Term Structure Of Futures Prices Research Articles

The Return-Volatility Relation in Commodity Futures Markets

By employing a continuous time stochastic volatility model, the dynamic relation between price returns and volatility changes in the commodity futures markets is analysed. An extensive daily database of gold and crude oil futures and futures options is used to estimate the model that is well suited to assess the return-volatility relation for the entire term structure of futures prices. The empirical results indicate a positive relation in the gold futures market and a negative relation in the crude oil futures market, especially over periods of high volatility principally driven by market-wide shocks. However, the opposite reaction occurs over quiet volatility periods when typically commodity-specific effects dominate. As leverage effect, volatility feedback effect and inventory effect do not adequately explain this reaction especially for the crude oil futures, the convenience yield effect is proposed. Accordingly, commodity futures markets in backwardation entail a positive relation, while futures markets in contango entail a negative relation.

Putting Smiles Back to the Futures

This article reports a practical approach to extend the classical Gabillon model to allow explicit modelling of commodity futures smiles. The original Gabillon model is first extended with a deterministic shift to fit the term structure of futures prices. The smile information of individual futures is extracted from the futures options markets in terms of the implied marginal distributions. An algorithm based on the copula technique is then developed to reconstruct the joint distribution of the underlying futures prices that is consistent with both the term structure of volatilities and the marginal distributions of individual futures. Examples are provided to illustrate the calibration procedure and options pricing.

Residual Model for Future Prices

This paper presents a new factor model for the term structure of futures prices of commodities. This model fills a gap in the literature by providing not only flexibility on the deterministic drivers of the term structure’s (TS) curve but also a clear meaning of the stochastic factors implied by the model. These benefits allow the user of the model to predict, and to protect himself against, changes in the slope and concavity of the TS curve. In particular, these new factors are identified as the spot price, the slope and the concavity of the curve, and they directly tackle the phenomena defined as contango and backwardation movements. It is shown that the model provides a good fit for the term structure’s curve under the historical measure. Conditions on the processes of the factors are obtained under an equivalent measure which ensures an absence of arbitrage. Explicit expressions for the term structure of volatilities and correlations are also provided. The paper concludes with a set of derivatives inspired by the new factors which could be used to protect an investor against contango and backwardation movements.

Markov models for commodity futures: theory and practice

The objective of this paper is to develop a generic, yet practical, framework for the construction of Markov models for commodity derivatives. We aim for sufficient richness to permit applications to a broad variety of commodity markets, including those that are characterized by seasonality and by spikes in the spot process. In the first, largely theoretical, part of the paper we derive a series of useful results concerning the low-dimensional Markov representation of the dynamics of an entire term structure of futures prices. Extending previous results in the literature, we cover jump-diffusive models with stochastic volatility as well as several classes of regime-switching models. To demonstrate the process of building models for a specific commodity market, the second part of the paper applies a selection of our theoretical results to the exercise of constructing and calibrating derivatives trading models for USD natural gas. Special attention is paid to the incorporation of empirical seasonality effects in futures prices, in implied volatilities and their ‘smile’, and in correlations between futures contracts of different maturities. European option pricing in our proposed gas model is closed form and of the same complexity as the Black–Scholes formula.

Black Gold and Fool's Gold: Speculation in the Oil Futures Market

This paper addresses the question of whether the oil price spike of 2003-2008 was a bubble. We document and discuss what is known about the level of speculation in the paper oil market. We then analyze the dynamics of the term structure of futures prices, both during the earlier period of 1985-2002 and during the spike. The dynamics of the term structure changed in important ways during this latter period, and we explain how this may have contributed to generating a bubble. We also explain how this answers the puzzle of the lack of accumulating above-ground inventories. Finally, we discuss the implications for regulatory reform of the paper oil markets.

