VIX term structure and VIX futures pricing with realized volatility

Using an extended LHARG model proposed by Majewski et al. (2015, J Econ, 187, 521–531), we derive the closed‐form pricing formulas for both the Chicago Board Options Exchange VIX term structure and VIX futures with
different maturities. Our empirical results suggest that the quarterly and yearly components of lagged realized volatility should be added into the model to capture the long‐term volatility dynamics. By using the realized volatility based on high‐frequency data, the proposed model provides superior pricing performance compared with the classic Heston–Nandi GARCH model under a variance‐dependent pricing kernel, both in‐sample and out‐of‐sample. The improvement is more pronounced during high volatility periods.