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.
After revision:  When applied to SPX data, the estimated model and implied distributions produce variance swap rates that are consistent with the VIX volatility index. The implied densities are relatively stable over time and pick up some of the monthly effects that occur from option expiration.