Approximation for convenience yield in commodity futures pricing

The pricing of commodity futures contracts is important both for professionals and academics. It is often argued that futures prices include a convenience yield, and this article uses a simple trading strategy to approximate the impact of convenience yields. The approximation requires only three variables—underlying asset price volatility, futures contract price volatility, and the futures contract time to maturity. The approximation is tested using spot and futures prices from the London Metals Exchange contracts for copper, lead, and zinc with quarterly observations drawn from a 25‐year period from 1975 to 2000. Matching Euro‐Market interest rates are used to estimate the risk‐free rate. The convenience yield approximation is both statistically and economically important in explaining variation between the futures price and the spot price after adjustment for interest rates. © 2002 Wiley Periodicals, Inc. Jrl Fut Mark 22:1005–1017, 2002     

On commodity price limits

This paper examines the behavior of futures prices and trader positions around the occurrence of price limits in commodity futures markets. We ask whether limit events are the result of shocks to fundamental volatility or the result of temporary volatility induced by the trading of noncommercial market participants (speculators). We find little evidence that limits events are the result of speculative activity, but instead associated with shocks to fundamentals that lead to persistent price changes. When futures trading halts price discovery migrates to options markets, but option prices provide a biased estimate of subsequent future prices when trading resumes.     

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     

Migration of price discovery in semiregulated derivatives markets

This study investigates the information content of futures option prices when the underlying futures price is regulated and the futures option price is not. The New York Board of Trade (NYBOT) provides the empirical setting for this regulatory mismatch. Many commodity derivatives markets regulate the prices of all derivatives on a single underlying commodity simultaneously. Some exchanges, including the NYBOT, regulate only their futures contracts, leaving the options on these futures contracts unregulated. This study takes a particular interest in the option‐implied futures price when the observed futures price is locked limit. © 2006 Wiley Periodicals, Inc. Jrl Fut Mark 26:209–241, 2006     

Clustering in the futures market: Evidence from S&P 500 futures contracts

We document trade price clustering in the futures markets. We find clustering at prices of x.00 and x.50 for S&P 500 futures contracts. While trade price clustering is evident throughout time to maturity of these contracts, there is a dramatic change when the S&P 500 futures contract is designated a front‐month contract (decrease in clustering) and a back‐month contract (increase in clustering). We find that trade price clustering is a positive function of volatility and a negative function of volume or open interest. In addition, we find a high degree of clustering in the daily opening and closing prices, but a lower degree of clustering in the settlement prices. © 2004 Wiley Periodicals, Inc. Jrl Fut Mark 24:413–428, 2004     

Volatility dynamics of NYMEX natural gas futures prices

We examine the volatility dynamics of NYMEX natural gas futures prices via the partially overlapping time‐series model of Smith (2005. Journal of Applied Econometrics, 20, 405–422). We show that volatility exhibits two important features: (1) volatility is greater in the winter than in the summer, and (2) the persistence of price shocks and, hence, the correlations among concurrently traded contracts, displays substantial seasonal and cross‐sectional variation in a way consistent with the theory of storage. We demonstrate that, by ignoring the seasonality in the volatility dynamics of natural gas futures prices, previous studies have suggested sub‐optimal hedging strategies. © 2008 Wiley Periodicals, Inc. Jrl Fut Mark 28:438–463, 2008     

Why do expiring futures and cash prices diverge for grain markets?

