VIX Futures Research Articles

Instantaneous squared VIX and VIX derivatives

AbstractIn this paper, we propose a parsimonious and efficient model to price derivatives written on VIXs with different horizons. Our model is built on Luo and Zhang's (2012, J Futures Markets, 32, 1092–1123) concept of the instantaneous squared VIX (ISVIX) that is the sum of instantaneous diffusive and jump variances of the SPX return. Modeling the ISVIX as a mean‐reverting jump‐diffusion process with a stochastic long‐term mean, we obtain analytical formulas for VIX options and futures. Estimation with VIX term structure and calibration with VIX options data show that our model performs well in matching both time series and cross‐sectional VIX derivatives market prices.

Practical Applications of Hedging High-Yield and Emerging Market Bond Tail Risk With VIX® Futures

Practical Applications Summary In Hedging High-Yield and Emerging Market Bond Tail Risk with VIX® Futures, published in the Fall 2019 issue of The Journal of Alternative Investments, Berlinda Liu and Hong Xie (S&P Dow Jones Indices) suggest a different approach to hedging tail risk in certain segments of the fixed-income market. VIX® futures are based on the implied volatility of equities and therefore are not an obvious choice for hedging the tail risk of bonds. Nevertheless, the authors show that there is a negative correlation between returns for high-yield bonds and VIX futures, and the strength of the inverse relationship increases during down markets. The same holds true for emerging market bonds. This should not be too surprising given that credit risk is positively correlated with equity market risk. In this light, VIX becomes a viable alternative hedging instrument for bonds with significant credit risk. The question then becomes how much does this protection cost? Because there are significant roll costs associated with VIX futures, a static hedge will create a drag on returns—but a dynamic hedge can effectively reduce losses during times of stress.

Hedging High-Yield and Emerging Market Bond Tail Risk with VIX® Futures

In this article, the authors suggest a different approach to hedging tail risk in certain segments of the fixed-income market. VIX^® futures are based on the implied volatility of equities and therefore are not an obvious choice for hedging the tail risk of bonds. Nevertheless, the authors show that there is a negative correlation between returns for credit-focused bonds and VIX futures, and the strength of the inverse relationship increases during down markets, precisely when the hedge is most needed. This should not be too surprising given that credit risk is positively correlated with equity market risk. In this light, VIX futures, tradable instruments linked to the VIX, become a viable alternative hedging instrument for bonds with significant credit risk. Because there are significant roll costs associated with VIX futures during non-stressed periods, a static hedge will create a drag on returns, but a dynamic hedge can effectively reduce credit-focused bond losses during times of stress. <b>TOPICS:</b>Emerging markets, tail risks, futures and forward contracts

A dimension‐invariant cascade model for VIX futures

AbstractWe propose a new stochastic volatility model by allowing for a cascading structure of volatility components. The model, under a minor assumption, allows us to add as many components as desired with no additional parameters, effectively defeating the curse of dimensionality often encountered in traditional models. We derive a semi‐closed‐form solution to the VIX futures price, and find that our six‐factor model with only six parameters can closely fit spot VIX and VIX futures prices from 2004 to 2015 and produce out‐of‐sample pricing errors of magnitudes similar to those of in‐sample errors.

Forecasting and trading on the VIX futures market: A neural network approach based on open to close returns and coincident indicators

Previous work has highlighted the difficulty of obtaining accurate and economically significant predictions of VIX futures prices. We show that both low prediction errors and a significant amount of profitability can be obtained by using a neural network model to predict VIX futures returns. In particular, we focus on open-to-close returns (OTCRs) and consider intraday trading strategies, taking into account non-lagged exogenous variables that closely reflect the information possessed by traders at the time when they decide to invest. The neural network model with only the most recent exogenous variables (namely, the return on the Indian BSESN index) is superior to an unconstrained specification with ten lagged and coincident regressors, which is actually a form of weak efficiency involving markets of different countries. Moreover, the neural network turns out to be more profitable than either a logistic specification or heterogeneous autoregressive models.

