Hedging in Futures and Options Markets with Basis Risk

This paper analyzes the hedging decisions for firms facing price and basis risk. Two conditions assumed in most models on optimal hedging are relaxed. Hence, (i) the spot price is not necessarily linear in both the settlement price and the basis risk and (ii) futures contracts and options on futures at different strike prices are available. The design of the first‐best hedging instrument is first derived and then it is used to examine the optimal hedging strategy in futures and options markets. The role of options as useful hedging tools is highlighted from the shape of the first‐best solution. © 2002 John Wiley & Sons, Inc. Jrl Fut Mark 22:59–72, 2002     

Risk aversion,disappointment aversion,and futures hedging

This article examines the effect of disappointment aversion on futures hedging. We incorporated a constant‐absolute‐risk‐aversion (CARA) utility function into the disappointment‐aversion framework of Gul (1991). It is shown that a more disappointment‐averse hedger will choose an optimal futures position closer to the minimum‐variance hedge than will a less‐disappointment‐averse hedger. The effect of disappointment aversion is stronger when the hedger is less risk averse. A small disappointment aversion will cause a near‐risk neutral hedger to take a drastically different position. In addition, a more‐risk‐averse or disappointment‐averse hedger will have a lower reference point. Numerical results indicate that the reference point of a disappointment‐averse hedger tends to be lower than that of a conventional loss‐averse hedger. Consequently, the disappointment‐averse hedger will act more conservatively, not exploiting profitable opportunities as much as the conventional loss averse hedger will. © 2002 John Wiley & Sons, Inc. Jrl Fut Mark 22:123–141, 2002     

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.     

Futures Hedging Under Disappointment Aversion

This article considers optimal futures hedging decisions when the hedger is disappointment‐averse (Gul, 1991). When the futures contract is a perfect hedge instrument, a disappointment‐averse hedger always holds a position closer to the full hedge than a nondisappointment‐averse hedger. In the presence of basis risk, the optimal futures position is either a partial hedge or a full hedge. Neither Texas hedge nor overhedge could be optimal. The effects of different degrees of disappointment aversion on futures trading are also analyzed. © 2001 John Wiley & Sons, Inc. Jrl Fut Mark 21:1029–1042, 2001     

Futures hedging under mark‐to‐market risk

This article introduces mark‐to‐market risk into the conventional futures hedging framework. It is shown that a hedger concerned with maximum daily loss will considerably reduce his futures position when the risk is taken into account. In case of a moderate hedge horizon, the hedger will hedge approximately 80% of his spot position. The effect of mark‐to‐market risk decreases very slowly as the hedge horizon increases. If the hedger is concerned with average daily loss, the effect is minimal for a moderate hedge horizon. © 2003 Wiley Periodicals, Inc. Jrl Fut Mark 23:389–398, 2003     

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     

Investor Sentiment and Return Predictability in Agricultural Futures Markets

This study examines the usefulness of trader‐position‐based sentiment index for forecasting future prices in six major agricultural futures markets. It has been found that large speculator sentiment forecasts price continuations. In contrast, large hedger sentiment predicts price reversals. Small trader sentiment hardly forecasts future market movements. An investigation was performed into various sentiment‐based timing strategies, and it was found that the combination of extreme large trader sentiments provides the strongest timing signal. These results are generally consistent with the hedging‐pressure theory, suggesting that hedgers pay risk premiums to transfer nonmarketable risks in futures markets. Moreover, it does not appear that large speculators in the futures markets possess any superior forecasting ability. © 2001 John Wiley & Sons, Inc. Jrl Fut Mark 21:929–952, 2001     

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     

Price discovery in commodity derivatives: Speculation or hedging?

We investigate whether commodity futures or options markets play a more important role in the price discovery process in the six most actively traded markets: crude oil, natural gas, gold, silver, corn, and soybeans. Using new information leadership techniques, we report new evidence and report that both markets make a meaningful contribution to price discovery in recent times; however, on average, options lead futures in reflecting new information for a majority of these commodities. We find that increased speculation, rather than hedging activity, in commodity derivatives is a key determinant of price discovery in the options markets.     

