Pricing the CBOE VIX Futures with the Heston–Nandi GARCH Model

We propose a closed-form pricing formula for the Chicago Board Options Exchange Volatility Index (CBOE VIX) futures based on the classic discrete-time Heston–Nandi GARCH model. The parameters are estimated using several sets of data, including the S&P 500 returns, the CBOE VIX, VIX futures prices and combinations of these data sources. Based on the resulting empirical pricing performances, we recommend the use of both VIX and VIX futures prices for a joint estimation of model parameters. Such estimation method can effectively capture the variations of the market VIX and the VIX futures prices simultaneously for both in-sample and out-of-sample analysis.