral tail probabilities and tail expectations beyond the minimum and maximum strike prices. We confirm the accuracy of the risk-neutral tail measures using simulated data. 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 left tail conditional expectation to a physical measure of tail risk significantly predicts the equity risk premium at longer return horizons of six months to twelve months with a significant improvement in ex- planatory power when compared to using the physical tail risk measure alone. We also find that both the risk-neutral left and right tail conditional expectations significantly predict the one-month ahead variance risk premium.