Forecasting oil price movements: Exploiting the information in the futures market

Relying on the cost of carry model, the long‐run relationship between spot and futures prices is investigated and the information implied in these cointegrating relationships is used to forecast out of sample oil spot and futures price movements. To forecast oil price movements, a vector error correction model (VECM) is employed, where the deviations from the long‐run relationships between spot and futures prices constitute the equilibrium error. To evaluate forecasting performance, the random walk model (RWM) is used as a benchmark. It was found that (a) in‐sample, the information in the futures market can explain a sizable portion of oil price movements; and (b) out‐of‐sample, the VECM outperforms the RWM in forecasting price movements of 1‐month futures contracts. © 2008 Wiley Periodicals, Inc. Jrl Fut Mark 28:34–56, 2008     

The cost of carry model and regime shifts in stock index futures markets: An empirical investigation

This article examines empirically the dynamic relationship between spot and futures prices in stock index futures markets employing a class of nonlinear, regime‐switching‐vector‐equilibrium‐correction models, which is novel in this context. Using data for the S&P 500 and the FTSE 100 over the post‐1987 crash period, it is shown that a long‐run relationship between spot and futures prices exists, which implies mean reversion of the basis. After providing strong evidence against the hypothesis of linear dynamics in the relationship under investigation, regime‐switching‐vector‐equilibrium‐correction models for spot and futures price movements are developed and shown to capture well the time‐series properties of our data, consistent with a large theoretical and empirical literature. © 2000 John Wiley & Sons, Inc. Jrl Fut Mark 20:603–624, 2000.     

The forward pricing function of the shipping freight futures market

This article investigates the unbiasedness hypothesis of futures prices in the freight futures market. Being the only market whose underlying asset is a service, it sets it apart from other markets investigated so far in the literature. Cointegration techniques, employed to examine this hypothesis, indicate that futures prices one and two months before maturity are unbiased forecasts of the realized spot prices, whereas a bias exists in the three-months futures prices. This mixed evidence is in agreement with studies in other markets and suggests that the acceptance or rejection of unbiasedness depends on the idiosyncrasies of the market under investigation and on the time to maturity of the contract. Despite the existence of a bias in the three-months prices, futures prices for all maturities are found to provide forecasts of the realized spot prices that are superior to forecasts generated from error correction, ARIMA, exponential smoothing, and random walk models. Hence it appears that users of the BIFFEX market receive accurate signals from the futures prices (regarding the future course of cash prices) and can use the information generated by these prices to guide their physical market decisions. © 1999 John Wiley & Sons, Inc. Jrl Fut Mark 19: 353–376, 1999     

A maximal affine stochastic volatility model of oil prices

This study develops and estimates a stochastic volatility model of commodity prices that nests many of the previous models in the literature. The model is an affine three‐factor model with one state variable driving the volatility and is maximal among all such models that are also identifiable. The model leads to quasi‐analytical formulas for futures and options prices. It allows for time‐varying correlation structures between the spot price and convenience yield, the spot price and its volatility, and the volatility and convenience yield. It allows for expected mean‐reversion in the short term and for an increasing expected long‐term price, and for time‐varying risk premia. Furthermore, the model allows for the situation in which options' prices depend on risk not fully spanned by futures prices. These properties are desirable and empirically important for modeling many commodities, especially crude oil. © 2009 Wiley Periodicals, Inc. Jrl Fut Mark 30:101–133, 2010     

Causality in the VIX futures market

This study examines the price‐discovery function and information efficiency of a fast growing volatility futures market: the Chicago Board of Option Exchange VIX futures market. A linear Engle–Granger cointegration test with an error correction mechanism (ECM) shows that during the full sample period, VIX futures prices lead spot VIX index, which implies that the VIX futures market has some price‐discovery function. But a modified Baek and Brock nonlinear Granger test detects bi‐directional causality between VIX and VIX futures prices, suggesting that both spot and futures prices react simultaneously to new information. Quarter‐by‐quarter investigations show that, on average, the estimated parameters are not significantly different from zero, thus providing further evidence supporting information efficiency in the VIX futures market. © 2011 Wiley Periodicals, Inc. Jrl Fut Mark     

Asymmetric information in commodity futures markets: Theory and empirical evidence

