The realized volatility of FTSE‐100 futures prices

Five‐minute returns from FTSE‐100 index futures contracts are used to obtain accurate estimates of daily index volatility from January 1986 to December 1998. These realized volatility measures are used to obtain inferences about the distributional and autocorrelation properties of FTSE‐100 volatility. The distribution of volatility measured daily is similar to lognormal while the volatility time series has persistent positive autocorrelation that displays long‐memory effects. The distribution of daily returns standardized using the measures of realized volatility is shown to be close to normal, unlike the unconditional distribution. © 2002 Wiley Periodicals, Inc. Jrl Fut Mark 22:627–648, 2002     

Multivariate realized volatility forecasts of agricultural commodity futures

We forecast the multivariate realized volatility of agricultural commodity futures by constructing multivariate heterogeneous autoregressive (MHAR) models with flexible heteroscedastic error structures that allow for non-Gaussian distribution, stochastic volatility, and heteroscedastic and serial dependence. We evaluate the forecast performances of various models based on both statistical and economic criteria. The in-sample and out-of-sample results suggest that the proposed MHAR models allowing for flexible heteroscedastic covariance structures outperform the benchmark MHAR models. In addition, the proposed Bayesian MHAR models allowing for t innovations improve both in-sample and out-of-sample forecast performance of the corresponding MHAR models with Gaussian innovations.     

VIX term structure and VIX futures pricing with realized volatility

Using an extended LHARG model proposed by Majewski et al. (2015, J Econ, 187, 521–531), we derive the closed-form pricing formulas for both the Chicago Board Options Exchange VIX term structure and VIX futures with different maturities. Our empirical results suggest that the quarterly and yearly components of lagged realized volatility should be added into the model to capture the long-term volatility dynamics. By using the realized volatility based on high-frequency data, the proposed model provides superior pricing performance compared with the classic Heston–Nandi GARCH model under a variance-dependent pricing kernel, both in-sample and out-of-sample. The improvement is more pronounced during high volatility periods.     

Persistence of volatility in futures markets

This article examines the characteristics of key measures of volatility for different types of futures contracts to provide a better foundation for modeling volatility behavior and derivative values. Particular attention is focused on analyzing how different measures of volatility affect volatility persistence relationships. Intraday realized measures of volatility are found to be more persistent than daily measures, the type of GARCH procedure used for conditional volatility analysis is critical, and realized volatility persistence is not coherent with conditional volatility persistence. Specifically, although there is a good fit between the realized and conditional volatilities, no coherence exists between their degrees of persistence, a counterintuitive finding that shows realized and conditional volatility measures are not a substitute for one another. © 2006 Wiley Periodicals, Inc. Jrl Fut Mark 26:571–594, 2006     

The information content of implied volatility in light of the jump/continuous decomposition of realized volatility

In the framework of encompassing regressions, the information content of the jump/continuous components of historical volatility is assessed when implied volatility is included as an additional regressor. The authors' empirical application focuses on daily and intradaily data for the S&P100 and S&P500 indexes, and daily data for the associated VXO and VIX implied volatility indexes. The results show that the total explanatory power of the encompassing regressions barely changes when the jump/continuous components are included, although the weekly and monthly continuous components are usually significant. This evidence supports the view that implied volatility has very high information content, even when extended decompositions of past realized volatility are used. Moreover, adding GARCH‐type volatility forecasts in the regressions confirms these results. © 2007 Wiley Periodicals, Inc. Jrl Fut Mark 27:337–359, 2007     

Time series volatility of commodity futures prices

This article examines the pattern of volatility over time of a series of commodity futures prices, and focuses in particular on the futures price variability as the maturity date of the futures contract approaches. In a rational expectations model of asymmetric information, the article provides conditions under which the Samuelson hypothesis—that the variability of futures prices increases as maturity approaches—will be true. © 2000 John Wiley & Sons, Inc. Jrl Fut Mark 20: 127–144, 2000     

The predictability of carbon futures volatility: New evidence from the spillovers of fossil energy futures returns

In this paper, we find new evidence for the carbon futures volatility prediction by using the spillovers of fossil energy futures returns as a powerful predictor. The in-sample results show that the spillovers have a significantly positive effect on carbon futures volatility. From the out-of-sample analysis with various loss functions, we find that fossil energy return spillovers significantly outperform the benchmark and show better forecasting performance than the competing models using dimension reduction, variable selection, and combination approaches. The predictive ability of the spillovers also holds in long-term forecasting and does not derive from other carbon-related variables. It can bring substantial economic gains in the portfolio exercise within carbon futures. Finally, we provide economic explanations on the predictive ability of the fossil energy return spillover by the channels of the carbon emission uncertainty and the investor sentiment on the warming climate.