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

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

“…Different from the above studies on the pricing of VIX futures by modeling the underlying asset stock price index, Yin et al (2021) proposed directly pricing VIX futures by modeling the logarithm of VIX based on the HAR model and pointed out the importance of using the information contained in VIX itself. Wang et al (2022) extended the direct pricing framework and proposed a new model for VIX futures by adding dynamic volatility with long‐ and short‐run components and dynamic jump intensity. Actually, this idea of a “direct pricing method” arose from volatility derivatives pricing by modeling the VIX logarithm under the continuous‐time model (Kaeck & Alexander, 2013; Mencía & Sentana, 2013; Park, 2016; Zang et al, 2017).…”

“…At present, there are two main categories of literature about VIX derivatives pricing. One is to model the S&P 500 index under continuous‐time stochastic volatility models (Zhang et al, 2010; Zhang & Zhu, 2006; S. P. Zhu & Lian, 2012; Zhu & Zhang, 2007) or based on discrete‐time Generalized AutoRegressive Conditional Heteroskedasticity (GARCH)‐type models (Guo & Liu, 2020; Wang et al, 2017; Xie et al, 2020; Yang & Wang, 2018; Yang et al, 2019), and the other way is to directly model VIX (the underlying asset of VIX futures; Kaeck & Alexander, 2013; Mencía & Sentana, 2013; Park, 2016; Wang et al, 2022; Yin et al, 2021; Zang et al, 2017). Compared with the former modeling method, the latter, also called the direct pricing method, does not require integration, which can effectively overcome the time‐consuming and sometimes inaccurate integration problems.…”

“…In contrast, our newly proposed method avoids the assumption of certain dynamics for the underlying stock index. Compared with Yin et al (2021) and Wang et al (2022), we assume that the conditional variance of the VIX logarithm depends on the observable dynamic jumps, which can make full use of the high-frequency information of the VIX itself. To the best of our knowledge, this is the first study to consider the high-frequency data of VIX in terms of VIX futures pricing.…”

Forecasting realized volatility: New evidence from time‐varying jumps in VIX

“…In addition, the occurrence of these jumps raises the probability of extreme movements in the underlying asset returns (Aït-Sahalia & Hurd, 2015;Bandi & Reno, 2016). Some recent studies (Wang et al, 2022;Yin et al, 2021) also argue that jumps in VIX are important for capturing the shocks of large and rare events, which will reinforce the pricing accuracy when the while numerous studies (Andersen et al, 2007;Busch et al, 2011;Corsi et al, 2010;Forsberg & Ghysels, 2007;Giot & Laurent, 2007) consider splitting up RV into its continuous sample path (C) and jump (J) components to use them as separate regressors when forecasting future RV, this paper uses the JI of VIX index to propose a new HAR-RV model for forecasting the RV of S&P 500 returns. Based on our knowledge, this is first study to make this attempt.…”

“…The works ofWang et al (2022) andYin et al (2021) model the VIX index using the heterogeneous autoregressive (HAR) structure and conclude that such a process gives a sufficient description of the underlying VIX series when pricing VIX derivatives. These studies also document that while applying the HAR process, the incorporation of jumps in VIX generates reliable pricing performances under various market circumstances.…”