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 note on utility‐based futures hedging performance measure

This note considers the estimator for the utility‐based hedging performance. It shows that the estimator incurs a downward bias, regardless of whether the conventional mean‐variance expected utility function or the more general risk‐averse utility function is adopted. Consequently, the usefulness of the futures contract is under‐estimated. © 2011 Wiley Periodicals, Inc. Jrl Fut Mark     

Optimal hedging with a regime‐switching time‐varying correlation GARCH model

The authors develop a Markov regime‐switching time‐varying correlation generalized autoregressive conditional heteroscedasticity (RS‐TVC GARCH) model for estimating optimal hedge ratios. The RS‐TVC nests within it both the time‐varying correlation GARCH (TVC) and the constant correlation GARCH (CC). Point estimates based on the Nikkei 225 and the Hang Seng index futures data show that the RS‐TVC outperforms the CC and the TVC both in‐ and out‐of‐sample in terms of variance reduction. Based on H. White's (2000) reality check, the null hypothesis of no improvement of the RS‐TVC over the TVC is rejected for the Nikkei 225 index contract but is not rejected for the Hang Seng index contract. © 2007 Wiley Periodicals, Inc. Jrl Fut Mark 27:495–516, 2007     

Dynamic hedging of paper with T bill futures

Despite the growing importance of the commercial paper market there is no empirical work investigating the hedging performance of dynamic hedging strategies versus traditional static hedging strategies. This article proposes a dynamic hedging model for commercial paper that takes advantage of time dependencies present in the joint density of commercial paper and T-bill futures. The hedging effectiveness of the dynamic model is compared to that of the static regression model. There is clear evidence that dynamic hedging is superior to static hedging in terms of both total variance reduction and expected utility maximization. These results hold even when transactions costs are explicitly taken into account. © 1998 John Wiley & Sons, Inc. Jrl Fut Mark 18:925–938, 1998     

Spot‐futures spread,time‐varying correlation,and hedging with currency futures

This article investigates the effects of the spot‐futures spread on the return and risk structure in currency markets. With the use of a bivariate dynamic conditional correlation GARCH framework, evidence is found of asymmetric effects of positive and negative spreads on the return and the risk structure of spot and futures markets. The implications of the asymmetric effects on futures hedging are examined, and the performance of hedging strategies generated from a model incorporating asymmetric effects is compared with several alternative models. The in‐sample comparison results indicate that the asymmetric effect model provides the best hedging strategy for all currency markets examined, except for the Canadian dollar. Out‐of‐sample comparisons suggest that the asymmetric effect model provides the best strategy for the Australian dollar, the British pound, the deutsche mark, and the Swiss franc markets, and the symmetric effect model provides a better strategy than the asymmetric effect model in the Canadian dollar and the Japanese yen. The worst performance is given by the naïve hedging strategy for both in‐sample and out‐of‐sample comparisons in all currency markets examined. © 2006 Wiley Periodicals, Inc. Jrl Fut Mark 26:1019–1038, 2006     

VIX futures and its closed‐form pricing through an affine GARCH model with realized variance

This paper studies the forecasting of volatility index (VIX) and the pricing of its futures by a generalized affine realized volatility model proposed by Christoffersen et al. This model is a weighted average of a GARCH and a pure realized variance (RV) model that incorporates each volatility component into the new dynamics. We rewrite the VIX in terms of both volatility components and then derive closed‐form formulas for the VIX forecasting and its futures pricing. Our empirical studies find that a unification of the GARCH and the RV in the modeling substantially improves the forecasting of this index and the pricing of its futures.     

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     

Optimal hedging with futures options

This paper explores the use of commodity options as risk management tools in incomplete markets with particular attention to alternative hedging strategies in the presence of basis and quantity risks. Hedgers typically face basis and quantity risks, which result in incomplete markets. In such markets, portfolios of commodity options prove a viable means of managing risks.Hedging opportunities are characterized using partial equilibrium frameworks, comparative statics, and an illustration from a simulation. A nonlinear optimization technique determines optimal portfolios of commodity options. All models examined are static two-date models. Therefore, they ignore the dynamic aspects of the hedger's problem, and distinguish neither American from European options, nor futures from forward markets.     

Lévy betas: Static hedging with index futures

This study considers calibration to forward‐looking betas by extracting information on equity and index options from prices using Lévy models. The resulting calibrated betas are called Lévy betas. The objective of the proposed approach is to capture market expectations for future betas through option prices, as betas estimated from historical data may fail to reflect structural change in the market. By assuming a continuous‐time capital asset pricing model (CAPM) with Lévy processes, we derive an analytical solution to index and stock options, thus permitting the betas to be implied from observed option prices. One application of Lévy betas is to construct a static hedging strategy using index futures. Employing Hong Kong equity and index option data from September 16, 2008 to October 15, 2009, we show empirically that the Lévy betas during the sub‐prime mortgage crisis period were much more volatile than those during the recovery period. We also find evidence to suggest that the Lévy betas improve static hedging performance relative to historical betas and the forward‐looking betas implied by a stochastic volatility model.     

A hedging deficiency in eurodollar futures

The eurodollar futures contract of the Chicago Mercantile Exchange is arguably the most successful of all futures contracts. The contract is structured such that its price does not converge to the price of the underlying eurodollar time deposit. Ignoring the daily settlement, one typically assumes that a eurodollar futures contract perfectly hedges an anticipated loan pegged to LIBOR, provided the loan rate is set at the eurodollar expiration. This article demonstrates that this hedge is not perfect, leaving a risk empirically estimated at four basis points, a seemingly small amount but considerably larger than the bid–ask spread on the futures. © 2006 Wiley Periodicals, Inc. Jrl Fut Mark 26:189–207, 2006     

Estimation bias of futures hedging performance: A note

The conventional approach applies an estimated optimal hedge ratio to evaluate and compare hedging performance. This note shows that the approach produces a biased result. Moreover, it tends to underestimate the true hedging performance. © 2006 Wiley Periodicals, Inc. Jrl Fut Mark 26:835–841, 2006     

A random coefficient autoregressive Markov regime switching model for dynamic futures hedging

The random coefficient autoregressive Markov regime switching model (RCARRS) for estimating optimal hedge ratios, which generalizes the random coefficient autoregressive (RCAR) and Markov regime switching (MRS) models, is introduced. RCARRS, RCAR, MRS, BEKK‐GARCH, CC‐GARCH, and OLS are compared with the use of aluminum and lead futures data. RCARRS outperforms all models out‐of‐sample for lead and is second only to BEKK‐GARCH for aluminum in terms of variancereduction point estimates. White's data‐snooping reality check null hypothesis of no superiority is rejected for BEKK‐GARCH and RCARRS for aluminum, but not for lead. © 2006 Wiley Periodicals, Inc. Jrl Fut Mark 26:103–129, 2006     

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     

Optimal futures hedging for energy commodities: An application of the GAS model

This paper applies generalized autoregressive score-driven (GAS) models to futures hedging of crude oil and natural gas. For both commodities, the GAS framework captures the marginal distributions of spot and futures returns and corresponding dynamic copula correlations. We compare within-sample and out-of-sample hedging effectiveness of GAS models against constant ordinary least square (OLS) strategy and time-varying copula-based GARCH models in terms of volatility reduction and Value at Risk reduction. We show that the constant OLS hedge ratio is not inherently inferior to the time-varying alternatives. Nonetheless, GAS models tend to exhibit better hedging effectiveness than other strategies, particularly for natural gas.