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.     

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     

Hedging,liquidity, and the competitive firm under price uncertainty

In this paper, the behavior of the competitive firm under price uncertainty when the firm has access to an intertemporally unbiased futures market is examined. Futures contracts are marked‐to‐market and thus require interim cash settlement of gains and losses. The firm is subject to a liquidity constraint in that it is forced to prematurely close its futures position on which the interim loss incurred exceeds a threshold level. It is shown that the liquidity constrained firm optimally opts for an under‐hedge should it be prudent. Furthermore, the prudent firm cuts down its optimal level of output in response to the presence of the liquidity constraint. As such, the liquidity risk created by the interim funding requirement of a futures hedge adversely affects the hedging and production decisions of the competitive firm under price uncertainty. © 2004 Wiley Periodicals, Inc. Jrl Fut Mark 24:697–706, 2004     

Liquidity risk and the hedging role of options

This study examines the impact of liquidity risk on the behavior of the competitive firm under price uncertainty in a dynamic two‐period setting. The firm has access to unbiased one‐period futures and option contracts in each period for hedging purposes. A liquidity constraint is imposed on the firm such that the firm is forced to terminate its risk management program in the second period whenever the net loss due to its first‐period hedge position exceeds a predetermined threshold level. The imposition of the liquidity constraint on the firm is shown to create perverse incentives to output. Furthermore, the liquidity constrained firm is shown to purchase optimally the unbiased option contracts in the first period if its utility function is quadratic or prudent. This study thus offers a rationale for the hedging role of options when liquidity risk prevails. © 2006 Wiley Periodicals, Inc. Jrl Fut Mark 26:789–808, 2006     

Optimal hedge ratios in the presence of common jumps

This study derives optimal hedge ratios with infrequent extreme news events modeled as common jumps in foreign currency spot and futures rates. A dynamic hedging strategy based on a bivariate GARCH model augmented with a common jump component is proposed to manage currency risk. We find significant common jump components in the British pound spot and futures rates. The out‐of‐sample hedging exercises show that optimal hedge ratios which incorporate information from common jump dynamics substantially reduce daily and weekly portfolio risk. © 2009 Wiley Periodicals, Inc. Jrl Fut Mark 30:801–807, 2010     

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     

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     

Futures hedging when the structure of the underlying asset changes: The case of the BIFFEX contract

This article is concerned with the hedging effectiveness of futures contracts whose underlying asset is an index, when the structure of this index is changing. The case of the freight futures (BIFFEX) contract is examined here. Investigation of this issue is particularly interesting as the composition of its underlying asset, the Baltic Freight Index (BFI), has been revised on a number of occasions in order to improve the hedging performance of the market; previous empirical evidence on the market indicates substantially lower variance reduction (4–19%), compared to other markets (up to 98%). The BFI is a weighted average dry‐cargo freight rate index, compiled from actual freight rates on 11 shipping routes that are dissimilar in terms of vessel sizes and transported commodities. The hedging effectiveness of the market is investigated using both constant and time‐varying hedge ratios, estimated through bivariate error correction GARCH models. Our results indicate that the effectiveness of the BIFFEX contract as a centre for risk management has strengthened over the recent years as a result of the more homogeneous composition of the index. This by itself indicates that the latest restructuring of the index, in November 1999, which is aimed at increasing its homogeneity even further, is likely to have a beneficial impact on the market. © 2000 John Wiley & Sons, Inc. Jrl Fut Mark 20:775–801, 2000     

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     

Liquidity and hedging effectiveness under futures mispricing: International evidence

We analyze the hedging effectiveness of positions that replicate stock indexes using corresponding futures contracts through the application of a dynamic, stochastic hedging strategy proposed by Lafuente, J. A. and Novales, A. (2003). Conclusive gains do not emerge in any of the markets analyzed over the period considered, relative to the use of a constant unit hedge ratio. These findings are consistent with the trend observed in the IBEX 35 futures market study of Lafuente, J. A. and Novales, A. (2003). Our empirical evidence suggests that, contrary to what happens in less liquid markets, the discrepancy between theoretical and quoted prices in index futures contracts in fully developed markets does not represent a noise factor that can be successfully exploited for hedging. © 2009 Wiley Periodicals, Inc. Jrl Fut Mark 29:1050–1066, 2009     

