Variance Risk Premium and VIX Pricing : A Simple GARCH Approach

This paper assesses variance risk premium and forecasts out-of-sample VIX under GARCH(1,1), GJR, and Heston-Nandi models. With the date-t GARCH parameters estimated in a moving window fashion from 3,500 daily returns of the S&P 500 index, a hypothetical date-t VIX turns out to be below the market VIX by 10.1~29.6% on average between January 1996 and January 2012. The out-of-sample underestimation could be interpreted as variance risk premium. Furthermore, parameters in conjectured formulas can be calibrated by the market VIX of Date t−1; these risk-neutral parameters forecast the date-t VIX accurately with errors of not more than 0.2% on average