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.     

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     

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。     

Time‐varying jump risk premia in stock index futures returns

This study tests the presence of time‐varying risk premia associated with extreme news events or jumps in stock index futures return. The model allows for a dynamic jump component with autoregressive jump intensity, long‐range dependence in volatility dynamics, and a volatility in mean structure separately for the normal and extreme news events. The results show significant jump risk premia in four stock market index futures returns including the DAX, FTSE, Nikkei, and S&P500 indices. Our results are robust to various specifications of conditional variance including the plain GARCH, component GARCH, and Fractionally Integrated GARCH models. We also find the time‐varying risk premium associated with normal news events is not significant across all indices. © 2011 Wiley Periodicals, Inc. Jrl Fut Mark 32:639–659, 2012     

Conditional OLS minimum variance hedge ratios

The paper presents a new methodology to estimate time dependent minimum variance hedge ratios. The so‐called conditional OLS hedge ratio modifies the static OLS approach to incorporate conditioning information. The ability of the conditional OLS hedge ratio to minimize the risk of a hedged portfolio is compared to conventional static and dynamic approaches, such as the naïve hedge, the roll‐over OLS hedge, and the bivariate GARCH(1,1) model. The paper concludes that, both in‐sample and out‐of‐sample, the conditional OLS hedge ratio reduces the basis risk of an equity portfolio better than the alternatives conventionally used in risk management. © 2004 Wiley Periodicals, Inc. Jrl Fut Mark 24:945–964, 2004     

Risk–return relationships in foreign‐currency futures following macroeconomic announcements

This study uses the tick data for foreign‐currency futures to examine risk–return relationships on macroeconomic announcements. This study—different from previous studies—examines the risk–return relationship by capturing the announcement effect on returns with announcement surprises and on volatilities with announcement dummies simultaneously in a Generalized Autoregressive Conditional Heteroskedasticity (GARCH) model. Strong risk–return relationships are detected for the first min after the announcements. Furthermore, the return–risk tradeoff ratios differ across currencies and across macroeconomic indicators. The same information can be more profitable when acted on the more liquid currency futures. © 2002 Wiley Periodicals, Inc. Jrl Fut Mark 22: 729–764, 2002     

A random coefficient autoregressive Markov regime switching model for dynamic futures hedging

The random coefficient autoregressive Markov regime switching model (RCARRS) for estimating optimal hedge ratios, which generalizes the random coefficient autoregressive (RCAR) and Markov regime switching (MRS) models, is introduced. RCARRS, RCAR, MRS, BEKK‐GARCH, CC‐GARCH, and OLS are compared with the use of aluminum and lead futures data. RCARRS outperforms all models out‐of‐sample for lead and is second only to BEKK‐GARCH for aluminum in terms of variancereduction point estimates. White's data‐snooping reality check null hypothesis of no superiority is rejected for BEKK‐GARCH and RCARRS for aluminum, but not for lead. © 2006 Wiley Periodicals, Inc. Jrl Fut Mark 26:103–129, 2006     

我国黄金期货市场套期保值功能的实证研究

本文选取2008年1月9日至2010年12月31日之间期货价格和现货价格数据,运用传统回归模型(OLS)、双变量向量自回归模型(B-VAR)、误差修正套期保值模型(ECM)、误差修正GARCH模型(EC-GARCH)对样本数据进行平稳性和协整关系检验,在估计最小风险套期保值比率的基础上发现:(1)我国黄金期货市场运行三年多来,通过黄金期货市场进行套期保值是有效的,可以较为明显地降低参与者面临的价格波动风险;(2)在具体进行套期保值操作时,应该根据套期保值时限长短的不同和预期效果的差异,采用不同的模型来合理确定自身的套期保值比例。在此基础上,本文提出了相关政策建议。     

