Pricing VIX Futures under the GJR–GARCH Process: An Analytical Approximation Method

This paper proposes to study volatility index (VIX) futures pricing by directly modeling the logarithmic VIX while incorporating observable dynamic jumps of the VIX, which are derived based on VIX high-frequency data. The impacts of several different interday and intraday jump tests for VIX futures prices are investigated. We obtain the analytical expression by deducing the forward iteration relations of the lagged logarithm VIX, as well as the conditional variance and jump intensity, and use the maximum likelihood method to estimate the parameters under the risk-neutral measure. The empirical results prove the superiority of our newly proposed model (especially the model based on the LM jump test), which indicates that considering the heteroscedasticity effect of conditional variance, introducing VIX high-frequency data information and separating realized jump variation from the realized variance are very important to obtain much more accurate VIX futures pricing.

Section: Literature Reviewmentioning

confidence: 95%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

Directly pricing VIX futures with observable dynamic jumps based on high‐frequency VIX

Jiang

Qiao

et al. 2022

“…From Equation (6) we find that the dynamic of

{VIX}_{t}

is totally driven by the conditional volatility

h_{t + 1}

. Previous studies on approximating VIX futures, including those of Lin (2007) and Xie et al (2020), have always implemented the Taylor expansion, based on the level of volatility

h_{t + 1}

. This approach is used due to the linear specification in the relevant GARCH equation.…”

Section: The Realized Garch Modelmentioning

confidence: 99%

“…Yang et al (2019) focused on an affine jump-GARCH model. Xie et al (2020) developed an approximation method using the GJR-GARCH model. 6 Hsieh and Ritchken (2005) found better results in (SPX) option pricing with the nonaffine GARCH models than with the affine models.…”

mentioning

confidence: 99%

Pricing VIX options with realized volatility

Tong

Huang

2021

We investigate the role of realized volatility in pricing VIX options by using the generalized affine realized volatility (GARV) model, and the Realized generalized autoregressive conditionally heteroscedastic (GARCH) model. We develop a closed-form pricing formula for the (affine) GARV model. For the (nonaffine) log-linear Realized GARCH model, we introduce a novel approximation approach to derive its analytical pricing formula. Empirical results show that models with realized volatility significantly outperform competing models based on daily returns only, both in-and out-of-sample. The Realized GARCH model offers the best pricing performance, as it has fewer constraints and a more flexible modeling structure.

VIX futures pricing based on high‐frequency VIX: A hybrid approach combining SVR with parametric models

Qiao

Jiang

2023

We propose a novel hybrid approach for volatility index (VIX) futures pricing by combining support vector regression (SVR) with parametric models. Realized semivariances calculated based on high‐frequency VIX are used to characterize the asymmetric shocks of VIX, and the direct pricing framework of the heterogeneous autoregressive model is extended by incorporating realized semivariances. VIX futures prices are first obtained via parametric models, then the predicted prices and realized semivariances are input into SVR to obtain the final predicted values. Empirical results indicate that the combination of SVR with parametric models significantly improves the pricing ability. This indicates the important information of high‐frequency VIX and the necessity of combining machine learning methods with parametric models to obtain more accurate predictions.