This article examines the theoretical and empirical implications of asymmetric information in commodity futures markets. In particular, it formulates and tests a theoretical model that recognizes two distinct categories of traders: hedgers, who participate in both spot and futures markets, and speculators, who participate only in the futures market. Speculators are assumed to possess differential information about the realized values of selected random variables. Multiperiod futures market equilibria are derived under competitive conditions, and the ability of futures markets to forecast changes in equilibrium spot market prices are examined. The key variable is shown to be the randomness and informational asymmetry in the aggregate supply by participating hedgers in the spot market, whose absence turns out to be the major determinant of the revelation of informational asymmetry. Moreover, under the assumption of independence of error forecasts for prices and spot market supplies, it is shown that futures market equilibrium ends up with linear expressions for prices and futures contract volumes. These linear expressions are then used to develop empirically testable models. The main empirical implications in these models revolve around the role of the basis as a predictor of future spot price changes. The paper provides an empirical investigation of these implications, using three commodities traded on the Winnipeg Commodity Exchange (WCE). © 1998 John Wiley & Sons, Inc. Jrl Fut Mark 18:803–825, 1998     

A No‐Arbitrage Fractional Cointegration Model for Futures and Spot Daily Ranges

The no‐arbitrage relation between futures and spot prices implies an analogous relation between futures and spot daily ranges. The long‐memory features of the range‐based volatility estimators are analyzed, and fractional cointegration is tested in a semi‐parametric framework. In particular, the no‐arbitrage condition is used to derive a long‐run relationship between volatility measures and to justify the use of a fractional vector error correction model (FVECM) to study their dynamic relationship. The out‐of‐sample forecasting superiority of FVECM, with respect to alternative models, is documented. The results highlight the importance of incorporating the long‐run equilibrium in volatilities to obtain better forecasts, given the information content in the volatility of futures prices. © 2011 Wiley Periodicals, Inc. Jrl Fut Mark 33:77–102, 2013     

A note on the superiority of the OLS hedge ratio

Suppose that spot and futures prices are generated from an error‐correction model. This note demonstrates that, although the OLS model is misspecified, it provides a hedge ratio that usually outperforms the hedge ratio derived from the correct error‐correction model. The opposite result is possible only when the postsample incurs a major structural change from the estimation sample. ©2005 Wiley Periodicals, Inc. Jrl Fut Mark 25:1121–1126, 2005     

Bias and backwardation in natural gas futures prices

This paper tests the fair‐game efficient‐markets hypothesis for the natural gas futures prices over the period 1990 through 2003. We find evidence consistent with the Keynesian notion of normal backwardation. Regressing the future spot prices on the lagged futures prices and using the Stock‐Watson (1993) procedure to correct for the correlation between the error terms and the futures prices, we find that natural gas futures are biased predictors of the corresponding future spot prices for contracts ranging from 3 to 12 months. These results cast a serious doubt on the commonly held view that natural gas futures sell at a premium over the expected future spot prices, and that this bias is due to the systematic risk of the futures price movements represented by a negative “beta.” We also find evidence for the Samuelson effect. © 2005 Wiley Periodicals, Inc. Jrl Fut Mark 25:281–308, 2005     

Market efficiency among futures with different maturities: Evidence from the crude oil futures market

Although many studies have investigated market efficiency of spot and futures prices, that among futures with different maturities has not been studied extensively. In this study, market efficiency and unbiasedness among such futures are defined and the concept of “consistently efficient (or consistently efficient and unbiased) market within n‐month maturity” is introduced. According to this definition, market efficiency and unbiasedness among WTI futures with different maturities are tested using cointegration analysis, and short‐term market efficiency, using an error correction model and GARCH‐M‐ECM. The results show that WTI futures are consistently efficient within 8‐month maturity and consistently efficient and unbiased within 2‐month maturity. © 2010 Wiley Periodicals, Inc. Jrl Fut Mark 31:487–501, 2011     

An analysis of the relationship between electricity and natural‐gas futures prices

This article analyzes the relationship between electricity futures prices and natural‐gas futures prices. We find that the daily settlement prices of New York Mercantile Exchange's (NYMEX's) California–Oregon Border (COB) and Palo Verde (PV) electricity futures contracts are cointegrated with the prices of its natural‐gas futures contract. The coefficient of natural‐gas futures prices in our model of COB electricity futures prices is not significantly different from the coefficient of gas prices in our model of PV electricity although there are differences in the production of electricity in these two service areas. The coefficients in our model do reflect differences in the consumption of electricity in the COB and PV service areas, however. Our trading‐rule simulations indicate that the statistically significant mean reversion found in the relationship between electricity and natural‐gas futures prices also is economically significant in both in‐sample and out‐of‐sample tests. © 2002 John Wiley & Sons, Inc. Jrl Fut Mark 22:95–122, 2002     

Do futures prices help forecast the spot price?

