Hedging long‐term commodity risk

This study focuses on the problem of hedging longer‐term commodity positions, which often arises when the maturity of actively traded futures contracts on this commodity is limited to a few months. In this case, using a rollover strategy results in a high residual risk, which is related to the uncertain futures basis. We use a one‐factor term structure model of futures convenience yields in order to construct a hedging strategy that minimizes both spot‐price risk and rollover risk by using futures of two different maturities. The model is tested using three commodity futures: crude oil, orange juice, and lumber. In the out‐of‐sample test, the residual variance of the 24‐month combined spot‐futures positions is reduced by, respectively, 77%, 47%, and 84% compared to the variance of a naïve hedging portfolio. Even after accounting for the higher trading volume necessary to maintain a two‐contract hedge portfolio, this risk reduction outweighs the extra trading costs for the investor with an average risk aversion. © 2003 Wiley Periodicals, Inc. Jrl Fut Mark 23:109–133, 2003     

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     

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     

TIME‐CHANGED ORNSTEIN–UHLENBECK PROCESSES AND THEIR APPLICATIONS IN COMMODITY DERIVATIVE MODELS

This paper studies subordinate Ornstein–Uhlenbeck (OU) processes, i.e., OU diffusions time changed by Lévy subordinators. We construct their sample path decomposition, show that they possess mean‐reverting jumps, study their equivalent measure transformations, and the spectral representation of their transition semigroups in terms of Hermite expansions. As an application, we propose a new class of commodity models with mean‐reverting jumps based on subordinate OU processes. Further time changing by the integral of a Cox–Ingersoll–Ross process plus a deterministic function of time, we induce stochastic volatility and time inhomogeneity, such as seasonality, in the models. We obtain analytical solutions for commodity futures options in terms of Hermite expansions. The models are consistent with the initial futures curve, exhibit Samuelson's maturity effect, and are flexible enough to capture a variety of implied volatility smile patterns observed in commodities futures options.     

Does the price of crude oil respond to macroeconomic news?

In a recent study, Kilian L. and Vega C. (2011) indicate that the daily price of crude oil is mostly unresponsive to macroeconomic news, and at times exhibits response‐coefficients that are counterintuitive. The authors conclude that the price of crude oil is predetermined to macro aggregates, and hence determined in a flow demand/supply framework. We make the argument that inferences on commodity price determination should be drawn from news responses only after the standard tests are subject to inventory (or stock) controls. Using daily and intraday price data and proxies for inventory levels, we reexamine the responsiveness of crude prices to macroeconomic news. Our evidence suggests a very limited role for stock levels in the responsiveness of crude oil. The prior conclusion that crude oil is priced primarily in a flow‐environment is supported by our data. © 2011 Wiley Periodicals, Inc. Jrl Fut Mark 32:536–559, 2012     

A contango‐constrained model for storable commodity prices

This article presents a model of commodity price dynamics under the risk‐neutral measure where the spot price switches between two distinct stochastic processes depending on whether or not inventory is being held. Specifically, the drift of the spot price is equal to the cost of carry when the stock is positive. Conversely, whenever the drift of the spot price is less than the cost of carry, no inventory is being held. The properties of the spot price and the forward curves implied by this model are illustrated and analyzed with the use of numerical examples. A comparison with the single‐factor model by E. S. Schwartz (1997) is also provided. © 2005 Wiley Periodicals, Inc. Jrl Fut Mark 25:1025–1044, 2005     

Futures hedging using dynamic models of the variance/covariance structure

Dynamic futures‐hedging ratios are estimated across seven markets using generalized models of the variance/covariance structure. The hedging performances of the resultant dynamic strategies are then compared with static and naïve strategies, both in‐ and out‐of‐sample. Bayesian‐adjusted hedge ratios also are employed as error purgers. The empirical results indicate that the generalized dynamic models are well specified and that their use in determining optimal hedge ratios can lead to improvements in hedging performance as measured by the volatilities of the returns on the optimally hedged position. © 2003 Wiley Periodicals, Inc. Jrl Fut Mark 23:241–260, 2003     

Pricing VIX futures: Evidence from integrated physical and risk‐neutral probability measures

This study derives closed‐form solutions to the fair value of VIX (volatility index) futures under alternate stochastic variance models with simultaneous jumps both in the asset price and variance processes. Model parameters are estimated using an integrated analysis of integrated volatility and VIX time series from April 21, 2004 to April 18, 2006. The stochastic volatility model with price jumps outperforms for the short‐dated futures, whereas additionally including a state‐dependent volatility jump can further reduce out‐of‐sample pricing errors for other futures maturities. Finally, adding volatility jumps enhances hedging performance except for the short‐dated futures on a daily‐rebalanced basis. © 2007 Wiley Periodicals, Inc. Jrl Fut Mark 27:1175–1217, 2007     

Examining futures price changes and volatility on the trading day after a limit‐lock day

This paper examines the effect that price limits have on futures prices by testing what happens to price changes and volatility on the trading day following a limit‐lock day. The results show evidence that prices continue to rise on average the day after an up‐limit day. In addition, limits appear to influence price volatility for some but not all of the futures contracts. However, since the findings vary across the different commodity futures contracts, it is likely that limits do not directly impact price volatility. © 2000 John Wiley & Sons, Inc. Jrl Fut Mark 20:445–466, 2000     

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.     