Hedging under model misspecification: All risk factors are equal,but some are more equal than others …

It is often difficult to distinguish among different option pricing models that consider stochastic volatility and/or jumps based on a cross‐section of European option prices. This can result in model misspecification. We analyze the hedging error induced by model misspecification and show that it can be economically significant in the cases of a delta hedge, a minimum‐variance hedge, and a delta‐vega hedge. Furthermore, we explain the surprisingly good performance of a simple ad‐hoc Black‐Scholes hedge. We compare realized hedging errors (an incorrect hedge model is applied) and anticipated hedging errors (the hedge model is the true one) and find that there are substantial differences between the two distributions, particularly depending on whether stochastic volatility is included in the hedge model. Therefore, hedging errors can be useful for identifying model misspecification. Furthermore, model risk has severe implications for risk measurement and can lead to a significant misestimation, specifically underestimation, of the risk to which a hedged position is exposed. © 2011 Wiley Periodicals, Inc. Jrl Fut Mark     

An empirical analysis of the relationship between hedge ratio and hedging horizon using wavelet analysis

In this article, optimal hedge ratios are estimated for different hedging horizons for 23 different futures contracts using wavelet analysis. The wavelet analysis is chosen to avoid the sample reduction problem faced by the conventional methods when applied to non‐overlapping return series. Hedging performance comparisons between the wavelet hedge ratio and error‐correction (EC) hedge ratio indicate that the latter performs better for more contracts for shorter hedging horizons. However, the performance of the wavelet hedge ratio improves with the increase in the length of the hedging horizon. This is true for both within‐sample and out‐of‐sample cases. © 2007 Wiley Periodicals, Inc. Jrl Fut Mark 27:127–150, 2007     

Dealing with downside risk in a multi‐commodity setting: A case for a “Texas hedge”?

This study analyzes the problem of multi‐commodity hedging from the downside risk perspective. The lower partial moments (LPM₂)‐minimizing hedge ratios for the stylized hedging problem of a typical Texas panhandle feedlot operator are calculated and compared with hedge ratios implied by the conventional minimum‐variance (MV) criterion. A kernel copula is used to model the joint distributions of cash and futures prices for commodities included in the model. The results are consistent with the findings in the single‐commodity case in that the MV approach leads to over‐hedging relative to the LPM₂‐based hedge. An interesting and somewhat unexpected result is that minimization of a downside risk criterion in a multi‐commodity setting may lead to a “Texas hedge” (i.e. speculation) being an optimal strategy for at least one commodity. © 2009 Wiley Periodicals, Inc. Jrl Fut Mark 30:290–304, 2010     

The use of term structure information in the hedging of mortgage‐backed securities

This article examines the importance of term structure variables in the hedging of mortgage‐backed securities (MBS) with Treasury futures. Koutmos, G., Kroner, K., and Pericli, A. (1998) find that the optimal hedge ratio is time varying; we determine the effect of yield levels and slopes on this variation. As these variables are closely tied with mortgage refinancing, intuition suggests them to be relevant determinants of the hedge ratio. It was found that a properly specified model of the time varying hedge ratio that excludes the level and slope of the yield curve from the information set would provide similar out‐of‐sample hedging results to a model in which term structure information is included. Thus, both the level of interest rates and the slope of the yield curve are unimportant variables in determining the empirically optimal hedge ratio between MBS and Treasury futures contracts. © 2005 Wiley Periodicals, Inc. Jrl Fut Mark 25:661–678, 2005     