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。     

A simplified approach to modeling the co‐movement of asset returns

The authors propose a simplified multivariate GARCH (generalized autoregressive conditional heteroscedasticity) model (the S‐GARCH model), which involves the estimation of only univariate GARCH models, both for the individual return series and for the sum and difference of each pair of series. The covariance between each pair of return series is then imputed from these variance estimates. The proposed model is considerably easier to estimate than existing multivariate GARCH models and does not suffer from the convergence problems that characterize many of these models. Moreover, the model can be easily extended to include more complex dynamics or alternative forms of the GARCH specification. The S‐GARCH model is used to estimate the minimum‐variance hedge ratio for the FTSE (Financial Times and the London Stock Exchange) 100 Index portfolio, hedged using index futures, and compared to four of the most widely used multivariate GARCH models. Using both statistical and economic evaluation criteria, it was found that the S‐GARCH model performs at least as well as the other models that were considered, and in some cases it was better. © 2007 Wiley Periodicals, Inc. Jrl Fut Mark 27:575–598, 2007     

Modeling discontinuous periodic conditional volatility: Evidence from the commodity futures market

This paper examines a wide variety of models that allow for complex and discontinuous periodic variation in conditional volatility. The value of these models (including augmented versions of existing models) is demonstrated with an application to high frequency commodity futures return data. Their use is necessary, in this context, because commodity futures returns exhibit discontinuous intraday and interday periodicities in conditional volatility. The former of these effects is well documented for various asset returns; however, the latter is unique amongst commodity futures returns, where contract delivery and climate are driving forces. Using six years of high‐frequency cocoa futures data, the results show that these characteristics of conditional return volatility are most adequately captured by a spline‐version of the periodic generalized autoregressive conditional heteroscedastic (PGARCH) model. This model also provides superior forecasts of future return volatility that are robust to variation in the loss function assumed by the user, and are shown to be beneficial to users of Value‐at‐Risk (VaR) models. © 2004 Wiley Periodicals, Inc. Jrl Fut Mark 24:805–834, 2004     

A Markov regime switching approach for hedging stock indices

In this paper we describe a new approach for determining time‐varying minimum variance hedge ratio in stock index futures markets by using Markov Regime Switching (MRS) models. The rationale behind the use of these models stems from the fact that the dynamic relationship between spot and futures returns may be characterized by regime shifts, which, in turn, suggests that by allowing the hedge ratio to be dependent upon the “state of the market,” one may obtain more efficient hedge ratios and hence, superior hedging performance compared to other methods in the literature. The performance of the MRS hedge ratios is compared to that of alternative models such as GARCH, Error Correction and OLS in the FTSE 100 and S&P 500 markets. In and out‐of‐sample tests indicate that MRS hedge ratios outperform the other models in reducing portfolio risk in the FTSE 100 market. In the S&P 500 market the MRS model outperforms the other hedging strategies only within sample. Overall, the results indicate that by using MRS models market agents may be able to increase the performance of their hedges, measured in terms of variance reduction and increase in their utility. © 2004 Wiley Periodicals, Inc. Jrl Fut Mark 24:649–674, 2004     

Optimal Futures Hedging Under Multichain Markov Regime Switching

Most of the existing Markov regime switching GARCH‐hedging models assume a common switching dynamic for spot and futures returns. In this study, we release this assumption and suggest a multichain Markov regime switching GARCH (MCSG) model for estimating state‐dependent time‐varying minimum variance hedge ratios. Empirical results from commodity futures hedging show that MCSG creates hedging gains, compared with single‐state‐variable regime‐switching GARCH models. Moreover, we find an average of 24% cross‐regime probability, indicating the importance of modeling cross‐regime dynamic in developing optimal futures hedging strategies. © 2012 Wiley Periodicals, Inc. Jrl Fut Mark 34:173–202, 2014     

中国线材期货价格指数波动率预测能力分析

利用上海期货交易所线材期货15分钟高频价格数据构造已实现波动率估计序列,并以此作为参考标准,运用6种损失函数以及Diebold-Mariano检验法检验4类不同波动率模型对线材期货价格波动的样本外预测能力,显示,中国线材期货市场,基于高频数据的GJR(1,1)模型具有最为出色的波动率预测能力,而在某些损失函数标准下,HYGARCH(1,d,1)与GARCH(1,1)模型也体现出了较好的波动率预测能力。     

我国黄金期货市场价格波动研究

以上海期货交易所2008年1月9日至2011年6月30日的黄金期货市场量价关系为研究对象,构建了GARCH(异方差)族模型检验我国黄金期货市场的价格波动特征.研究结果表明,当分别引入黄金期货市场的交易量和持仓量时,交易量对价格波动的影响在当期和滞后期均十分显著,而持仓量对价格波动的影响在当期显著,滞后期则不显著;当同时引入黄金期货市场交易量和持仓量时,他们对价格波动的解释作用增加,且当期统计检验显著,滞后期效应则不明显.     

