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.     

Assessing the asymmetric volatility linkages of energy and agricultural commodity futures during low and high volatility regimes

This study investigated the volatility linkages between energy and agricultural futures, including possible causes for these comovements, such as external macroeconomic and financial shocks during low and high volatility regimes. A combination of Markov-switching regressions and quadrivariate VAR–DCC–GARCH and VAR–BEKK–GARCH modeling revealed that external shocks have an asymmetric effect on the relationship of these assets with higher cross-correlations reported during high volatility regimes. This comovement effect outweighs the substitution effect between energy and agricultural products. Furthermore, the quadrivariate VAR–BEKK–GARCH model provides strong evidence of a bidirectional price volatility spillover between the agricultural and energy markets during periods of high volatility. Overall, the results suggest that energy futures can be effectively used for hedging in a portfolio comprising agricultural futures (and vice versa), while a combination of macroeconomic and financial index futures can serve as an effective hedging tool in investment portfolios comprising both energy and agricultural commodities.     

Economic uncertainty,trading activity,and commodity futures volatility

This paper investigates the dynamics of commodity futures volatility. I derive the variance decomposition for the futures basis and show unexpected excess returns result from new information about expected future interest rates, convenience yields, and risk premia. Measures of uncertainty in economic conditions have significant predictive power for realized volatility of commodity futures returns, after controlling for lagged volatility, returns, commodity index trading, hedging pressure, and other trading activity, even during the so-called “index financialization” period. During this period, hedge fund performance predicts volatility in grain commodities, which are affected by the US ethanol mandate.     

The market quality of commodity futures markets

To study the market quality of commodity futures markets, we construct a commodity futures market quality index from the perspective of liquidity, efficiency, and volatility. Based on the market quality index, the Chinese commodity futures market operates steadily. The metal futures market is more efficient and stable than the market for agricultural futures. The Chinese commodity futures market is less liquid and more volatile than the U.S. market. We examine the determinants of market quality and find that macroeconomic variables and futures market contracts are significantly related to the market quality of Chinese commodity futures.     

The implied volatility smirk of commodity options

This paper studies the implied volatility (IV) smirks in four commodity markets by adopting Zhang and Xiang's methodology. First, we document the term structure and dynamics of IV smirks. Overall, the commodity IV curves are negatively skewed with a positive curvature. Then we analyze the commodity and S&P 500 returns' predictability based on in‐sample and out‐of‐sample tests and find that the information embedded in IV smirks can significantly predict monthly commodity and S&P 500 returns. For example, the risk‐neutral fourth cumulant (FC) from the crude oil market outperforms all of the standard predictors in predicting the S&P 500 returns.     

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.     

The untold story of commodity futures in China

We investigate the behavior of commodity futures risk premia in China. In the presence of retail-dominance and barriers-to-entry, the term structure and momentum premia remain persistent, whereas hedging pressure, skewness, volatility, and liquidity premia are distorted by time-varying margins and strict position limits. Furthermore, open interest, currency, and inflation premia are sensitive to institutional settings. The observed premia cannot be attributed to common risks, sentiment, transactions costs, or data-snooping, but are related to liquidity, anchoring, and regulation-induced limits-to-arbitrage. We highlight the distinctive features of Chinese futures markets and assess the challenges posed to theories of commodity risk premia.     

Flow toxicity of high-frequency trading and its impact on price volatility: Evidence from the KOSPI 200 futures market

We examine the relation between high-frequency trading, flow toxicity, and short-term volatility during both normal and stressful periods. Using transaction data for the Korea Composite Stock Price Index 200 (KOSPI 200) futures, we find the Volume-Synchronized Probability of Informed Trading (VPIN) useful in measuring flow toxicity as it predicts short-term volatility effectively. We further show that high-frequency trading is negatively related to VPIN and short-term volatility during normal times but has a positive association during stressful periods. Finally, we advocate the use of bulk-volume classification (BVC) by presenting evidence that the initiator identified by BVC trades at more favorable prices than the true trade initiator.     

Existence of a calibrated regime switching local volatility model

By Gyöngy's theorem, a local and stochastic volatility model is calibrated to the market prices of all European call options with positive maturities and strikes if its local volatility (LV) function is equal to the ratio of the Dupire LV function over the root conditional mean square of the stochastic volatility factor given the spot value. This leads to a stochastic differential equation (SDE) nonlinear in the sense of McKean. Particle methods based on a kernel approximation of the conditional expectation, as presented in Guyon and Henry‐Labordère [Risk Magazine, 25, 92–97], provide an efficient calibration procedure even if some calibration errors may appear when the range of the stochastic volatility factor is very large. But so far, no global existence result is available for the SDE nonlinear in the sense of McKean. When the stochastic volatility factor is a jump process taking finitely many values and with jump intensities depending on the spot level, we prove existence of a solution to the associated Fokker–Planck equation under the condition that the range of the squared stochastic volatility factor is not too large. We then deduce existence to the calibrated model by extending the results in Figalli [Journal of Functional Analysis, 254(1), 109–153].