VIX Futures as a Market Timing Indicator

Our work relates to the literature supporting that the VIX also mirrors investor sentiment and, thus, contains useful information regarding future S&amp;P500 returns. The objective of this empirical analysis is to verify if the shape of the volatility futures term structure has signaling effects regarding future equity price movements, as several investors believe. Our findings generally support the hypothesis that the VIX term structure can be employed as a contrarian market timing indicator. The empirical analysis of this study has important practical implications for financial market practitioners, as it shows that they can use the VIX futures term structure not only as a proxy of market expectations on forward volatility, but also as a stock market timing tool.

Forecasting returns in the VIX futures market

This paper introduces a new forecasting model for VIX futures returns. The model is structural in nature and parsimonious, and contains parameters that are relatively easy to estimate. The forecasts of next day VIX futures returns based on this model are superior to those produced by a linear forecasting model that uses the same set of predictors. Moreover, the profits to a market-timing model based on the proposed forecasts are statistically and economically significant, and are robust to both the method used for adjusting for risk and transaction costs (up to around 15 basis points). In contrast, the forecasts generated by the linear forecasting model are not.

Derivatives pricing when supply and demand matter: Evidence from the term structure of VIX futures

AbstractWe decompose the VIX futures term structure into systematic components driving the VIX and idiosyncratic components reflecting demand by various types of futures end‐users. We model two distinct channels by which trading activity manifests itself into futures prices: a contemporaneous “level effect” across the term structure due to the aggregate size of nondealer net demand and a mean‐reverting “roll effect” due to large trades in specific contracts. The observed futures term structure was, on average, higher and steeper than it would have been in the absence of the observed nondealer demand, but the impact varies in sign and magnitude over time.

The Joint S&amp;amp;P 500/VIX Smile Calibration Puzzle Solved

Since VIX options started trading in 2006, many researchers have tried to build a model that jointly and exactly calibrates to the prices of S&P 500 (SPX) options, VIX futures and VIX options. So far the best attempts, which used parametric continuous-time jump-diffusion models on the SPX, only produced an approximate fit. In this article we solve this longstanding puzzle using a completely different approach: a nonparametric discrete-time model. Given a VIX future maturity T1, we build a joint probability measure on the SPX at T1, the VIX at T1, and the SPX at T2 = T1 + 30 days which is perfectly calibrated to the SPX smiles at T1 and T2, and the VIX future and VIX smile at T1. Our model satisfies the martingality constraint on the SPX as well as the requirement that the VIX at T1 is the implied volatility of the 30-day log-contract on the SPX. We prove by duality that the existence of such a model means that the SPX and VIX markets are jointly arbitrage-free. The joint calibration puzzle is cast as a dispersion-constrained martingale transport problem which is solved using (an extension of) the Sinkhorn algorithm, in the spirit of De March and Henry-Labordere (2019). The algorithm identifies joint SPX/VIX arbitrages should they arise. Our numerical experiments show that the algorithm performs very well in both low and high volatility regimes. Finally we explain how to handle the fact that the VIX future and SPX option monthly maturities do not perfectly coincide, and how to extend the two-maturity model to include all available monthly maturities.

Selling VIX Futures and Options for Portfolio Return Enhancement

The term structure of VIX futures is generally upward sloping. The persistent VIX contango may result in abnormally strong performance for VIX futures selling or VIX call writing strategies. However, the high volatility of volatility and significant jump risk may expose short uncovered VIX positions to extreme tail risk. In this paper we consider the performance of VIX futures and call option selling in a portfolio context in 2008 and 2016 as well as over a 10+ year period beginning in 2006. In addition, we consider alternative strategies including VIX futures spread strategies, and the dynamically de-levering VIX futures selling strategies represented by the VPD and VPN indexes. The VPD Index had annual returns that were much higher than those of the S&P 500 Index in 2009 and 2016 (years without large spikes in VIX), but the VPD returns were lower than those of the S&P 500 in 2008 and 2018, years with significant upward spikes in the VIX Index. While the goal of the study is not to make a particular recommendation for a VIX-based investment strategy, meaningful portfolio return enhancements are possible over particular time periods with small allocations to VIX selling. A large allocation to uncovered selling of VIX instruments could have substantial volatility jump risk exposure which can result in economically meaningful and potentially catastrophic losses. However, the VPN Index - which sells VIX futures, holds money market instruments and buys VIX calls – had lower volatility and less severe maximum drawdowns than the stock and commodity benchmark indexes studied in the period of analysis.

