The Dark Matter in Equity Index Volatility Dynamics: Assessing the Economic Rationales for Unspanned Risks

Abstract

If the evolution of the equity price index, its volatility, and the pricing kernel were to be absent of unspanned risks, it would counterfactually imply that (i) the expected excess return of out-of-the-money calls on equity is positive and (ii) the expected excess return of straddles is zero. Remedying these contradictions, we equip the pricing kernel process with unspanned risks, embed (unspanned) jump risks, and allow return volatility to contain unspanned risks. The empirical evidence from weekly and farther-dated options is supportive of our theory of economically relevant unspanned risks, and reveals “dark matter” in option risk premiums.