Black Gold & Fool’s Gold: Speculation in the Oil Futures Market

This paper addresses the question of whether the oil price spike of 2003-2008 was a bubble. We document and discuss what is known about the level of speculation in the paper oil market. We then analyze the dynamics of the term structure of futures prices, both during the earlier period of 1985-2002 and during the spike. The dynamics of the term structure changed in important ways during this latter period, and we explain how this may have contributed to generating a bubble. We also explain how this answers the puzzle of the lack of accumulating above-ground inventories. Finally, we discuss the implications for regulatory reform of the paper oil markets.

Markov Models for Commodity Futures: Theory and Practice

This objective of this paper is to develop a generic, yet practical framework for construction of Markov models for commodity derivatives. We aim for sufficient richness to permit applications to a broad variety of commodity markets, including those that are characterized by seasonality and by spikes in the spot process. In the first, largely theoretical, part of the paper we derive a series of useful results about low-dimensional Markov representation of the dynamics of an entire term structure of futures prices. Extending previous results in the literature, we cover jump-diffusive models with stochastic volatility as well as several classes of regime-switch models. To demonstrate the process of building models for a specific commodity market, the second part of the paper applies a selection of our theoretical results to the exercise of constructing and calibrating derivatives trading models for USD natural gas. Special attention is paid to the incorporation of empirical seasonality effects in futures prices, in implied volatilities and their smile, and in correlations between futures contracts of different maturities. European option pricing in our proposed gas model is closed-form and of the same complexity as the Black-Scholes formula.

Petroleum spreads and the term structure of futures prices

We employ the term structure of gasoline and heating oil prices, proxied by convenience yields, to explain the variation in the spread between the prices of gasoline and crude oil and the prices of heating oil and crude oil. We demonstrate that the marginal convenience yields in the gasoline and heating oil markets explained much of the variation in the spreads between 1986 and 1999. The evidence indicates the importance of a disaggregated treatment of the term structure of prices: the convenience yield is found to explain a substantially higher amount of the variation in the spread when it is decomposed by maturity, even after controls for seasonality and inventory levels are implemented. These findings support the notion that the futures term structure contains information beyond what can be garnered via obvious or easily available proxies of current supply and demand. The findings are also supported in an alternate specification that tests for the origins of information spillover (leadership) between the commodities: it is demonstrated that decomposed convenience yields explain a substantial portion of the volatility spillover from the gasoline and heating oil markets to the crude market.

The Strategic and Tactical Value of Commodity Futures

Investors face numerous challenges when seeking to estimate the prospective performance of a long-only investment in commodity futures. For instance, historically, the average annualized excess return of the average individual commodity futures has been approximately zero and commodity futures returns have been largely uncorrelated with one another. The prospective annualized excess return of a rebalanced portfolio of commodity futures, however, can be “equity-like.“ Some security characteristics (such as the term structure of futures prices) and some portfolio strategies have historically been rewarded with above-average returns. It is important to avoid naive extrapolation of historical returns and to strike a balance between dependable sources of return and possible sources of return.

ON FINITE DIMENSIONAL REALIZATIONS FOR THE TERM STRUCTURE OF FUTURES PRICES

We consider HJM type models for the term structure of futures prices, where the volatility is allowed to be an arbitrary smooth functional of the present futures price curve. Using a Lie algebraic approach we investigate when the infinite dimensional futures price process can be realized by a finite dimensional Markovian state space model, and we give general necessary and sufficient conditions, in terms of the volatility structure, for the existence of a finite dimensional realization. We study a number of concrete applications including a recently developed model for gas futures. In particular we provide necessary and sufficient conditions for when the induced spot price is a Markov process. In particular we can prove that the only HJM type futures price models with spot price dependent volatility structures which generically possess a spot price realization are the affine ones. These models are thus the only generic spot price models from a futures price term structure point of view.

The Strategic and Tactical Value of Commodity Futures

Investors face numerous challenges when seeking to estimate the prospective performance of a longonly investment in commodity futures. For instance, historically, the average annualized excess return of the average individual commodity futures has been approximately zero and commodity futures returns have been largely uncorrelated with one another. The prospective annualized excess return of a rebalanced portfolio of commodity futures, however, can be "equity-like." Some security characteristics (such as the term structure of futures prices) and some portfolio strategies have historically been rewarded with above-average returns. It is important to avoid naive extrapolation of historical returns and to strike a balance between dependable sources of return and possible sources of return.

