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.

This paper proposes a simple but rich framework to directly price volatility index (VIX) futures by applying the heterogeneous autoregressive structure and asymmetric jumps to the logarithm of the VIX. Compared with other discrete‐time models, our model imposes fewer parameter constraints. The analytical solution is also free from time‐consuming and sometimes unstable numerical integration. Empirical results suggest that our model can significantly reduce pricing errors compared with existing models using realized variance, both in‐ and out‐of‐sample. The improvement indicates that besides looking for a better measure of current volatility, it is also important to utilize information embedded in the VIX itself.

The equity market is not trading around the clock, and the overnight information has been proved be important for understanding pricing anomalies, improving volatility forecasting accuracy, and so forth. However, there is little research investigating its impact on option pricing. In this paper, we provide a framework that integrates intraday, overnight returns, and realized volatility simultaneously within an augmented Autoregressive Volatility model. The analytical option-pricing formula for the new model is derived through the closed-form moment generation function. The empirical results based on S&P 500 index options show that distinguishing the overnight component from daily returns has the potential capability to reduce the pricing errors, both in-sample and out-of-sample.

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