Before revision:  When applied to SPX  data, the estimated model and implied distributions produce variance swap rates that are consistent with the VIX , and also pick up some of the monthly effects that occur from option expiration. We find that parsimony of the Heston model is beneficial because we are able to decipher behavior in estimated parameters and implied measures, whereas the richer Heston model with jumps produces a better fit but also has implied behavior that is less revealing .
After revision:  When applied to SPX data, the estimated model and implied distributions produce variance swap rates that are consistent with the VIX , and also pick up some of the monthly effects that occur due to the options' expiration, indicating that the volatility-uncertainty premium could experience cyclic effects due to the maturity date of the options .