In recent years, cash and futures prices have failed to converge at expiration for selected corn, soybean, and wheat commodity contracts. This lack of convergence raises questions about the effectiveness of arbitrage activities, and increases concerns about the usefulness of these contracts for hedging. We describe the delivery process for these contracts, and show that it embeds a valuable real option on the long side—the option to exchange the deliverable for another futures contract. As the relative volatility of cash and futures prices increases, this option increases in value, which disconnects the cash market from the deliverable instrument in a futures contract. Our estimates of this option's value show that it may create significant price divergence. We parameterize an option pricing model using data on these three commodities from 2000 to 2008 and show that the option model fits closely to recent episodes of non‐convergence, which lends support to the importance of real option effects. © 2010 Wiley Periodicals, Inc. Jrl Fut Mark

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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     

Futures price limit moves as options

This note demonstrates that an asset's price in an environment with price limit rules can be replicated by the price of a portfolio consisting of a riskless asset and two synthetic options. A procedure is developed to unbundle the unobservable option values imbedded in the actual futures price and impute a theoretical true futures price. Using this framework, evidence from the Treasury Bond futures market suggests that theoretical true futures prices diverge from actual futures prices, on average, 3 h prior to the activation of price limit rules, indicating that price limit moves might be predictable. The reversal of both the actual futures prices and the theoretical futures prices back within the limit range after a limit move provides support for the possibility that traders tend to overreact when market prices are near price limits. © 2002 Wiley Periodicals, Inc. Jrl Fut Mark 22:901–913, 2002     

Liquidity supply and volatility: futures market evidence

This article examines the provision of liquidity in futures markets as price volatility changes. We find that customer trading costs do not increase with volatility. However, for three of the four contracts studied, the nature of liquidity supply changes with volatility. Specifically, for relatively inactive contracts, customers as a group trade more with each other and less with market makers, on higher volatility days. By contrast, for the most active contract, trading between customers and market makers increases with volatility. We also find that market makers' income per contract decreases with volatility for one of the least active contracts in our sample, but is not significantly affected by volatility for the other contracts. These results are consistent with the idea that, for high‐cost, inactive contracts, market makers react to temporary increases in volatility by raising their bid‐ask spreads significantly, and customers provide increased liquidity through standing limit orders. An implication of our results is that electronic systems, where market maker participation is not required, are able to supply adequate liquidity during volatile periods. © 2001 John Wiley & Sons, Inc. Jrl Fut Mark 21:1–17, 2001     

Volatility spillover effects and cross hedging in corn and crude oil futures

Using a volatility spillover model, we find evidence of significant spillovers from crude oil prices to corn cash and futures prices, and that these spillover effects are time‐varying. Results reveal that corn markets have become much more connected to crude oil markets after the introduction of the Energy Policy Act of 2005. Furthermore, when the ethanol–gasoline consumption ratio exceeds a critical level, crude oil prices transmit positive volatility spillovers into corn prices and movements in corn prices are more energy‐driven. Based on this strong volatility link between crude oil and corn prices, a new cross‐hedging strategy for managing corn price risk using oil futures is examined and its performance is studied. Results show that this cross‐hedging strategy provides only slightly better hedging performance compared with traditional hedging in corn futures markets alone. The implication is that hedging corn price risk in corn futures markets alone can still provide relatively satisfactory performance in the biofuel era. © 2010 Wiley Periodicals, Inc. Jrl Fut Mark     

Natural gas prices and the gas storage report: Public news and volatility in energy futures markets

This study examines the short‐term volatility of natural gas prices through an examination of the intraday prices of the nearby natural gas futures contract traded on the New York Mercantile Exchange. The influence on volatility of what many regard as a key element of the information set influencing the natural gas market is investigated. Specifically, we examine the impact on natural gas futures price volatility of the Weekly American Gas Storage Survey report compiled and issued by the American Gas Association during the period January 1, 1999 through May 3, 2002 and the subsequent weekly report compiled and issued by the U.S. Energy Information Administration after May 6, 2002. We find that the weekly gas storage report announcement was responsible for considerable volatility at the time of its release and that volatility up to 30 minutes following the announcement was also higher than normal. Aside from these results, we document pronounced price volatility in this market both at the beginning of the day and at the end of the day and offer explanations for such behavior. Our results are robust to the manner in which the mean percentage change in the futures price is estimated and to correlation of these changes both within the day and across days. © 2004 Wiley Periodicals, Inc. Jrl Fut Mark 24:283–313, 2004     

Intraday price‐reversal patterns in the currency futures market: The impact of the introduction of GLOBEX and the euro

