Directly pricing VIX futures: the role of dynamic volatility and jump intensity

ABSTRACT

We extend the direct pricing framework and propose a new generalized model for VIX futures by adding the time-varying component volatility as well as jump intensity to the logarithm of underlying VIX series. We also switch to the normal jump component on which the simpler and faster analytical filter can be applied. Compared with the nested benchmark models, these extensions are supported by significant pricing performance improvements both in- and out-of-sample. In particular, our generalized model can reduce the pricing errors substantially in the high VIX level period and for long maturity contracts. Our research highlights the importance of those newly added features of the VIX series when pricing VIX derivatives.

KEYWORDS:

• VIX futures
• volatility components
• dynamic jump intensity
• analytical filter

JEL CLASSIFICATION:

• C19
• C22
• C80

Acknowledgments

The authors thank Prof. David Peel (the editor) and two anonymous referees, whose suggestions help a lot to improve the article. The authors also claim financial supports from the National Natural Science Foundation of China (71871060 and 72071046).

Disclosure statement

No potential conflict of interest was reported by the author(s).

Notes

¹ CV corresponds to the DHAR model in Yin, Bian, and Wang (2021).

² CVCJ corresponds to the DHAR-Kou model in Yin, Bian, and Wang (2021) and the only difference is that the jump size in theirs follows the double exponential distribution proposed by Kou (2002).

³ We also calculate the mean percentage error (MPE) and mean absolute percentage error (MAPE) that are expressed as a ratio of the VIX futures market price. The conclusions from these two measures are not changed and the results can be provided upon request.

⁴ As MAE and RMSE draw a similar conclusion, the more popular measure RMSE is used to give an illustration.

⁵ To verify that the out-of-sample pricing performances are robust to the different choices of estimation window length and the updated frequency, we conduct alternative analyses based on the rolling window of 252 and 504 trading days with the parameters updated every 44 and 22 trading days, respectively. The conclusions from these two settings are quite similar and the results can be provided upon request.

Additional information

Funding

The work was supported by the National Natural Science Foundation of China [71871060,72071046].