This study proposes a futures‐based unobserved components model for commodity spot prices. Prices quoted at the same time incorporate the same information, but are affected differently, resulting in the different shapes of futures curves. This model utilizes information from part of the futures curve to improve forecasting accuracy of the spot price. Applying this model to oil market data, I find that the model forecasts outperform the literature benchmark (the no‐change forecast) and futures prices forecasts in multiple dimensions, with smaller average error variation over the sample period and higher chance of smaller absolute error in each period.     

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。     

Valuing real options using implied binomial trees and commodity futures options

A real option on a commodity is valued using an implied binomial tree (IBT) calibrated using commodity futures options prices. Estimating an IBT in the absence of spot options (the norm for commodities) allows real option models to be calibrated for the first time to market‐implied probability distributions for commodity prices. In addition, the existence of long‐dated futures options means that good volatility estimates may now be incorporated into capital budgeting evaluations of real options projects with long planning horizons. An example is given using gold futures options and a real option to extract gold from a mine. A detailed out‐of‐sample test is included that shows how IBT option pricing errors evolve on subtrees emanating from future levels of the underlying asset. © 2007 Wiley Periodicals, Inc. Jrl Fut Mark 27:203–226, 2007     

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.     

THE STOCHASTIC VOLATILITY MODEL OF BARNDORFF‐NIELSEN AND SHEPHARD IN COMMODITY MARKETS

We consider the non‐Gaussian stochastic volatility model of Barndorff‐Nielsen and Shephard for the exponential mean‐reversion model of Schwartz proposed for commodity spot prices. We analyze the properties of the stochastic dynamics, and show in particular that the log‐spot prices possess a stationary distribution defined as a normal variance‐mixture model. Furthermore, the stochastic volatility model allows for explicit forward prices, which may produce a hump structure inherited from the mean‐reversion of the stochastic volatility. Although the spot price dynamics has continuous paths, the forward prices will have a jump dynamics, where jumps occur according to changes in the volatility process. We compare with the popular Heston stochastic volatility dynamics, and show that the Barndorff‐Nielsen and Shephard model provides a more flexible framework in describing commodity spot prices. An empirical example on UK spot data is included.     

Estimating the optimal hedge ratio with focus information criterion

In recent years, the error‐correction model without lags has been used in estimating the minimum‐variance hedge ratio. This article proposes the use of the same error‐correction model, but with lags in spot and futures returns in estimating the hedge ratio. In choosing the lag structure, use of the Akaike information criterion (AIC) and recently proposed focus information criterion (FIC) by G. Claeskens and N. L. Hjort (2003) is suggested. The proposed methods are applied to 24 different futures contracts. Even though the FIC hedge ratio is expected to perform better in terms of mean‐squared error, the AIC hedge ratio is found to perform as well as the FIC and better than the simple hedge ratios in terms of hedging effectiveness. © 2005 Wiley Periodicals, Inc. Jrl Fut Mark 25:1011– 1024, 2005     

Asset storability and price discovery in commodity futures markets: A new look

This article examines the price discovery performance of futures markets for storable and nonstorable commodities in the long run, allowing for the compounding factor of stochastic interest rates. The evidence shows that asset storability does not affect the existence of cointegration between cash and futures prices and the usefulness of future markets in predicting future cash prices. However, it may affect the magnitude of bias of futures markets’ estimates (or predictions) for future cash prices. These findings have several important implications for commodity production decision making, commodity hedging, and commodity price forecasting. © 2001 John Wiley & Sons, Inc. Jrl Fut Mark 21:279–300, 2001     

Detecting and modeling changing volatility in the copper futures market

Copper futures returns are characterized by negative skewness and excess kurtosis. Research has not yet examined this nonnormality, which contributes to their volatility. To date little attention has been paid to the modeling of these series. Therefore, the purpose of this paper is to (i) detect alternating subperiods of volatility by using a method that uses an iterated cumulative sum of squares (ICSS) algorithm to identify breakpoints in the series; and (ii) compare the ability of five models (the random walk, GARCH, EGARCH, AGARCH, and the GJR model) to capture the volatility within each ICSS identified subperiod. These tests were applied to two copper futures series (open to close and close to close prices). Results indicate that the ranking (in terms of the root mean square error) is similar for both series. That is, the GARCH or EGARCH model rank first and second, depending on the series, followed by the GJR model. AGARCH and the random walk models perform poorly.© 1999 John Wiley & Sons, Inc. Jrl Fut Mark 19: 79–100, 1999     

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