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.     

Volatility and maturity effects in the Nikkei index futures

Many financial data series are found to exhibit stochastic volatility. Some of these time series are constructed from contracts with time-varying maturities. In this paper, we focus on index futures, an important subclass of such time series. We propose a bivariate GARCH model with the maturity effect to describe the joint dynamics of the spot index and the futures-spot basis. The setup makes it possible to examine the Samuelson effect as well as to compare the hedge ratios under scenarios with and without the maturity effect. The Nikkei-225 index and its futures are used in our empirical analysis. Contrary to the Samuelson effect, we find that the volatility of the futures price decreases when the contract is closer to its maturity. We also apply our model to futures hedging, and find that both the optimal hedge ratio and the hedging effectiveness critically depend on both the maturity and GARCH effects. © 1999 John Wiley & Sons, Inc. Jrl Fut Mark 19: 895–909, 1999     

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.     

沪深300股指期货与标准普尔500指数套期保值效果的比较研究

采用OLS、ECM、GARCH模型分别对沪深300股指期货和标准普尔500股指期货的最优套期保值比率及其套期保值效果进行了对比分析,结果表明:无论是沪深300还是标准普尔500股指期货,如果不考虑期货与现货之间的协整关系,得出的最优套期保值比率均偏小,致使套期保值效果不能达到最佳;基于套期保值效果稳定性方面考虑,最优套期保值模型均是GARCH模型;不管是在样本内还是样本外沪深300股指期货的套期保值效果均比标准普尔500股指期货的套期保值效果差。我国政府应该采取相应措施,引导股指期货市场进一步完善和发展。     

Cash trading and index futures price volatility

This study examines the effect of cash market liquidity on the volatility of stock index futures. Two facets of cash market liquidity are considered: (1) the level of liquidity trading proxied by the expected New York Stock Exchange (NYSE) trading volume and (2) the noise composition of trading proxied by the average NYSE trading commission cost. Under the framework of spline–GARCH with a liquidity component, both the quarterly average commission cost and the quarterly expected NYSE volume are negatively associated with the ex ante daily volatility of S&P 500 and NYSE composite index futures. Conversely, liquidity and noise trading in the cash market both dampen futures price volatility, ceteris paribus. This negative association between secular cash trading liquidity and daily futures price volatility is amplified during times of market crisis. These results retain statistical significance and materiality after controlling for bid–ask bounce of futures prices and volume of traded futures contracts. This study establishes empirical evidence to affirm the conventional prediction of a liquidity–volatility relationship: the liquidity effect is secular and persistent across markets. © 2010 Wiley Periodicals, Inc. Jrl Fut Mark 31:465–486, 2011     

Asymmetric covariance in spot‐futures markets

This article studies how the spot‐futures conditional covariance matrix responds to positive and negative innovations. The main results of the article are achieved by obtaining the Volatility Impulse Response Function (VIRF) for asymmetric multivariate GARCH structures, extending Lin (1997) findings for symmetric GARCH models. This theoretical result is general and can be applied to analyze covariance dynamics in any financial system. After testing how multivariate GARCH models clean up volatility asymmetries, the Asymmetric VIRF is computed for the Spanish stock index IBEX‐35 and its futures contract. The empirical results indicate that the spot‐futures variance system is more sensitive to negative than positive shocks, and that spot volatility shocks have much more impact on futures volatility than vice versa. Additionally, evidence is obtained showing that optimal hedge ratios are insensitive to the well‐known asymmetric volatility behavior in stock markets. © 2003 Wiley Periodicals, Inc. Jrl Fut Mark 23:1019–1046, 2003     

Testing mean reversion in financial market volatility: Evidence from S&P 500 index futures

This article presents a comprehensive study of continuous time GARCH (generalized autoregressive conditional heteroskedastic) modeling with the thintailed normal and the fat‐tailed Student's‐t and generalized error distributions (GED). The study measures the degree of mean reversion in financial market volatility based on the relationship between discrete‐time GARCH and continuoustime diffusion models. The convergence results based on the aforementioned distribution functions are shown to have similar implications for testing mean reversion in stochastic volatility. Alternative models are compared in terms of their ability to capture mean‐reverting behavior of futures market volatility. The empirical evidence obtained from the S&P 500 index futures indicates that the conditional variance, log‐variance, and standard deviation of futures returns are pulled back to some long‐run average level over time. The study also compares the performance of alternative GARCH models with normal, Student's‐ t, and GED density in terms of their power to predict one‐day‐ahead realized volatility of index futures returns and provides some implications for pricing futures options. © 2008 Wiley Periodicals, Inc. Jrl Fut Mark 28:1–33, 2008     

