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.
Group for Research in Decision Analysis