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     

The realized volatility of FTSE‐100 futures prices

Five‐minute returns from FTSE‐100 index futures contracts are used to obtain accurate estimates of daily index volatility from January 1986 to December 1998. These realized volatility measures are used to obtain inferences about the distributional and autocorrelation properties of FTSE‐100 volatility. The distribution of volatility measured daily is similar to lognormal while the volatility time series has persistent positive autocorrelation that displays long‐memory effects. The distribution of daily returns standardized using the measures of realized volatility is shown to be close to normal, unlike the unconditional distribution. © 2002 Wiley Periodicals, Inc. Jrl Fut Mark 22:627–648, 2002     

Systemic risk in market microstructure of crude oil and gasoline futures prices: A Hawkes flocking model approach

We propose the Hawkes flocking model that assesses systemic risk in high-frequency processes at the two perspectives—endogeneity and interactivity. We examine the futures markets of West Texas Intermediate (WTI) crude oil and gasoline for the past decade, and perform a comparative analysis with conditional value-at-risk as a benchmark measure. In terms of high-frequency structure, we derive the empirical findings. The endogenous systemic risk in WTI was significantly higher than that in gasoline, and the level at which gasoline affects WTI was constantly higher than that in the opposite case. Moreover, although the relative influence's degree was asymmetric, its difference has gradually reduced.     

The relationship between spot and futures prices: Evidence from the crude oil market

This article examines the relationship between the spot and futures prices of WTI crude oil using a sample of daily data. Linear causality testing reveals that futures prices lead spot prices, but nonlinear causality testing reveals a bidirectional effect. This result suggests that both spot and futures markets react simultaneously to new information. © 1999 John Wiley & Sons, Inc. Jrl Fut Mark 19: 175–193, 1999     

Density forecasts of crude‐oil prices using option‐implied and ARCH‐type models

The predictive accuracy of competing crude‐oil price forecast densities is investigated for the 1994–2006 period. Moving beyond standard ARCH type models that rely exclusively on past returns, we examine the benefits of utilizing the forward‐looking information that is embedded in the prices of derivative contracts. Risk‐neutral densities, obtained from panels of crude‐oil option prices, are adjusted to reflect real‐world risks using either a parametric or a non‐parametric calibration approach. The relative performance of the models is evaluated for the entire support of the density, as well as for regions and intervals that are of special interest for the economic agent. We find that non‐parametric adjustments of risk‐neutral density forecasts perform significantly better than their parametric counterparts. Goodness‐of‐fit tests and out‐of‐sample likelihood comparisons favor forecast densities obtained by option prices and non‐parametric calibration methods over those constructed using historical returns and simulated ARCH processes. © 2010 Wiley Periodicals, Inc. Jrl Fut Mark 31:727–754, 2011     

Modes of fluctuation in metal futures prices

This article examines the stochastic structure of metal futures prices. First, this article presents a stationary multi‐factor model of fluctuations in the futures price curve. Next, the model is extended to allow for time variation in the factors or “modes” of fluctuation. The model is estimated using futures price data for three very different metals: copper, which is an industrial metal; gold, which is a precious metal; and silver, which is in transition from a precious metal to an industrial metal. The estimation results show that the shapes and importance of the various modes of fluctuation for gold and silver are much different from those for copper. Gold and silver futures price curves can be adequately modeled as a time‐varying one‐factor model. Copper, however, has a more complicated structure and should be modeled as a time‐varying two‐ or three‐factor model. © 2000 John Wiley & Sons, Inc. Jrl Fut Mark 20:219–242, 2000     

Time series volatility of commodity futures prices

This article examines the pattern of volatility over time of a series of commodity futures prices, and focuses in particular on the futures price variability as the maturity date of the futures contract approaches. In a rational expectations model of asymmetric information, the article provides conditions under which the Samuelson hypothesis—that the variability of futures prices increases as maturity approaches—will be true. © 2000 John Wiley & Sons, Inc. Jrl Fut Mark 20: 127–144, 2000     

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     

Effects of nondiscretionary trading on futures prices

This paper examines the effects of the nondiscretionary trading demands of volatility index (VIX) exchange-traded products (ETPs) issuers on the prices and volumes in the VIX futures. We find that the ETPs' informationless, mechanical rebalancing of futures positions to maintain the constant maturity of the index and the promised leverage ratios of the VIX ETPs have significantly positive predictive power for end-of-day futures returns. We also show that the impact on price has diminished through time from increased liquidity provided by hedge funds, and the “natural” hedging of the issuers' inverse products.     

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     

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