CBOE VIX and Jump-GARCH option pricing models

We simulate the VIXs implied in GARCH option pricing models incorporating the variance and jump premiums. By estimating the parameters through a joint estimation as well as a risk-neutral estimation, we compare the implied VIXs with the CBOE VIX in terms of their error size and unbiasedness. Our empirical results show that the model incorporating both premiums can generate the implied VIX that is more consistent with the CBOE VIX: The errors of the model with both premiums are smaller than those of the other models, and the biasedness towards the CBOE VIX is also moderated. However, there is still a limit to explain the dynamics of the CBOE VIX and VIX options sufficiently even in the most flexible model. This finding is consistent with that of Bardgett et al. (2019) who show that S&P 500 and VIX derivatives contain conflicting information on variance. For robustness, we conduct an out-of-sample analysis by updating the estimation period and the evaluation period year-by-year, which also supports the result of an in-sample analysis.