VIX forecasting and variance risk premium: A new GARCH approach

•Innovatively, GARCH is utilized to forecast one-day out-of-sample VIXs.•Variance risk premium is assessed by three GARCH models.•Before 22 September 2003, variance risk premium is about 20–30%.•After 22 September 2003, variance risk premium is about 10–13%.•Risk-neutral GARCH models forecast out-of-sample VIXs with errors within ±0.3%.

This paper proposes to forecast VIX under GARCH(1,1), GJR, and Heston–Nandi models, and to assess variance risk premium innovatively. The one-day out-of-sample VIXs, computed with traditional empirical GARCH parameters, turn out to be below the market VIXs by roughly 20–30% (10–13%) on average before (after) 22 September 2003. The underestimation is interpreted as a kind of variance risk premium, which for the later part of the data turns out to be significantly smaller. On the other hand, risk-neutral GARCH models can be obtained by calibration against the prior-day market VIX. For the same dataset, the risk-neutral parameters forecast the one-day out-of-sample VIXs with errors within −0.30 to 0.03% on average.