Spot VIX Research Articles

Estimation of VIX futures through Gaussian factor models

In this paper we investigate VIX dynamics through a two-factor Gaussian model, following Avellaneda and Papanicolaou (2019). Two strategies were adopted. First, we considered constant market price of risk. Second, we included time-varying market price of risk. In both cases, we estimated the model following two different approaches. In the first, we used a sample encompassing seven VIX future contracts and also the spot VIX. In the second, we dropped the spot VIX from the sample. We found that this removal provided a better adjustment between empirical and estimated data.

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.

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.

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.

VIX Christmas Effect

An anomaly may exist in the U.S. stock market in which the VIX trades lower during the first 17 to 22 days of December. This is potentially due to a Christmas effect, in which trading activity slows before Christmas. The authors test this hypothesis using two approaches, one from the spot VIX and the other from the VIX futures term structure. In addition, the authors test the holiday explanation, in which the VIX declines prior to holidays because trading activity declines.

Tracking the VIX

Volatility has emerged as an important and distinct asset class over the past decade. The popularity of volatility stems from its unique properties—namely, its negative correlation with equity returns and its usefulness as insurance against tail risk. Trading applications of volatility-related securities and financial instruments involve, among others, short-term trading to exploit shifts in volatility (realized, implied, or expected implied volatility), hedging an equity exposure, and modifying the risk of an asset allocation mix. This article examines the tracking performance of VIX futures and seven popular volatility exchange-traded products (ETPs) on the spot VIX index. The empirical findings suggest limited tracking ability of all the products under review because the magnitude of the respective tracking errors is significant. Therefore, even though a plethora of volatility products currently exist, there is still potential room for additional VIX ETP offerings that would attempt to track spot VIX following either a physical or a synthetic replication method. <b>TOPICS:</b>Analysis of individual factors/risk premia, tail risks, volatility measures

Tracking the VIX Index

Volatility has emerged as an important distinct asset class over the past decade. The popularity of volatility stems from its unique properties, namely its negative correlation with equity returns and its usefulness as insurance against tail risk. Trading applications of volatility-related securities and financial instruments involve among others short-term trading in order to exploit shifts in volatility (realized, implied or expected implied volatility), hedging an equity exposure and modifying the risk of an asset allocation mix.This paper examines the tracking performance of VIX futures and seven popular volatility Exchange Traded Products (ETPs) on the spot VIX index. The empirical findings suggest limited tracking ability of all the products under review as the magnitude of the respective tracking errors is significant. Therefore, even though there is a plethora of volatility products nowadays, there is still potential room for additional VIX ETP offerings that would attempt to track spot VIX following either a physical or a synthetic replication method.

The VIX Futures Basis: Evidence and Trading Strategies

The VIX index, based on the volatility implied by options on the S&P 500 index, is one of the most watched market indicators. Futures and options written on the VIX are among the most actively traded derivative contracts. But the VIX is quite different from other derivatives underliers. One can’t buy and hold implied volatility, so the cost-of-carry model followed by nearly all futures contracts on financial instruments and storable commodities does not work for the VIX. For nonstorable underlyings, the futures price is not constrained by arbitrage against the cash market and is mostly determined by the market’s forecast of the spot price at futures maturity. If the VIX futures price is the market’s expectation about implied volatility at contract maturity, the futures basis may contain information about which way the VIX is going to move next to close the gap. On the other hand, if VIX futures prices contain a volatility risk premium, the future should lie above the spot VIX on average and is expected to converge toward the spot VIX over time, rather than the reverse. This risk premium can be captured on average by shorting the nearby VIX contract, but the position is exposed to risk that VIX may spike upward if the stock market falls sharply. This risk can be partly hedged using long contracts in the S&P index future. The authors examine these issues and find, as previous researchers have, that the VIX futures basis does not predict the change in the VIX. However, a hedged trade to capture the volatility risk premium can be highly profitable.