A simplified pricing model for volatility futures

We develop a general model to price VIX futures contracts. The model is adapted to test both the constant elasticity of variance (CEV) and the Cox–Ingersoll–Ross formulations, with and without jumps. Empirical tests on VIX futures prices provide out‐of‐sample estimates within 2% of the actual futures price for almost all futures maturities. We show that although jumps are present in the data, the models with jumps do not typically outperform the others; in particular, we demonstrate the important benefits of the CEV feature in pricing futures contracts. We conclude by examining errors in the model relative to the VIX characteristics. © 2010 Wiley Periodicals, Inc. Jrl Fut Mark 31:307–339, 2011     

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     

Risk Management in Agricultural Markets: A Review

This article surveys and evaluates the current state of knowledge about producers' marketing strategies to manage price and revenue risk for farm commodities. The review highlights gaps between concepts and their implementation. Many well‐developed models of price behavior exist, but appropriate characterization and estimation of the probability distributions of commodity prices remain elusive. Hence, the preferred measure of price risk is ambiguous. Numerous models of optimal marketing portfolios for farmers have been specified, but their behavior appears to be inconsistent with most, if not all, of these models. In addition, some research suggests that farmers can earn speculative profits, which is inconsistent with notions of efficient markets. The conclusions discuss what academic research can and cannot accomplish in relation to assisting producers with risk‐management decisions. © 2001 John Wiley & Sons, Inc. Jrl Fut Mark 21:953–985, 2001     

The impact of skewness in the hedging decision

The impact of skewness in the hedger's objective function is tested using a model of hedging derived from a third‐order Taylor Series approximation of expected utility. To determine the effect of price skewness upon hedging and speculation, analytical results are derived using an example of cotton storage. Findings suggest that when forward risk premiums and price skewness in the spot asset have opposite signs, speculation increases relative to the mean‐variance model. When the signs are identical, speculation will decrease, contradicting findings of mean‐variance models. © 2006 Wiley Periodicals, Inc. Jrl Fut Mark 26:503–520, 2006     

Transitory real‐time property rights and exchange intellectual property

American exchanges own the price quotations they generate. Access to real‐time price information is highly valued by most market participants. This enables exchanges to exact royalties from the sale of such market information. In this sense, an exchange's ownership of its price quotations is akin to owning a property right in a perishable commodity (i.e., fresh market price quotations) that is most valuable for only a transitory or limited period of time. The implications of exchange ownership of price data extend beyond financial markets. Recently, Woodard (2000) has noted that some internet auction operators have asserted ownership over the prices they generate. This study reviews the legal origin and nature of the property right to price quotations generated on U.S. futures exchanges and assesses whether exchange ownership should be transitory. The legal basis for transitory real‐time (real and personal) property rights is discussed and the economic implications are considered. © 2003 Wiley Periodicals, Inc. Jrl Fut Mark 23:891–913, 2003     

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     

Derivative pricing model and time‐series approaches to hedging: A comparison

This research compares derivative pricing model and statistical time‐series approaches to hedging. The finance literature stresses the former approach, while the applied economics literature has focused on the latter. We compare the out‐of‐sample hedging effectiveness of the two approaches when hedging commodity price risk using futures contracts. For various methods of parameter estimation and inference, we find that the derivative pricing models cannot out‐perform a vector error‐correction model with a GARCH error structure. The derivative pricing models' unpalatable assumption of deterministically evolving futures volatility seems to impede their hedging effectiveness, even when potentially foresighted optionimplied volatility term structures are employed. © 2005 Wiley Periodicals, Inc. Jrl Fut Mark 25:613–641, 2005     

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     

Modeling seasonality in agricultural commodity futures

The stochastic behavior of agricultural commodity prices is investigated using observations of the term structures of futures prices over time. The continuous time dynamics of (log‐) commodity prices are modeled as a sum of a deterministic seasonal component, a non‐stationary state‐variable, and a stationary state‐variable. Futures prices are established by standard no‐arbitrage arguments and the Kalman filter methodology is used to estimate the model parameters for corn futures, soybean futures, and wheat futures based on weekly data from the Chicago Board of Trade for the period 1972–1997. Furthermore, in a discussion of the estimated seasonal patterns in agricultural commodity prices, the paper provides empirical evidence on the theory of storage that predicts a negative relationship between stocks of inventory and convenience yields; in particular, convenience yields used in this analysis are extracted using the Kalman filter. © 2002 Wiley Periodicals, Inc. Jrl Fut Mark 22:393–426, 2002     

Do volatility determinants vary across futures contracts? Insights from a smoothed Bayesian estimator

We apply a new Bayesian approach to multiple‐contract futures data. It allows the volatility of futures prices to depend upon physical inventories and the contract's time to delivery—and it allows those parametric effects to vary over time. We investigate price movements for lumber contracts over a 13‐year period and find a time‐varying negative relationship between lumber inventories and lumber futures price volatility. The Bayesian approach leads to different conclusions regarding the size of the inventory effect than does the standard method of parametric restrictions across contracts. The inventory effect is smaller for the most recent contracts when the inventory levels are larger. In contrast, the Bayesian approach does not lead to substantively different conclusions about the time‐to‐delivery effect than do traditional classical methods. © 2009 Wiley Periodicals, Inc. Jrl Fut Mark 30:257–277, 2010