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

If the evolution of equity index volatility and the pricing kernel were to be absent of risks unspanned by index futures, it would counterfactually imply that (i) the expected excess return of OTM calls on futures is positive, (ii) the expected excess return of straddles is approximately zero, and (iii) futures returns and changes in volatility are perfectly correlated. Remedying these contradictions, we consider a specification of market incompleteness that equips the pricing kernel and volatility dynamics with unspanned risks and generates negative local time risk premiums. The empirical evidence is supportive of our theory of economically relevant unspanned risks