Dark Matter in (Volatility and) Equity Option Risk Premiums

Abstract

Emphasizing the statistics of jumps crossing the strike and local time, we develop a decomposition
of equity option risk premiums. Operationalizing this theoretical treatment, we equip the pricing kernel process with unspanned risks, embed (unspanned) jump risks, and allow equity return volatility to contain unspanned risks. Unspanned risks are consistent with negative risk premiums for jumps crossing the strike and local time and imply negative risk premiums for out-of-the-money call options and straddles. The empirical evidence from weekly and fartherdated index options is supportive of our theory of economically relevant unspanned risks and reveals “dark matter” in option risk premiums.

Keywords: Unspanned equity volatility and jump risks, unspanned risks in the pricing kernel, dark matter, option risk premiums