An empirical analysis of dynamic multiscale hedging using wavelet decomposition

This study investigates the hedging effectiveness of a dynamic moving‐window OLS hedging model, formed using wavelet decomposed time‐series. The wavelet transform is applied to calculate the appropriate dynamic minimum‐variance hedge ratio for various hedging horizons for a number of assets. The effectiveness of the dynamic multiscale hedging strategy is then tested, both in‐ and out‐of‐sample, using standard variance reduction and expanded to include a downside risk metric, the scale‐dependent Value‐at‐Risk. Measured using variance reduction, the effectiveness converges to one at longer scales, while a measure of VaR reduction indicates a portion of residual risk remains at all scales. Analysis of the hedge portfolio distributions indicate that this unhedged tail risk is related to excess portfolio kurtosis found at all scales.     

An empirical analysis of the relationship between the hedge ratio and hedging horizon: A simultaneous estimation of the short‐ and long‐run hedge ratios

This article analyzes the effects of the length of hedging horizon on the optimal hedge ratio and hedging effectiveness using 9 different hedging horizons and 25 different commodities. We discuss the concept of short‐ and long‐run hedge ratios and propose a technique to simultaneously estimate them. The empirical results indicate that the short‐run hedge ratios are significantly less than 1 and increase with the length of hedging horizon. We also find that hedging effectiveness increases with the length of hedging horizon. However, the long‐run hedge ratio is found to be close to the naïve hedge ratio of unity. This implies that, if the hedging horizon is long, then the naïve hedge ratio is close to the optimum hedge ratio. © 2004 Wiley Periodicals, Inc. Jrl Fut Mark 24:359–386, 2004     

Fractional cointegration and futures hedging

This article examines the performance of various hedge ratios estimated from different econometric models: The FIEC model is introduced as a new model for estimating the hedge ratio. Utilized in this study are NSA futures data, along with the ARFIMA-GARCH approach, the EC model, and the VAR model. Our analysis identifies the prevalence of a fractional cointegration relationship. The effects of incorporating such a relationship into futures hedging are investigated, as is the relative performance of various models with respect to different hedge horizons. Findings include: (i) Incorporation of conditional heteroskedasticity improves hedging performance; (ii) the hedge ratio of the EC model is consistently larger than that of the FIEC model, with the EC providing better post-sample hedging performance in the return–risk context; (iii) the EC hedging strategy (for longer hedge horizons of ten days or more) incorporating conditional heteroskedasticty is the dominant strategy; (iv) incorporating the fractional cointegration relationship does not improve the hedging performance over the EC model; (v) the conventional regression method provides the worst hedging outcomes for hedge horizons of five days or more. Whether these results (based on the NSA index) can be generalized to other cases is proposed as a topic for further research. © 1999 John Wiley & Sons, Inc. Jrl Fut Mark 19: 457–474, 1999     

Hedging performance analysis of energy markets: Evidence from copula quantile regression

This study investigates hedging performance with respect to different market structures for energy-related commodities, including West Texas Intermediate crude oil, Brent crude oil, Chinese crude oil, and Heating oil. Copula quantile regression functions and the generalized autoregressive conditionally heteroscedasticity model are combined to analyze the nonlinear impact of dependence and the heterogeneous impact of market structure changes on hedging performance. Results show that hedging performance presents nonlinearity and market structure changes have surprisingly strong heterogeneous effects on the quantile hedge ratio, where bearish and bullish have lower hedge ratios than normal markets, which is captured better by Clayton copula quantile regression. Additionally, the trend of hedging effectiveness over different market structures also shows an inverted U shape. After changing data frequency or the types of futures contracts, the conclusions remain the same. Our empirical findings imply that hedgers are supposed to adjust the hedging number of futures according to market structure changes to hedge price risk effectively.     