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     

Production,liquidity, and futures price dynamics

This study examines the optimal design of a futures hedge program for the competitive firm under output price uncertainty. All futures contracts are unbiased and marked to market in that they require interim cash settlement of gains and losses. The futures price dynamics follows a first-order autoregression with a random walk serving as a special case. The firm's futures hedge program is constituted of an endogenous provision for premature termination, which depends on how the futures prices are autocorrelated. Succinctly, the firm voluntarily commits to premature liquidation of its futures position on which the interim loss incurred exceeds a predetermined threshold level if the futures prices are positively autocorrelated. In this case, the liquidity constrained firm optimally opts for an over-hedge if its preferences exhibit either constant or increasing absolute risk aversion. If the futures prices are uncorrelated or negatively autocorrelated, the firm prefers to be liquidity unconstrained and thus adopts a full-hedge to completely eliminate the output price risk. © 2008 Wiley Periodicals, Inc. Jrl Fut Mark 28:749–762, 2008     

Optimal hedging under nonlinear borrowing cost,progressive tax rates,and liquidity constraints

Empirical research using optimal hedge ratios usually suggests that producers should hedge much more than they do. In this study, a new theoretical model of hedging is derived. Optimal hedge and leverage ratios and their relationship with yield risk, price variability, basis risk, taxes, and financial risk are determined using alternative assumptions. The motivation to hedge is provided by progressive tax rates and cost of bankruptcy. An empirical example for a wheat and stocker‐steer producer is provided. Results show that there are many factors, often assumed away in the literature, that make farmers hedge little or not at all. Progressive tax rates provide an incentive for farmers to hedge in order to reduce their tax liabilities and increase their after‐tax income. Farmers will hedge when the cost of hedging is less than the benefits of hedging that come from reducing tax liabilities, liquidity costs, or bankruptcy costs. When tax‐loss carryback is allowed, hedging decreases as the amount of tax loss that can be carried back increases. Higher profitability makes benefits from futures trading negligible and hedging unattractive, since farmers move to higher income brackets with near constant marginal tax rates. Increasing basis risk or yield risk also reduce the incentive to hedge. © 2000 John Wiley & Sons, Inc. Jrl Fut Mark 20: 375–396, 2000     

Bernoulli speculator and trading strategy risk

In a continuous‐time model of a complete information economy, we examine the case of a “pure” speculator who chooses to trade only on forward or futures contracts written on interest‐rate‐sensitive instruments. Assuming logarithmic utility, we assess whether his strategy exhibits the same structure as when he uses primitive assets only. It turns out that when interest rates follow stochastic processes, as in the model of Heath, Jarrow, and Morton (1992), where the instantaneous forward rate is driven by an arbitrary number of factors, the speculative trading strategy involving forwards exhibits an extra term vis‐a‐vis the one using futures or primitive assets. This extra term, different from a Merton–Breeden dynamic hedge, is novel and can be interpreted as a hedge against an “endogenous risk,” namely the interest‐rate risk brought about by the optimal trading strategy itself. Thus, only the strategy using futures (or the cash assets themselves) involves a single speculative term, even for the Bernoulli speculator. This result illustrates another major aspect of the marking to market feature that differentiates futures and forwards, and thus has some bearing on the issue of the optimal design of financial contracts. Real financial markets being, in fact, incomplete, the additional “endogenous” risk associated with forwards cannot be hedged perfectly. Since using futures eliminates the latter, risk‐averse agents will find them attractive in relation to forward contracts, other things being equal. © 2000 John Wiley & Sons, Inc. Jrl Fut Mark 20: 507–523, 2000     

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     

Minimum‐variance futures hedging under alternative return specifications

It is widely believed that the conventional futures hedge ratio, is variance‐minimizing when it is computed using percentage returns or log returns. It is shown that the conventional hedge ratio is variance‐minimizing when computed from returns measured in dollar terms but not from returns measured in percentage or log terms. Formulas for the minimum‐variance hedge ratio under percentage and log returns are derived. The difference between the conventional hedge ratio computed from percentage and log returns and the minimum‐variance hedge ratio is found to be relatively small when directly hedging, especially when using near‐maturity futures. However, the minimum‐variance hedge ratio can vary significantly from the conventional hedge ratio computed from percentage or log returns when used in cross‐hedging situations. Simulation analysis shows that the incorrect application of the conventional hedge ratio in crosshedging situations can substantially reduce hedging performance. © 2005 Wiley Periodicals, Inc. Jrl Fut Mark 25:537–552, 2005