The information content of implied volatility in agricultural commodity markets

In this article we compare the incremental information content of lagged implied volatility to GARCH models of conditional volatility for a collection of agricultural commodities traded on the New York Board of Trade. We also assess the relevance of the additional information provided by the implied volatility in a risk management framework. It is first shown that past squared returns only marginally improve the information content provided by the lagged implied volatility. Secondly, value‐at‐risk (VaR) models that rely exclusively on lagged implied volatility perform as well as VaR models where the conditional variance is modelled according to GARCH type processes. These results indicate that the implied volatility for options on futures contracts in agricultural commodity markets provides relevant volatility information that can be used as an input to VaR models. © 2003 Wiley Periodicals, Inc. Jrl Fut Mark 23:441–454, 2003     

Optimal futures hedging for energy commodities: An application of the GAS model

This paper applies generalized autoregressive score-driven (GAS) models to futures hedging of crude oil and natural gas. For both commodities, the GAS framework captures the marginal distributions of spot and futures returns and corresponding dynamic copula correlations. We compare within-sample and out-of-sample hedging effectiveness of GAS models against constant ordinary least square (OLS) strategy and time-varying copula-based GARCH models in terms of volatility reduction and Value at Risk reduction. We show that the constant OLS hedge ratio is not inherently inferior to the time-varying alternatives. Nonetheless, GAS models tend to exhibit better hedging effectiveness than other strategies, particularly for natural gas.     

The Asymmetric Commodity Inventory Effect on the Optimal Hedge Ratio

Hedging strategies for commodity prices largely rely on dynamic models to compute optimal hedge ratios. This study illustrates the importance of considering the commodity inventory effect (effect by which the commodity price volatility increases more after a positive shock than after a negative shock of the same magnitude) in modeling the variance–covariance dynamics. We show by in‐sample and out‐of‐sample forecasts that a commodity price index portfolio optimized by an asymmetric BEKK–GARCH model outperforms the symmetric BEKK, static (OLS), or naïve models. Robustness checks on a set of commodities and by an alternative mean‐variance optimization framework confirm the relevance of taking into account the inventory effect in commodity hedging strategies.     

Jumping hedges: An examination of movements in copper spot and futures markets

Price risk is an important factor for both copper purchasers, who use the commodity as a major input in their production process, and copper refiners, who must deal with cash‐flow volatility. Information from NYMEX cash and futures prices is used to examine optimal hedging behavior for agents in copper markets. A bivariate GARCH‐jump model with autoregressive jump intensity is proposed to capture the features of the joint distribution of cash and futures returns over two subperiods with different dominant pricing regimes. It is found that during the earlier producerpricing regime this specification is not needed, whereas for the later exchange pricing era jump dynamics stemming from a common jump across cash and futures series are significant in explaining the dynamics in both daily and weekly data sets. Results from the model are used to under‐take both within‐sample and out‐of‐sample hedging exercises. These results indicate that there are important gains to be made from a time‐varying optimal hedging strategy that incorporates the information from the common jump dynamics. © 2006 Wiley Periodicals, Inc. Jrl Fut Mark 26:169–188, 2006     

Estimating the connectedness of commodity futures using a network approach

Using a network approach of variance decompositions, we measure the connectedness of 18 commodity futures and characterize both static and dynamic connectedness. Our results show that metal futures are net transmitters of shocks to other futures, and agricultural futures are vulnerable to shocks from the others. Furthermore, almost two-thirds of the volatility uncertainty for commodity futures are due to the connectedness of shocks across the futures market. Dynamically, we find connectedness always increases in times of turmoil. An analysis of connectedness networks suggests that investors could be forewarned that the connectedness of various classes of futures could threaten their portfolios.     

