This paper investigates the information contained in S&P 500 returns, VIX levels, S&P 500 and VIX option prices. We develop a rigorous time-series estimation approach and provide an extensive model specification analysis. We find that the S&P 500 and VIX derivatives markets contain conflicting information on variance, especially in times of market stress. Furthermore, jumps and a stochastic level of reversion for the variance help reproduce the tails of returns and variance risk-neutral distributions as well as term structures of volatility smiles. Finally, we observe that they add significant value in representing variance risk premia accurately.
Groupe d’études et de recherche en analyse des décisions