The Portfolio Diversification Potential of Long VIX Futures and Options Strategies

It is well established that the VIX Index tends to be negatively correlated with equity markets. This suggests that VIX futures and options may have the potential to provide significant diversification benefits for traditional portfolios. However, since the term structure of VIX futures is generally upward sloping, long VIX futures positions can place a significant drag on portfolio performance. In this paper we consider the performance of strategies that buy VIX futures or VIX call options in a portfolio context in 2008 and 2016, as well as over a 10+ year period from 2006 to 2017. In addition, we consider alternative strategies including long S&P 500® protective put strategies and the dynamic S&P 500 plus VIX call buying strategy of the VXTH index. Meaningful portfolio diversification benefits for risk-averse investors are possible over particular time periods with small allocations to long VIX futures or call options, but there can be substantial portfolio drag if large allocations are made over long time periods during which there are flat to rising stock markets.

Transitory Fear: Explaining Changes in the VIX Futures Basis

Following the 2004 introduction of VIX futures, they have become an increasingly important hedging instrument and aid for portfolio diversification. We examine changes in the futures basis which, owing to their unique characteristics, can be interpreted as changes in expectations of future VIX (“fear”) levels. We find that higher levels of VIX are associated with a narrowing of the futures basis, suggesting that investors view “fear” as transitory, and a flatter forward curve. We propose news sentiment as one plausible explanation for changes in the basis. A wider (narrower) basis accompanies the more positive (negative) news associated with a falling (rising) VIX index.

A Dimension-invariant Cascade Model for VIX Futures

We propose a new model of volatility by allowing for a cascading structure of volatility components. The cascading feature is achieved by introducing an increasing structure to the speed of mean reversion. It allows us to add as many components as desired with no additional parameter, effectively defeating the curse of dimensionality often seen in traditional models. The flexibility in choosing the number of components enables rich dynamics in the term structure of both spot VIX and VIX futures, without the need to introduce price jumps. We derive a semi-closed form solution to the VIX futures price, and find that our 6-factor model with only 6 parameters can closely fit spot VIX and VIX futures data from 2004 to 2015 and produce out of sample pricing errors of magnitudes similar to those of in-sample errors.

Does increased hedging lead to decreased price efficiency? The case of VIX ETPs and VIX futures

AbstractWe examine the impact of the introduction of VIX exchange‐traded products (ETPs) on the information content and pricing efficiency of VIX futures. We document that trades in VIX futures have become less informative and that pricing errors exhibit more persistence after the introduction of VIX ETPs. In addition, we observe that the price process of the VIX futures has become noisier over time. These findings suggest that the introduction of the VIX ETPs had a prominent effect on the properties and dynamics of the VIX futures.

Pricing Bermudan Variance Swaptions Using Multinomial Trees

In a recent study, Zhao et al. (2017) presented a tree methodology to evaluate the expected generalized realized variance in a general stochastic volatility model; it provided an efficient way of calculating the fair value of the strike for variance swaps. In this article, the authors expand the methodology to price nonlinear derivatives written on realized variance. They introduce a new option contract, a Bermudan variance swaption, defined as an option on variance swap with early exercise dates. Within the same framework they also show how to value forward-start variance swaps, VIX futures, and VIX options. Numerical tests show that the methodology is efficient and accurate.