An N‐factor Gaussian model of oil futures prices

AbstractThis article studies the ability of an N‐factor Gaussian model to explain the stochastic behavior of oil futures prices when estimated with the use of all available price information, as opposed to traditional approaches of aggregating data for a set of maturities. A Kalman filter estimation procedure that allows for a time‐dependent number of daily observations is used to calibrate the model. When applied to all daily oil futures price transactions from 1992 to 2001, the model performs very well, requiring at least three factors to explain the term structure of futures prices, but four factors to fit the volatility term structure. The model also performs very well for daily copper futures transactions from 1992 to 2001 and for out‐of‐sample daily oil futures transactions from 2002 to 2004. © 2006 Wiley Periodicals, Inc. Jrl Fut Mark 26:243–268, 2006

An N-Factor Gaussian Model of Oil Futures Prices

This paper studies the ability of an N-factor Gaussian model to explain the stochastic behavior of oil futures prices when estimated using all available price information, as opposed to traditional approaches of aggregating data for a set of maturities. A Kalman filter estimation procedure that allows for a time-dependent number of daily observations is used to calibrate the model. When applied to all daily oil futures price transactions from 1992 to 2001, the model performs very well requiring at least three factors to explain the term structure of futures prices, but four factors to fit the volatility term structure. The model also performs very well for daily copper futures transactions from 1992 to 2001 and for out-of-sample daily oil futures transactions from 2002 to 2004.

The Tactical and Strategic Value of Commodity Futures

Historically, commodity futures have had excess returns similar to those of equities. But what should we expect in the future? The usual risk factors are unable to explain the time-series variation in excess returns. In addition, our evidence suggests that commodity futures are an inconsistent, if not tenuous, hedge against unexpected inflation. Further, the historically high average returns to a commodity futures portfolio are largely driven by the choice of weighting schemes. Indeed, an equally weighted long-only portfolio of commodity futures returns has approximately a zero excess return over the past 25 years. Our portfolio analysis suggests that the a long-only strategic allocation to commodities as a general asset class is a bet on the future term structure of commodity prices, in general, and on specific portfolio weighting schemes, in particular. In contrast, we provide evidence that there are distinct benefits to an asset allocation overlay that tactically allocates using commodity futures exposures. We examine three trading strategies that use both momentum and the term structure of futures prices. We find that the tactical strategies provide higher average returns and lower risk than a long-only commodity futures exposure.

Comparing alternative assumptions on the term structure of futures prices: Reply

AbstractDonald Lien and Yan Wang (this issue) suggest an alternative test for different specifications of the term structure of futures prices, as used in our recently published paper in The Journal of Futures Markets. Our paper (Y. V. Veld‐Merkoulova and F. A. de Roon, 2003) focuses on developing optimal hedging strategies in case sufficiently long‐term futures contracts are not available (or not actively traded) on the exchange. One of the preliminary steps underlying this strategy was to compare linear and log‐linear term structures of futures prices in order to choose an appropriate specification. Although this is not the main issue of our paper, it is certainly important to use the correct econometric procedure in testing alternative model specifications. The results found by Lien and Wang do not contradict our conclusion that a linear term structure of futures yields is superior to a linear term structure of futures prices. However, as we point out here, the tests suggested by Lien and Wang are not without flaws. © 2004 Wiley Periodicals, Inc. Jrl Fut Mark 24:1101–1104, 2004

Pricing Term Structure Risk in Futures Markets

One-period expected returns on futures contracts with different maturities differ because of risk premia in the spreads between futures and spot prices. We analyze the expected returns for futures contracts with different maturities using the information that is present in the current term structure of futures prices. A simple affine one-factor model that implies a constant covariance between the pricing kernel and the cost-of-carry cannot be rejected for heating oil and German Mark futures contracts. For gold and soybean futures, the risk premia depend on the slope of the current term structure of futures prices, while for live cattle futures, the evidence is mixed.