VIX Futures Research Articles

On the analysis of time-varying causality between VIX exchange-traded products and VIX futures contracts in high and low volatility regimes

PurposeThe authors analyse the nature of nonlinear long-run causal dynamics between VIX futures and exchange-traded products (ETPs).Design/methodology/approachNonlinear long-run causal relations between daily price movements in ETPs and futures are established through a Markov switching vector error correction model (MS-VECM).FindingsThe authors observe time variation in causality with the volatility of volatility. In particular, demand pressures for VIX ETNs and futures can change in different regimes. The authors observe two regimes where regime 1 is classified as low-mean low-volatility, while regime 2 is classified as high-mean high-volatility. The convergence to the long-run equilibrium in the low-mean low-volatility regime is faster than the high-mean high-volatility regime. The nature of the time varying lead lag relations demonstrates the opportunities for arbitrage.Originality/valueThe linear causal relations between VXX and VIX futures are well established, with leads and lags generally found to be short-lived with arbitrage relations holding. The authors go further to capture the time-varying causal relationships through a Markovian process. The authors establish the nonlinear causal relations between inverse and leveraged products where causal relations are not yet documented.

Which Way Does the Wind Blow Between SPX Futures and VIX Futures?

ABSTRACTThe negative correlation between returns and volatility is well known. However, there is no consensus on whether returns cause changes in volatility or vice versa. In this paper, we investigate the contemporaneous relation between the VIX futures and E‐mini S&P 500 futures markets with the aim of shedding new light on the relation between market returns and implied volatility. We use the E‐mini S&P 500 futures (often referred to as SPX futures) as a proxy for stock market returns and VIX futures as a proxy for expectations of implied volatility. We consistently find that stock returns cause changes in expectations of implied volatility. To estimate the coefficients of interest, we use an identification through heteroskedasticity approach which takes advantage of predictable intraday shifts in volatility in the two futures markets.

Analytical computation of conditional moments in the extended Cox–Ingersoll–Ross process with regime switching: Hybrid PDE system solutions with financial applications

In this paper, we introduce a novel analytical approach for the computation of the nth conditional moments of an m-state regime-switching extended Cox–Ingersoll–Ross process driven by a continuous-time finite-state irreducible Markov chain. This approach is applicable for all integers n≥1 and m≥1, thereby ensuring wide-ranging utility. The key of our investigation is a complex hybrid system of inter-connected PDEs, derived through a utilization of the Feynman–Kac formula for regime-switching diffusion processes. Our exploration into the solutions of this hybrid PDE system culminates in the derivation of exact closed-form formulas for the conditional moments for diverse values of n and m. Additionally, we study the asymptotic characteristics of the first conditional moments for the 2-state regime-switching Cox–Ingersoll–Ross process, particularly focusing on the effects of the symmetry inherent in the Markov chain’s intensity matrix and the implications of various parameter configurations. Highlighting the practicality of our methodology, we conduct Monte Carlo simulations to not only corroborate the accuracy and computational efficacy of our proposed approach but also to demonstrate its applicability to real-world applications in financial markets. A principal application highlighted in our study is the valuation of VIX futures and VIX options within a dynamic, mean-reverting, hybrid regime-switching framework. This exemplifies the potential of our analytical method to significantly impact contemporary financial modeling and derivative pricing.

Pricing VIX Futures and Options With Good and Bad Volatility of Volatility

ABSTRACTThis article studies the pricing of VIX futures and options by directly modeling the dynamics of VIX, based on realized semivariances computed from high‐frequency data of VIX. We derive the closed‐form pricing formula for both the VIX futures and options. The empirical results show that the new model provides superior pricing performance compared with the model based on conventional unsigned realized variance and the classic Heston‐Nandi GARCH model, both in sample and out of sample. Our study confirms that the decomposition of realized variance into upside and downside components helps to improve the pricing performance for VIX futures and options.

Trading activity of VIX futures and options around FOMC announcements

This research investigates the information content of volatility trading in VIX derivatives under a high-frequency framework. We provide empirical evidence that the abnormal order imbalances of VIX futures and call (put) options are significantly negative (positive) during FOMC embargoes. Our results remain robust under various empirical approaches for examining FOMC announcements. We also find that the VIX return (trading volume) is negatively (positively) associated with FOMC announcements. Overall, we document short-lived informational advantages in the VIX derivatives market and provide evidence of potential information leakage during FOMC embargoes.

