Efficient Out-of-Sample Pricing of VIX Futures

Self Cite

We are the first to study the pricing and hedging of VIX options via Monte Carlo (MC) under GARCH(1,1) and Glosten–Jagannathan–Runkle GARCH(1,1) models. Our pricing is ab initio and out‐of‐sample and can be implemented in real time. Importantly, we propose the so‐called single‐option hedge error, a better measure than that of Bakshi et al., and suggest several techniques to expedite MC by over 1000 times, which rivals the potential speedup of quantum computers. Empirically, our proposed approach outperforms two types of benchmarks; further, the asymmetric Glosten–Jagannathan–Runkle outperforms the symmetric GARCH. Overall, our paper has both theoretical and practical implications.

“…Given Equation (2) and the law of iterated expectation, one can obtain the following variance‐VIX equation (Liu et al, 2015):

{X}_{t}^{2}={100}^{2}\times 365(c{v}_{t+1}+d)=C{v}_{t+1}+D,

c=\frac{1-{\xi }^{30}}{30(1-\xi )},d={V}_{L}(1-c),

C={100}^{2}\times 365c,D={100}^{2}\times 365d,

\xi =\alpha +\beta +0.5\gamma ,{V}_{L}=\omega /(1-\xi ),

where

{X}_{t}

denotes VIX on day t . Guo and Liu (2020) argue and we agree that it is easy and better to work with calendar days in Equation (3). Note that

{X}_{t}^{2}-D

is guaranteed to be positive if computed from Equation (3) with stable parameters (i.e.,

\xi \lt 1

) and positive

\omega

.…”

Section: Theoretical Frameworksupporting

confidence: 68%

Section: Vix-variance Equationmentioning

confidence: 60%

Section: Data Descriptionmentioning

confidence: 80%

Section: Hedging Errorsmentioning

confidence: 92%

“…Following Guo and Liu (2020), we use root mean square pricing errors (RMSE) and mean absolute pricing errors (MAE) to assess the performance of the pricing models. Specifically, RMSE is…”

Section: Out-of-sample Pricing Errorsmentioning

confidence: 99%

See 3 more Smart Citations

GARCH pricing and hedging of VIX options

Liu

Jiao

Guo

2022

Self Cite

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

Jiang

Qiao

et al. 2022

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.

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.