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 higher moments

This study proposes a utility‐based framework for the determination of optimal hedge ratios (OHRs) that can allow for the impact of higher moments on hedging decisions. We examine the entire hyperbolic absolute risk aversion family of utilities which include quadratic, logarithmic, power, and exponential utility functions. We find that for both moderate and large spot (commodity) exposures, the performance of out‐of‐sample hedges constructed allowing for nonzero higher moments is better than the performance of the simpler OLS hedge ratio. The picture is, however, not uniform throughout our seven spot commodities as there is one instance (cotton) for which the modeling of higher moments decreases welfare out‐of‐sample relative to the simpler OLS. We support our empirical findings by a theoretical analysis of optimal hedging decisions and we uncover a novel link between OHRs and the minimax hedge ratio, that is the ratio which minimizes the largest loss of the hedged position. © 2011 Wiley Periodicals, Inc. Jrl Fut Mark 32:909–944, 2012     

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     

Minimum variance cross hedging under mean‐reverting spreads,stochastic convenience yields,and jumps: Application to the airline industry

Exchange traded futures contracts often are not written on the specific asset that is a source of risk to a firm. The firm may attempt to manage this risk using futures contracts written on a related asset. This cross hedge exposes the firm to a new risk, the spread between the asset underlying the futures contract and the asset that the firm wants to hedge. Using the specific case of the airline industry as motivation, we derive the minimum variance cross hedge assuming a two‐factor diffusion model for the underlying asset and a stochastic, mean‐reverting spread. The result is a time‐varying hedge ratio that can be applied to any hedging horizon. We also consider the effect of jumps in the underlying asset. We use simulations and empirical tests of crude oil, jet fuel cross hedges to demonstrate the hedging effectiveness of the model. © 2009 Wiley Periodicals, Inc. Jrl Fut Mark 29:736–756, 2009     

Estimating the optimal hedge ratio with focus information criterion

In recent years, the error‐correction model without lags has been used in estimating the minimum‐variance hedge ratio. This article proposes the use of the same error‐correction model, but with lags in spot and futures returns in estimating the hedge ratio. In choosing the lag structure, use of the Akaike information criterion (AIC) and recently proposed focus information criterion (FIC) by G. Claeskens and N. L. Hjort (2003) is suggested. The proposed methods are applied to 24 different futures contracts. Even though the FIC hedge ratio is expected to perform better in terms of mean‐squared error, the AIC hedge ratio is found to perform as well as the FIC and better than the simple hedge ratios in terms of hedging effectiveness. © 2005 Wiley Periodicals, Inc. Jrl Fut Mark 25:1011– 1024, 2005     

The incremental value of a futures hedge using realized volatility

A number of prior studies have developed a variety of multivariate volatility models to describe the joint distribution of spot and futures, and have applied the results to form the optimal futures hedge. In this study, the authors propose a new class of multivariate volatility models encompassing realized volatility (RV) estimates to estimate the risk‐minimizing hedge ratio, and compare the hedging performance of the proposed models with those generated by return‐based models. In an out‐of‐sample context with a daily rebalancing approach, based on an extensive set of statistical and economic performance measures, the empirical results show that improvement can be substantial when switching from daily to intraday. This essentially comes from the advantage that the intraday‐based RV potentially can provide more accurate daily covariance matrix estimates than RV utilizing daily prices. Finally, this study also analyzes the effect of hedge horizon on hedge ratio and hedging effectiveness for both the in‐sample and the out‐of‐sample data. © 2009 Wiley Periodicals, Inc. Jrl Fut Mark 30:874–896, 2010     

A Markov regime switching approach for hedging stock indices

In this paper we describe a new approach for determining time‐varying minimum variance hedge ratio in stock index futures markets by using Markov Regime Switching (MRS) models. The rationale behind the use of these models stems from the fact that the dynamic relationship between spot and futures returns may be characterized by regime shifts, which, in turn, suggests that by allowing the hedge ratio to be dependent upon the “state of the market,” one may obtain more efficient hedge ratios and hence, superior hedging performance compared to other methods in the literature. The performance of the MRS hedge ratios is compared to that of alternative models such as GARCH, Error Correction and OLS in the FTSE 100 and S&P 500 markets. In and out‐of‐sample tests indicate that MRS hedge ratios outperform the other models in reducing portfolio risk in the FTSE 100 market. In the S&P 500 market the MRS model outperforms the other hedging strategies only within sample. Overall, the results indicate that by using MRS models market agents may be able to increase the performance of their hedges, measured in terms of variance reduction and increase in their utility. © 2004 Wiley Periodicals, Inc. Jrl Fut Mark 24:649–674, 2004     