Pricing VIX futures with mixed frequency macroeconomic information

This paper develops a new mixed frequency macro affine stochastic volatility (MacroSV) model and presents a closed-form formula for pricing VIX futures. In our model, the variance is decomposed into long-run and short-run components and the long-run component is driven by the macroeconomic variables. The result from the Monte Carlo experiment shows that the new model outperforms the benchmark model in terms of VIX futures pricing. The results of MacroSV-type models suggest that there is a significant relationship between the volatility and macroeconomic variables. The in-sample forecast results indicate that the models with mixed frequency macroeconomic information outperform the benchmark Heston model. For the out-of-sample pricing, the MacroSV model with the economic information of PPI for the United States has an improvement of 16% over the Heston model.

Which Way Does the Wind Blow Between SPX Futures and VIX Futures?

Which Way Does the Wind Blow Between SPX Futures and VIX Futures?

Disturbed Correlations: On the varying Sensitivity of VIX Futures to Extreme S&P 500 Returns

Disturbed Correlations: On the varying Sensitivity of VIX Futures to Extreme S&P 500 Returns

When passive funds affect prices: evidence from volatility and commodity ETFs

Abstract This article studies exchange-traded funds’ (ETFs) price impact in the most ETF-dominated asset classes: volatility (VIX) and commodities. I propose a new way to measure ETF-related price distortions based on the specifics of futures contracts. This allows me to isolate a component in VIX futures prices that is strongly related to the rebalancing of ETFs. I derive a novel decomposition of ETF trading demand into leverage rebalancing, calendar rebalancing, and flow rebalancing, and show that trading against ETFs is risky. Leverage rebalancing has the largest effects on the ETF-related price component. This rebalancing amplifies price changes and exposes ETF counterparties to variance.

Forecasting VIX: the illusion of forecast evaluation criteria

The study uses daily realized volatility measures in order to gain forecast accuracy over stocks’ market implied volatility, as proxied by VIX Index. We evaluate forecast accuracy by incorporating a traditional statistical loss function, along with an objective-based evaluation criterion, that is the cumulative returns earned from the different HAR-type volatility models, through a simple yet effective trading exercise on VIX futures. Findings, illustrate how illusive the choice between the two metrics may be, as it ends in two contradicting results.

VIX MODELING FOR A MARKET INSIDER

In this paper, we extend the popular Barndorff–Nielsen–Shephard stochastic volatility model to the case of a pure-jump Ornstein–Uhlenbeck equation with non-vanishing stochastic mean-reversion level. Based on this setup, we derive representations for the squared VIX process and related VIX futures prices. Having these results at hand, we introduce an initially enlarged filtration which models the view of a VIX market insider who has knowledge about the future behavior of the stochastic mean-reversion level of the squared volatility process available. In this enlarged filtration framework, we infer an explicit representation for the anticipative VIX process and obtain the associated time dynamics. We finally investigate the pricing of variance swaps under both backward- and forward-looking information.

Global financial crisis, funding constraints, and liquidity of VIX futures

We explore the effect of funding constraints on the trading costs of VIX futures. With an increase in funding constraints during a crisis (non-crisis) period, we observe a corresponding increase (decrease) in the proportional effective spread, quoted spread, order cost, asymmetric information, and trade sizes. The leveraged traders play a possible channel in the relationship between funding constraints and trading costs. When leveraged traders face scarce capital during a crisis (non-crisis) period, they increase (decrease) their net long positions to increase (decrease) the hedging pressure that leads to an increase (decrease) in trading costs that decreases (increases) the liquidity.

Cryptocurrency Momentum and VIX premium

The cryptocurrency momentum premium, defined as the risk premium exposure to the cryptocurrencies with higher past return, is a key factor in the cryptocurrency market. In this paper, we investigate whether VIX, VIX premium (Cheng, 2019), or economic policy uncertainty (EPU) can predict changes in cryptocurrency momentum premiums. The empirical analysis indicates that higher VIX premiums can increase the one-month-ahead momentum premium, and that VIX and EPU levels are not predictors of momentum premiums. Overall, we demonstrate that uncertainty can affect the cryptocurrency momentum premium through VIX futures rather than VIX itself or news-based information (i.e., EPU).