This article assesses the intraday price‐reversal patterns of seven major currency futures contracts traded on the Chicago Mercantile Exchange over 1988–2003 after 1‐day returns and opening gaps. Significant intraday price‐reversal patterns are observed in five of the seven currency futures contracts, following large price changes. Additional tests are conducted in three subperiods (1988–1992, 1993–1998, and 1999–2003) to examine the impact of the introduction of electronic trading on GLOBEX in 1992 (to assess how a near 24‐hour trading session might impact the next‐day opening and closing futures prices) and the introduction of the euro in 1999 (to assess its impact on price predictability in other futures markets). It is found that the introduction of the GLOBEX in 1992 significantly reduced pricing errors in currency futures in the second subperiod, making the currency futures markets fairly efficient. However, the introduction of the new currency, the euro, and the disappearance of several European currencies in 1999, resulted in significant price patterns (mostly reversals and some persistence) in most of the currency futures, indicating inefficiencies in the third subperiod. © 2006 Wiley Periodicals, Inc. Jrl Fut Mark 26:1089–1130, 2006     

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     

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     

The time-to-maturity pattern of futures price sensitivity to news

This paper examines the effect time-to-maturity has on how sensitive futures prices are to news flows. Unscheduled daily news flows that relate to the underlying asset of a futures contract are related to the daily realized volatility of futures to calculate a price-news sensitivity ratio. The observed pattern follows an inverted U-shape relationship and has a bearing on whether the maturity effect will be noticeable in a futures contract. This paper also shows that by examining the peak-to-maturity of the price sensitivity to news pattern, it is possible to better identify which contracts are more likely to yield higher volatility.     

Forecasting futures returns in the presence of price limits

In a futures market with a daily price‐limit rule, trading occurs only at prices within limits determined by the previous day's settlement price. Price limits are set in dollars but can be expressed as return limits. When the daily return limit is triggered, the true equilibrium futures return (and price) is unobservable. In such a market, investors may suffer from information loss if the return “moves the limit.” Assuming normally distributed futures returns with unknown means but known volatilities, we develop a Bayesian forecasting model in the presence of return limits and provide some numerical predictions. Our innovation is the derivation of the predictive density for futures returns in the presence of return limits. © 2005 Wiley Periodicals, Inc. Jrl Fut Mark 25:199–210, 2005     

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 STRUCTURAL RISK‐NEUTRAL MODEL FOR PRICING AND HEDGING POWER DERIVATIVES

We develop a structural risk‐neutral model for energy market modifying along several directions the approach introduced in Aïd et al. In particular, a scarcity function is introduced to allow important deviations of the spot price from the marginal fuel price, producing price spikes. We focus on pricing and hedging electricity derivatives. The hedging instruments are forward contracts on fuels and electricity. The presence of production capacities and electricity demand makes such a market incomplete. We follow a local risk minimization approach to price and hedge energy derivatives. Despite the richness of information included in the spot model, we obtain closed‐form formulae for futures prices and semiexplicit formulae for spread options and European options on electricity forward contracts. An analysis of the electricity price risk premium is provided showing the contribution of demand and capacity to the futures prices. We show that when far from delivery, electricity futures behave like a basket of futures on fuels.     

Expiration‐day effects—An Asian twist

This study examines the intraday trading activities of index stocks on the common expiration day of index derivatives. In Hong Kong, index futures and index options use an Asian‐style settlement procedure. All contracts are settled against the estimated average settlement price, an arithmetic average of the underlying cash index taken every five minutes on the expiration day. Trading volume and total trade count on the expiration day are both found to be higher than normal. Most important, trading intensifies in terms of volume and frequency close to the five‐minute time marks. The study does not find significant price reversal and price compression patterns. Although significant order imbalance pattern is found on some expiration days, the results show no association between order imbalance pattern and the next‐day return. © 2009 Wiley Periodicals, Inc. Jrl Fut Mark 28:430–450, 2009