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Because VIX has a negative correlation to the S&P 500 index and a number of hedge fund strategies, the literature has suggested that long positions in VIX can reduce the risk and higher moment exposures of these investments. However, the VIX index is not tradeable. VIX futures are traded, but have materially different performance from the VIX index. The front month futures underperformed by over 4% per month between March 2004 and July 2009. Over this time period, the front month futures had a correlation of 0.84 to, and a volatility 60% of that of, the VIX index. The second month futures contract underperformed by almost 1% per month with a correlation of 0.76 and a standard deviation of only 40% of the VIX index. While a significant negative risk premium exists in VIX futures, the attractive positive skewness and excess kurtosis properties of the futures are similar to those of the index. Both VIX futures and the VIX index are asymmetric, rising more quickly as the S&P 500 index falls and falling more slowly as stock prices rise.

The 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.

Long-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.

High 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.

The 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.

The purpose of this paper is to examine the volatility spillover and lead-lag relationship between the Chicago Board Options Exchange volatility index (VIX) and the major agricultural future markets before and during the Coronavirus disease 2019 (COVID-19) outbreak.

The methods used were the vector autoregression-Baba, Engle, Kraft and Kroner-generalized autoregressive conditional heteroskedasticity method, the Wald test and wavelet transform method.

The findings indicate that prior to the COVID-19 outbreak, there was a two-way volatility spillover impact between the majority of the sample markets. In comparison, volatility transmission between the VIX index and the agricultural future market was significantly lower following the COVID-19 outbreak, the authors observed greater coherence at higher frequencies than at lower frequencies, implying that the interdependence between the two VIX indices and the agricultural future market was stronger over a longer time-frequency domain and the VIX’s signalling effect on various agricultural future prices after the COVID-19 outbreak was significantly lower.

The authors conducted the first comprehensive investigation of the VIX’s correlation with major agricultural futures, especially during COVID-19. The findings contribute to a better understanding of the risk transmission mechanism between the VIX and major agricultural commodities futures contracts. And our findings have significant implications for investors and portfolio managers, as well as for policymakers who are concerned about the price of agricultural futures.

This paper studies the performance of commonly employed stochastic volatility and jump models in the consistent pricing of The CBOE Volatility Index (VIX) and The S&P 500 Index (SPX) options. With the existence of active markets for volatility derivatives and options on the underlying instrument, the need for models that are able to price these markets consistently has increased. Although pricing formulas for VIX and vanilla options are now available for commonly used models exhibiting stochastic volatility and/or jumps, it remains to be shown whether these are able to price both markets consistently. This paper fills this vacuum.

In particular, the Heston model, the Heston model with jumps in returns and the Heston model with simultaneous jumps in returns and variance (SVJJ) are jointly calibrated to market quotes on SPX and VIX options together with VIX futures.

The full flexibility of having jumps in both returns and volatility added to a stochastic volatility model is essential. Moreover, we find that the SVJJ model with the Feller condition imposed and calibrated jointly to SPX and VIX options fits both markets poorly. Relaxing the Feller condition in the calibration improves the performance considerably. Still, the fit is not satisfactory, and we conclude that one needs more flexibility in the model to jointly fit both option markets.

Compared to existing literature, we derive numerically simpler VIX option and futures pricing formulas in the case of the SVJ model. Moreover, the paper is the first to study the pricing performance of three widely used models to SPX options and VIX derivatives.

Since the introduction of VIX to measure the spot volatility in the stock market, VIX and its futures have been widely considered to be the standard of underlying investor sentiment. This study aims to examine how the magnitude of contango or backwardation (MCB volatility risk factor) derived from VIX and VIX3M may affect the pricing of assets.

This paper focuses on the statistical inference of three defined MCB risk factors when cross-examined with Fama–French’s five factors: the market factor R_m–R_f, the size factor SMB (small minus big), the value factor HML (high minus low B/M), the profitability factor RMW (robust minus weak) and the investing factor CMA (conservative minus aggressive). Robustness checks are performed with the revised HML-Dev factor, as well as with daily data sets.