Delivery horizon and grain market volatility

We study the difference in the volatility dynamics of CBOT corn, soybeans, and oats futures prices across different delivery horizons via a smoothed Bayesian estimator. We find that futures price volatilities in these markets are affected by inventories, time to delivery, and the crop progress period and that there are important differences in the effects across delivery horizons. We also find that price volatility is higher before the harvest starts in most cases compared to the volatility during the planting period. These results have implications for hedging, options pricing, and the setting of margin requirements. © 2010 Wiley Periodicals, Inc. Jrl Fut Mark 30:846–873, 2010     

我国期货市场的波动性与有效性--基于三大交易市场的实证分析

通过对中国三大期货市场的铜、黄豆和小麦三种主要期货品种收益率的分布与波动性的实证分析 ,论证了其时间序列存在ARCH效应 ;运用GARCH模型对这三种期货品种进行了拟合分析和统计检验 ,检验结果表明这三个期货品种的波动性均具有很高的持续性 ,但大连黄豆的波动持续性弱于上海铜和郑州小麦 ,其波动性受各种外部冲击的影响较大 ;通过GARCH( 1 ,1 )的市场有效性检验 ,论证了中国期货市场尚未达到弱式有效 ,市场风险较大。     

Speculation and volatility—A time-varying approach applied on Chinese commodity futures markets

Experts have long discussed and empirically investigated whether speculative activity increases volatility on commodity futures markets. Little empirical research, however, analyzes the role of speculators on commodity futures markets in China. Using time-varying vector autoregression models with stochastic volatility, this paper investigates for four heavily traded metal and agricultural contracts, how the relationship between returns volatility and speculation evolves over time. Our findings indicate that speculative activity has little to no impact on volatility. On the contrary, for all commodities examined, returns volatility seems to amplify speculation.     

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.     

Long memory in commodity futures volatility: A wavelet perspective

The authors reexamine the volatility of agricultural commodity futures for evidence of fractional integration, providing new empirical results and extending the extant literature in important dimensions. First, they utilize two relatively new estimators based on wavelets, which are generally superior to, for example, the popular estimator by J. Geweke and S. Porter‐Hudak (GPH; 1983) and exact maximum likelihood estimators (MLEs) on the basis of mean squared error (MSE). Second, they provide simulations to contrast their point estimates with those obtained by a fractionally integrated GARCH (generalized autoregressive conditional heteroscedasticity) model. Third, they conduct a wavelet coef.cient decomposition of futures volatility. They .nd that futures volatilities display the self‐similarity property consistent with long memory and that futures volatilities exhibit persistent long memory with .nite unconditional variance. © 2007 Wiley Periodicals, Inc. Jrl Fut Mark 27:411–437, 2007     

A copula‐based regime‐switching GARCH model for optimal futures hedging

The article develops a regime‐switching Gumbel–Clayton (RSGC) copula GARCH model for optimal futures hedging. There are three major contributions of RSGC. First, the dependence of spot and futures return series in RSGC is modeled using switching copula instead of assuming bivariate normality. Second, RSGC adopts an independent switching Generalized Autoregressive Conditional Heteroscedasticity (GARCH) process to avoid the path‐dependency problem. Third, based on the assumption of independent switching, a formula is derived for calculating the minimum variance hedge ratio. Empirical investigation in agricultural commodity markets reveals that RSGC provides good out‐of‐sample hedging effectiveness, illustrating importance of modeling regime shift and asymmetric dependence for futures hedging. © 2009 Wiley Periodicals, Inc. Jrl Fut Mark 29:946–972, 2009     

VIX futures and its closed‐form pricing through an affine GARCH model with realized variance

This paper studies the forecasting of volatility index (VIX) and the pricing of its futures by a generalized affine realized volatility model proposed by Christoffersen et al. This model is a weighted average of a GARCH and a pure realized variance (RV) model that incorporates each volatility component into the new dynamics. We rewrite the VIX in terms of both volatility components and then derive closed‐form formulas for the VIX forecasting and its futures pricing. Our empirical studies find that a unification of the GARCH and the RV in the modeling substantially improves the forecasting of this index and the pricing of its futures.     

Market volatility and the demand for hedging in stock index futures

This study examines the relation between stock market volatility and the demand for hedging in S&P 500 stock index futures contracts. Open interest is used as a proxy for hedging demand. The analysis employs unique data that identify separately the open interest of large hedgers, large speculators, and smaller traders. Volatility estimates are decomposed into expected and unexpected components, to assess whether traders’ reactions to volatility depend upon its predictability. Results indicate that daily open interest for hedgers increases when unexpected volatility increases. Increases in unexpected volatility may cause hedgers to raise their estimates of future expected volatility, and hence increase their demand for hedging. Open interest of speculators is not related to expected volatility, and is only weakly related to unexpected volatility. The increase in the participation of hedgers in periods of higher volatility is significantly larger than the increase in the participation of speculators. The results suggest that increases in stock market volatility increase the demand for hedging. © 2000 John Wiley & Sons, Inc. Jrl Fut Mark 20: 105–125, 2000