The Missing Tail Risk in Option Prices

This paper contributes to the literature on deviations from rational expectations in financial markets and to the literature on evaluating density forecasts. We first develop a novel statistic to evaluate the overall accuracy of distributional forecasts, and find two methods that yield accurate distributional forecasts. We then propose another statistic to examine the relative accuracy over the entire distribution range. Our results indicate more oil price realizations in the left tail than predicted. We argue that this finding points to a persistent behavioral forecasting bias and a departure from the rational expectations hypothesis. Investors hence underestimate left tail risk and under-insure against very low oil prices.