The inclusions of the MCB volatility risk factor, either defined as a spread of monthly VIX3M/VIX and its monthly MA(20), or as a monthly net return of VIX3M/VIX, generally enhance the explanatory power of all factors in the Fama and French’s model, in particular the market factor R_m–R_f and the value factor HML, and the investing factor CMA also displays a significant and positive correlation with the MCB risk factor. When the more in-time adjusted HML-Dev factor, suggested by Asness (2014), replaces the original HML factor, results are generally better and more intuitive, with a higher R² for the market factor and more explanatory power with HML-Dev.

This paper introduces the term structure of VIX to Fama–French’s asset pricing model. The MCB risk factor identifies underlying configurations of investor sentiment. The sensitivities to this timing indicator will significantly relate to returns across individual stocks or portfolios.

The Basel II Accord requires that banks and other authorized deposit‐taking institutions (ADIs) communicate their daily risk forecasts to the appropriate monetary authorities at the beginning of each trading day, using one or more risk models to measure value‐at‐risk (VaR). The risk estimates of these models are used to determine capital requirements and associated capital costs of ADIs, depending in part on the number of previous violations, whereby realized losses exceed the estimated VaR. The purpose of this paper is to address the question of risk management of risk, namely VaR of VIX futures prices.

The authors examine how different risk management strategies performed before, during and after the 2008‐2009 global financial crisis (GFC).

The authors find that an aggressive strategy of choosing the supremum of the univariate model forecasts is preferred to the other alternatives, and is robust during the GFC.

The paper examines how different risk management strategies performed before, during and after the 2008‐2009 GFC, and finds that an aggressive strategy of choosing the supremum of the univariate model forecasts is preferred to the other alternatives, and is robust during the GFC.

As global exchanges have listed volatility derivatives competitively, volatility has been recognized as a new investment vehicle and/or a hedging means for traditional financial assets such as stocks and bonds. Following this trend, KRX has begun to announce VKOSPI from KOSPI200 index options prices since April 13, 2009 and listed VKOSPI futures on November 17, 2014. However, VKOSPI futures has still not been activated than those listed in developed countries. In this paper, we investigate the informational efficiency of VKOSPI futures and analyze the illiquidity problem of VKOSPI futures. More specifically, we execute a VAR analysis of VKOSPI, VKOSPI futures, VIX and VIX futures to find out their lead-lag relations. In addition, we further conduct a Granger causality test, impulse response analysis and variance decomposition to examine their dynamic relations. According to the results, we find that VKOSPI leads VKOSPI futures and that VIX and VIX futures lead VKOSPI and VKOSPI futures significantly. Based on the results above, lastly, we propose several policies to make the VKOSPI futures market more active and informative.

This study aims to investigate the co-volatility patterns between cryptocurrencies and conventional asset classes across global markets, encompassing 26 global indices ranging from equities, commodities, real estate, currencies and bonds.

It used a multivariate factor stochastic volatility model to capture the dynamic changes in covariance and volatility correlation, thus offering empirical insights into the co-volatility dynamics. Unlike conventional research on price or return transmission, this study directly models the time-varying covariance and volatility correlation.

The study uncovers pronounced co-volatility movements between cryptocurrencies and specific indices such as GSCI Energy, GSCI Commodity, Dow Jones 1 month forward and U.S. 10-year TIPS. Notably, these movements surpass those observed with precious metals, industrial metals and global equity indices across various regions. Interestingly, except for Japan, equity indices in the USA, Canada, Australia, France, Germany, India and China exhibit a co-volatility movement. These findings challenge the existing literature on cryptocurrencies and provide intriguing evidence regarding their co-volatility dynamics.

This study significantly contributes to applying asset pricing models in cryptocurrency markets by explicitly addressing price and volatility dynamics aspects. Using the stochastic volatility model, the research adding methodological contribution effectively captures cryptocurrency volatility's inherent fluctuations and time-varying nature. While previous literature has primarily focused on bitcoin and a few other cryptocurrencies, this study examines the stochastic volatility properties of a wide range of cryptocurrency indices. Furthermore, the study expands its scope by examining global asset markets, allowing for a comprehensive analysis considering the broader context in which cryptocurrencies operate. It bridges the gap between traditional asset pricing models and the unique characteristics of cryptocurrencies.