Driven by Fear? The Tail Risk Premium in the Crude Oil Futures Market∗

Oil prices are notoriously difficult to forecast and exhibit wild swings or “excess volatility ” that are difficult to rationalize by changes in fundamentals alone. This paper offers an explanation for these phenomena based on time varying disaster prob-abilities and disaster fears. Using information from crude oil options and futures we document economically large jump tail premia in the crude oil derivative market. These premia vary substantially over time and significantly forecast crude oil futures and spot returns. Our results suggest that oil futures prices overshoot (undershoot) in the pres-ence of upside (downside) tail fears in order to allow for smaller (larger) risk premia thereafter. We show that this overshooting (undershooting) is amplified for the spot price because of time varying benefits from holding inventory that work in the same direction. The novel oil price uncertainty measures yield additional insights into the relationship between the oil market and macroeconomic outcomes