Forecasting volatility

The forecasting ability of the most popular volatility forecasting models is examined and an alternative model developed. Existing models are compared in terms of four attributes: (1) the relative weighting of recent versus older observations, (2) the estimation criterion, (3) the trade‐off in terms of out‐of‐sample forecasting error between simple and complex models, and (4) the emphasis placed on large shocks. As in previous studies, we find that financial markets have longer memories than reflected in GARCH(1,1) model estimates, but find this has little impact on outofsample forecasting ability. While more complex models which allow a more flexible weighting pattern than the exponential model forecast better on an in‐sample basis, due to the additional estimation error introduced by additional parameters, they forecast poorly out‐of‐sample. With the exception of GARCH models, we find that models based on absolute return deviations generally forecast volatility better than otherwise equivalent models based on squared return deviations. Among the most popular time series models, we find that GARCH(1,1) generally yields better forecasts than the historical standard deviation and exponentially weighted moving average models, though between GARCH and EGARCH there is no clear favorite. However, in terms of forecast accuracy, all are dominated by a new, simple, nonlinear least squares model, based on historical absolute return deviations, that we develop and test here. © 2005 Wiley Periodicals, Inc. Jrl Fut Mark 25:465–490, 2005     

Intradaily periodicity and volatility spillovers between international stock index futures markets

This paper examines short‐run information transmission between the U.S. and U.K. markets using the S&P 500 and FTSE 100 index futures. Ultrahighfrequency futures data are employed—which have a number of advantages over the low‐frequency spot data commonly used in previous studies—in establishing that volatility spillovers are in fact bidirectional. The generalized autoregressive conditionally heteroskedastic model (GARCH) is employed to estimate the mean and volatility spillovers of intraday returns. A Fourier flexible function is utilized to filter the intradaily periodic patterns that induce serial correlation in return volatility. It was found that estimates of volatility persistence and speed of information transmission are seriously affected by intradaily periodicity. The bias in parameter estimation is removed by filtering out the intradaily periodic component of the transaction data. Contrary to previous findings, there is evidence of spillovers in volatility between the U.S. and U.K. markets. Results indicate that the volatility of the U.S. market is affected by the most recent volatility surprise in the U.K. market. © 2005 Wiley Periodicals, Inc. Jrl Fut Mark 25:553–585, 2005     

Return distributions and volatility forecasting in metal futures markets: Evidence from gold,silver, and copper

The characterization of return distributions and forecast of asset‐price variability play a critical role in the study of financial markets. This study estimates four measures of integrated volatility—daily absolute returns, realized volatility, realized bipower volatility, and integrated volatility via Fourier transformation (IVFT)—for gold, silver, and copper by using high‐frequency data for the period 1999 through 2008. The distributional properties are investigated by applying recently developed jump detection procedures and by constructing financial‐time return series. The predictive ability of a GARCH (1,1) forecasting model that uses various volatility measures is also examined. Three important findings are reported. First, the magnitude of the IVFT volatility estimate is the greatest among the four volatility measures. Second, the return distributions of the three markets are not normal. However, when returns are standardized by IVFT and realized volatility, the corresponding return distributions bear closer resemblance to a normal distribution. Notably, the application of financial‐time sampling technique is helpful in obtaining a normal distribution. Finally, the IVFT and realized volatility proxies produce the smallest forecasting errors, and increasing the time frequency of estimating integrated volatility does not necessarily improve forecast accuracy. © 2010 Wiley Periodicals, Inc. Jrl Fut Mark 31:55–80, 2011     

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.     

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