Canonical valuation and hedging of index options

Canonical valuation is a nonparametric method for valuing derivatives proposed by M. Stutzer (1996). Although the properties of canonical estimates of option price and hedge ratio have been studied in simulation settings, applications of the methodology to traded derivative data are rare. This study explores the practical usefulness of canonical valuation using a large sample of index options. The basic unconstrained canonical estimator fails to outperform the traditional Black–Scholes model; however, a constrained canonical estimator that incorporates a small amount of conditioning information produces dramatic reductions in mean pricing errors. Similarly, the canonical approach generates hedge ratios that result in superior hedging effectiveness compared to Black–Scholes‐based deltas. The results encourage further exploration and application of the canonical approach to pricing and hedging derivatives. © 2007 Wiley Periodicals, Inc. Jnl Fut Mark 27: 771–790, 2007     

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     

Pricing and Hedging the Smile with SABR: Evidence from the Interest Rate Caps Market

This is the first comprehensive study of the SABR (stochastic alpha‐beta‐rho) model (Hagan, Kumar, Lesniewski, & Woodward, 2002) on the pricing and hedging of interest rate caps. I implement several versions of the SABR interest rate model and analyze their respective pricing and hedging performance using two years of daily data with seven different strikes and ten different tenors on each trading day. In‐sample and out‐of‐sample tests show that the fully stochastic version of the SABR model exhibits excellent pricing accuracy and, more importantly, captures the dynamics of the volatility smile over time very well. This is further demonstrated through examining delta‐hedging performance based on the SABR model. My hedging result indicates that the SABR model produces accurate hedge ratios that outperform those implied by the Black model. © 2012 Wiley Periodicals, Inc. Jrl Fut Mark 32:773‐791, 2012     

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     

A novel risk management framework for natural gas markets

This paper examines dynamic hedges in the natural gas futures markets for different horizons and explores the gains from devising risk management strategies. Despite the substantial progress made in developing hedging models, forecast combinations have not been explored. We fill this gap by proposing a framework for combining hedge-ratio predictions. Composite hedge ratios lead to significant reduction in portfolio risk, whether spot prices are partially predictable or not. We offer insights on hedging effectiveness across seasons, backwardation-contango conditions and the asymmetric profiles of long-short hedgers. We conclude that forecast combinations better reconcile realized performance with the hedging process, mitigating model instability.     

Futures hedging using dynamic models of the variance/covariance structure

Dynamic futures‐hedging ratios are estimated across seven markets using generalized models of the variance/covariance structure. The hedging performances of the resultant dynamic strategies are then compared with static and naïve strategies, both in‐ and out‐of‐sample. Bayesian‐adjusted hedge ratios also are employed as error purgers. The empirical results indicate that the generalized dynamic models are well specified and that their use in determining optimal hedge ratios can lead to improvements in hedging performance as measured by the volatilities of the returns on the optimally hedged position. © 2003 Wiley Periodicals, Inc. Jrl Fut Mark 23:241–260, 2003     

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     

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.     

Dynamic hedging with futures: A copula‐based GARCH model

In a number of earlier studies it has been demonstrated that the traditional regression‐based static approach is inappropriate for hedging with futures, with the result that a variety of alternative dynamic hedging strategies have emerged. In this study the authors propose a class of new copula‐based GARCH models for the estimation of the optimal hedge ratio and compare their effectiveness with that of other hedging models, including the conventional static, the constant conditional correlation (CCC) GARCH, and the dynamic conditional correlation (DCC) GARCH models. With regard to the reduction of variance in the returns of hedged portfolios, the empirical results show that in both the in‐sample and out‐of‐sample tests, with full flexibility in the distribution specifications, the copula‐based GARCH models perform more effectively than other dynamic hedging models. © 2008 Wiley Periodicals, Inc. Jrl Fut Mark 28:1095–1116, 2008