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RWP 23-02, March 2023

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.

JEL classifications: C52, C58, G12, G17, G41, Q47

Article Citation

  • Brown, Jason P., Nida Çakır Melek, Johannes Matschke, and Sai A. Sattiraju. 2023. “The Missing Tail Risk in Option Prices.” Federal Reserve Bank of Kansas City, Research Working Paper no. 23-02, March. Available at External Link


Jason P. Brown

Vice President and Economist

Jason Brown is a Vice President and Economist in the Economic Research Department of the Federal Reserve Bank of Kansas City. In this role, he coordinates the regional and commod…

Nida Çakır Melek

Senior Economist

Nida Çakır Melek is a senior economist in the Economic Research Department of the Federal Reserve Bank of Kansas City. She joined the Bank in August 2013 after receiving her Ph.D…

Johannes Matschke


Johannes Matschke is an economist in the Macroeconomics and Monetary Policy Division at the Federal Reserve Bank of Kansas City. He joined the Bank in 2021 after obtaining his Ph…