Risk management with options and futures under liquidity risk

Futures hedging creates liquidity risk through marking to market. Liquidity risk matters if interim losses on a futures position have to be financed at a markup over the risk‐free rate. This study analyzes the optimal risk management and production decisions of a firm facing joint price and liquidity risk. It provides a rationale for the use of options on futures in imperfect capital markets. If liquidity risk materializes, the firm sells options on futures in order to partly cover this liquidity need. It is shown that liquidity risk reduces the optimal hedge ratio and that options are not normally used before a liquidity need actually arises. © 2009 Wiley Periodicals, Inc. Jrl Fut Mark 29:297–318, 2009     

Production and hedging under Knightian uncertainty

This article introduces Knightian uncertainty into the production and futures hedging framework. The firm has imprecise information about the probability density function of spot or futures prices in the future. Decision‐making under such scenario follows the “max‐min” principle. It is shown that inertia in hedging behavior prevails under Knightian uncertainty. In a forward market, there is a region for the current forward price within which full hedge is the optimal hedging policy. This result may help explain why the one‐to‐one hedge ratio is commonly observed. Also inertia increases as the ambiguity with the probability density function increases. When hedging on futures markets with basis risk, inertia is established at the regression hedge ratio. Moreover, if only the futures price is subject to Knightian uncertainty, the utility function has no bearing on the possibility of inertia. © 2000 John Wiley & Sons, Inc. Jrl Fut Mark 20: 397–404, 2000     

Production and hedging under state‐dependent preferences

This study examines the behavior of the competitive firm under output price uncertainty and state‐dependent preferences. When there is a futures market for hedging purposes, the firm's optimal production decision is independent of the output price uncertainty and of the state‐dependent preferences. If the futures contracts are unbiased, the firm's optimal futures position is an over‐hedge or an under‐hedge, depending on whether the firm is correlation averse or correlation loving, and on whether the output price is positively or negatively expectation dependent on the state variable. When the firm has access not only to the unbiased futures but also to fairly priced options, sufficient conditions are derived under which the firm's optimal hedge position includes both hedging instruments. This study thus establishes a hedging role of options, which is over and above that of futures, in the case of state‐dependent preferences. © 2011 Wiley Periodicals, Inc. Jrl Fut Mark 32:945–963, 2012     

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     

Hedging under counterparty credit uncertainty

This study investigates optimal production and hedging decisions for firms facing price risk that can be hedged with vulnerable contracts, i.e., exposed to nonhedgeable endogenous counterparty credit risk. When vulnerable forward contracts are the only hedging instruments available, the firm's optimal level of production is lower than without credit risk. Under plausible conditions on the stochastic dependence between the commodity price and the counterparty's assets, the firm does not sell its entire production on the vulnerable forward market. When options on forward contracts are also available, the optimal hedging strategy requires a long put position. This provides a new rationale for the hedging role of options in the over‐the‐counter markets exposed to counterparty credit risk. © 2008 Wiley Periodicals, Inc. Jrl Fut Mark 28: 248–263, 2008     

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     

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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What to do if a dollar is not a dollar? The impact of inflation risk on production and risk management

An entrepreneur faces two types of risk: one from income generation, one from income spending. His income from firm profits is risky due to output price fluctuations and other risks. As a consumer, he is also exposed to inflation risk since he maximizes expected utility of real income. This article focuses on optimal production and risk management decisions of a risk‐averse entrepreneur jointly facing tradable output price risk and untradable inflation risk. Inflation risk applies multiplicatively to the entrepreneur's entire nominal income. Relative risk aversion and the risks' joint distribution determine the effect of introducing a futures market on production. For dependent risks, this effect may be negative if relative risk aversion is above one. Relative risk aversion and the joint distribution also determine optimal risk management with futures contracts where speculation on a real risk premium and cross hedging may be conflicting objectives. © 2002 Wiley Periodicals, Inc. Jrl Fut Mark 22:371–386, 2002     

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     

Drift matters: An analysis of commodity derivatives

This article presents a reduced‐form, two‐factor model to price commodity derivatives, which generalizes the model by Schwartz and Smith (2000). The model allows for two mean‐reverting stochastic factors and therefore implies that spot and futures prices can be stationary. An empirical study for the crude oil market tests the new model. Out‐of‐sample pricing and hedging results for futures and forwards show that the new model dominates the nonstationary model by Schwartz and Smith in the following sense: It works equally well for short‐term contracts but leads to major improvements for long‐term contracts. This finding is particularly relevant for typical applications like the valuation of commodity‐linked real assets with long maturities. © 2005 Wiley Periodicals, Inc. Jrl Fut Mark 25:211–241, 2005     

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