The jump leverage risk premium

Abstract

Jumps in asset prices are ubiquitous, yet the apparent high price of jump risk observed empirically is commonly viewed as puzzling. We develop new model-free short-time risk-neutral variance expansions, allowing us to clearly delineate the importance of jumps in generating both price and variance risks. We find that simultaneous jumps in the price and the stochastic volatility and/or jump intensity of the market commands a sizeable risk premium. The existence of “jump leverage” risk premium may be rationalized in the context of equilibrium-based models by jumps in the conditional moments of the underlying fundamentals and/or changes in investors' risk aversion.