Volatility ETFs and ETNs

The advent of ETFs and ETNs linked to the S&amp;P 500 VIX Futures Indices has broadened access to volatility trading. But there still remain significant misconceptions about the relationship of these products with spot VIX and the volatility term structure. In this article, the authors distinguish between portfolio hedge and distributional properties of these S&amp;P 500 VIX futures index based instruments versus those of a theoretical position in spot VIX. They also demonstrate the impact of the term structure and quantify how it manifests itself in roll loss. <b>TOPICS:</b>Exchange-traded funds and applications, volatility measures, futures and forward contracts

The Efficiency of the VIX Futures Market: A Panel Data Approach

This article examines whether VIX futures prices are unbiased and efficient predictors of the VIX index. The particular empirical analysis differs from the usually applied tests in that it uses a panel estimation approach. Panel regression has several advantages as it offers more flexibility in modeling the efficiency of several futures contract with overlapping datasets. As a result, this methodology enables the authors to include all daily closing prices of VIX futures contracts that expired between May 2004 and December 2009, a total of 64 contracts. The empirical findings support the hypothesis that VIX futures are good predictors of spot VIX values. The tests show that the VIX futures with a forecast horizon up to 23 days do not incorporate a significant risk premium and, thus, can be considered as unbiased and efficient estimators of the relevant spot VIX levels.

The Efficiency of the VIX Futures Market:A Panel Data Approach

This study examines whether VIX futures prices are unbiased and efficient predictors of the VIX index. The particular empirical analysis differs from the usually applied tests in that it uses a panel estimation approach. Panel regression has several advantages as it offers more flexibility in modelling the efficiency of several futures contract with overlapping dataset. As a result, this methodology enables us to include all daily closing prices of VIX futures contracts that expired between May 2004 and December 2009, a total of 64 contracts. The empirical findings support the hypothesis that VIX futures are good predictors of spot VIX values. The tests show that the VIX futures with a forecast horizon up to 23 days do not incorporate a significant risk premium and thus, can be considered as unbiased and efficient estimators of the relevant spot VIX levels.

Causality in the VIX futures market

AbstractThis study examines the price‐discovery function and information efficiency of a fast growing volatility futures market: the Chicago Board of Option Exchange VIX futures market. A linear Engle–Granger cointegration test with an error correction mechanism (ECM) shows that during the full sample period, VIX futures prices lead spot VIX index, which implies that the VIX futures market has some price‐discovery function. But a modified Baek and Brock nonlinear Granger test detects bi‐directional causality between VIX and VIX futures prices, suggesting that both spot and futures prices react simultaneously to new information. Quarter‐by‐quarter investigations show that, on average, the estimated parameters are not significantly different from zero, thus providing further evidence supporting information efficiency in the VIX futures market. © 2011 Wiley Periodicals, Inc. Jrl Fut Mark

Access to Volatility Via Listed Futures

Volatility has emerged has an important asset class in last decade. Often referred to as the investor fear gauge, it can be a potentially useful diversification tool in a broad equity portfolio, especially under down markets. However, it is not possible to trade spot VIX directly. With launch of S&O 500 VIX Futures Index Series in January 2009, a variety of popular exchange traded products linked to these indices offer broad market access to volatility trading. In this paper, we elaborate on portfolio hedge and distributional properties of VIX futures based indices versus those of spot VIX.

Directional Exposure to Volatility Via Listed Futures

Volatility, or the second moment of the price distribution of an asset, has emerged as an important asset class in the last decade. It is actively traded through over-the counter (OTC) variance and volatility swaps, and through exchange listed VIX futures and options. While VIX? has achieved widespread recognition, it remains very challenging to replicate spot VIX. The S&P 500 VIX Short-Term Futures Index is the first index to offer directional exposure to volatility through publicly traded futures markets. This paper provides a background on the construction, replicability and characteristics of this index.

Directional Exposure to Volatility via Listed Futures S&amp;P 500 VIX Short-Term Futures Index

Volatility has emerged as an important asset class in the last decade. It is actively traded through over-the counter swaps, and more recently through exchange listed VIX futures and options. While VIX has achieved widespread recognition, it remains very challenging to replicate spot VIX. The S&P 500 VIX Short-Term Futures Index is the first index to offer replicable, directional exposure to volatility using exchange-listed futures contracts. The index is comprised of two near term VIX futures contracts, which are rebalanced daily in equal increments in order to maintain a constant one month maturity. While the correlation between spot VIX and the S&P 500 VIX Short-Term Futures Index is not perfect, it is a healthy 87%. More importantly, the correlation of the index to the S&P 500 is -76%, similar to the correlation of spot VIX to the S&P 500 of -74%. The index has a positive return 95% of the time that the S&P 500 has a loss of more than 1%. During days of sharp market declines, index returns are usually greater in value than corresponding S&P 500 losses. Dedicated long positions in the index are expected to decline during normal volatility regimes. Not only is volatility mean reverting to a theoretical expected long term return of zero, but the index is also expected to suffer from roll loss due to term structure decay. Conversely, short positions in the index provide exposure to a forward starting volatility arbitrage strategy.