The empirical linkages among market returns, return volatility, and trading volume: Evidence from the S&P 500 VIX Futures

The purpose of this study is to examine the relationships between return and trading volume as well as between return volatility and trading volume by analyzing the asymmetric relationships of contemporaneity and lead-lags between these factors for the S&P 500 VIX Futures Index. We apply the threshold model with the GJR-GARCH framework for empirical analysis herein. The main findings demonstrate that the threshold effects exist in both the contemporaneous and lead-lag relationships between return-volume and volatility-volume. Moreover, the delayed effects of a one-trading-day lag through to three-trading-day lags exist from trading volume to returns and return volatility. Larger trading volume is beneficial for investors to gain returns, but it also leads to higher volatility. The implication of our findings offers a suggestion as to the opportune timing for investors to buy S&P 500 VIX Futures.

STATISTICS OF VIX FUTURES AND APPLICATIONS TO TRADING VOLATILITY EXCHANGE-TRADED PRODUCTS

We study the dynamics of VIX futures and ETNs/ETFs. We find that contrary to classical commodities, VIX and VIX futures exhibit large volatility and skewness, consistent with the absence of cash-and-carry arbitrage. The constant-maturity futures (CMF) term-structure can be modeled as a stationary stochastic process in which the most likely state is contango with VIX [Formula: see text] and a long-term futures price [Formula: see text]. We analyze the behavior of ETFs and ETNs based on constant-maturity rolling futures strategies, such as VXX, XIV and VXZ, assuming stationarity and through a multi-factor model calibrated to historical data. We find that buy-and-hold strategies consisting of shorting ETNs that roll long futures, or buying ETNs that roll short futures, will produce theoretically-sure profits if it is assumed that CMFs are stationary and ergodic. To quantify further, we estimate a 2-factor lognormal model with mean-reverting factors to VIX and CMF historical data from 2011 to 2016. The results confirm the profitability of buy-and-hold strategies, but also indicate that the latter have modest Sharpe ratios, of the order of [Formula: see text] or less, and high variability over 1-year horizon simulations. This is due to the surges in VIX and CMF backwardations which are observed sporadically in the volatility futures market.

Tracking VIX with VIX Futures: Portfolio Construction and Performance

We study a series of static and dynamic portfolios of VIX futures and their effectiveness to track the VIX index. We derive each portfolio using optimization methods, and evaluate its tracking performance from both empirical and theoretical perspectives. Among our results, we show that static portfolios of different VIX futures fail to track VIX closely. VIX futures simply do not react quickly enough to movements in the spot VIX. In a discrete-time model, we design and implement a dynamic trading strategy that adjusts daily to optimally track VIX. The model is calibrated to historical data and a simulation study is performed to understand the properties exhibited by the strategy. In addition, comparing to the volatility ETN, VXX, we find that our dynamic strategy has a superior tracking performance.

Inversion of Convex Ordering: Local Volatility Does Not Maximize the Price of VIX Futures

It has often been stated that, within the class of continuous stochastic volatility models calibrated to vanillas, the price of a VIX future is maximized by the Dupire local volatility model. In this article we prove that this statement is incorrect: we build a continuous stochastic volatility model in which a VIX future is strictly more expensive than in its associated local volatility model. More generally, in this model, strictly convex payoffs on a squared VIX are strictly cheaper than in the associated local volatility model. This corresponds to an inversion of convex ordering between local and stochastic variances, when moving from instantaneous variances to squared VIX, as convex payoffs on instantaneous variances are always cheaper in the local volatility model. We thus prove that this inversion of convex ordering, which is observed in the SPX market for short VIX maturities, can be produced by a continuous stochastic volatility model. We also prove that the model can be extended so that, as suggested by market data, the convex ordering is preserved for long maturities.

The Market Impact of Uninformed Flows: Evidence from the VIX Futures Market

What is the market impact of predictable order flow? Leveraged exchange-traded products are useful for answering this question because they generate daily rebalancing flows whose size, sign and timing are predictable. This paper presents new evidence from the market for leveraged volatility (VIX) products. I find that the daily rebalancing imposes a substantial implicit cost on investors, but there is no evidence that the impact is driven by predatory trading. On the contrary, I show that larger and more predictable flows have smaller price impact coeffcients, and that trading ahead of rebalancing flows is not profitable after transaction costs.