The lead–lag relation between VIX futures and SPX futures

We analyze the lead–lag relation between VIX futures and SPX futures. The two futures markets are weakly connected when market volatility is low. By contrast, when volatility is high, their prices are highly negatively correlated, with VIX futures leading SPX futures. However, the tightness of the lead–lag relation prevents the formation of profitable trading strategies in a setup that includes transaction costs. An analysis of the time variation in the lead–lag relation finds that an improvement in the relative liquidity of one market strengthens the lead of that market. Moreover, the hedging activities of market makers influence the lead–lag relation.

Empirical performance of component GARCH models in pricing VIX term structure and VIX futures

Empirical performance of component GARCH models in pricing VIX term structure and VIX futures

Causality of price movements in VIX exchange-traded products and VIX futures contracts

PurposeThe authors analyse six actively traded VIX Exchange Traded Products (ETPs) including 1x long, −1x inverse and 2x leveraged products. The authors assess their impact on the VIX Futures index benchmark.Design/methodology/approachLong-run causal relations between daily price movements in ETPs and futures are established, and the impact of rebalancing activity of leveraged and inverse ETPs evidenced through causal relations in the last 30 min of daily trading.FindingsHigh frequency lead lag relations are observed, demonstrating opportunities for arbitrage, although these tend to be short-lived and only material in times of market dislocation.Originality/valueThe causal relations between VXX and VIX Futures are well established with leads and lags generally found to be short-lived and arbitrage relations holding. The authors go further to capture 1x long, −1x inverse as well as 2x leveraged ETNs and the corresponding ETFs, to give a broad representation across the ETP market. The authors establish causal relations between inverse and leveraged products where causal relations are not yet documented.

A general framework for a joint calibration of VIX and VXX options

We analyze the VIX futures market with a focus on the exchange-traded notes written on such contracts, in particular we investigate the VXX notes tracking the short-end part of the futures term structure. Inspired by recent developments in commodity smile modelling, we present a multi-factor stochastic-local volatility model that is able to jointly calibrate plain-vanilla options both on VIX futures and VXX notes, thus going beyond the failure of purely stochastic or simply local-volatility models. We discuss numerical results on real market data by highlighting the impact of model parameters on implied volatilities.

On the right jump tail inferred from the VIX market

This paper addresses the role of the right jump tail under the risk-neutral measure, as a proxy for fear-of-fear, in the return predictability implicit in the VIX market. A simulation establishes that the right jump tail dominates the left jump tail in explaining various risk measures and their associated term structures. Using VIX futures and options from 2006 until 2020, the superior predictive power for futures returns afforded by the variance-of-variance risk premium (VVRP) is shown to arise predominantly from the right jump tail risk. A separate consideration of the continuous and jump tail components of the VVRP outperforms the alternative models in an out-of-sample forecasting exercise and generates non-trivial economic value, especially over short horizons. However, the impact of right jump tail is weak on option returns and only evident for short maturities, suggesting that the fear component cannot be the sole factor explaining the observed losses incurred on the delta-hedged VIX options.

Cross-impact in Derivative Markets

Trading a financial asset pushes its price as well as the prices of other assets, a phenomenon known as cross-impact. The empirical estimation of this effect on complex financial instruments, such as derivatives, is an open problem, tackled in this issue�s cover article �Cross-impact in Derivative Markets� by Michael Benzaquen, Mehdi Tomas and Iacopo Mastromatteo. To address this, the authors consider a setting in which the prices of derivatives is a deterministic function of stochastic factors where trades on both factors and derivatives induce price impact. Benzaquen, Tomas and Mastromatteo show that a specific cross-impact model satisfies key properties which make its estimation tractable in applications. Using E-Mini futures, European call and put options and VIX futures, the authors estimate cross-impact and show our simple framework successfully captures some of the empirical phenomenology. Benzaquen et al�s framework for estimating cross-impact on derivatives may be used in practice for estimating hedging costs or building liquidity metrics on derivative markets.

Intraday momentum in the VIX futures market

This study examines intraday momentum in the unexplored VIX futures market and verifies its existence through various empirical tests. The intraday momentum of VIX futures appears to be robust across contracts with different expirations, intraday returns with different time intervals, different trading sessions, and multiple sub-periods. We propose that the hedging demand of VIX option market makers may contribute to the intraday momentum. Our empirical evidence shows that intraday momentum persists only when the net gamma exposure of VIX options is negative and the effect weakens when European investors are away from the market, supporting our proposed explanation. Strikingly, we also find that trading strategies based on intraday momentum can generate an average annualized return of up to nearly 18%.