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     

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     

Semistatic and sparse variance‐optimal hedging

We consider the problem of hedging a contingent claim with a “semistatic” strategy composed of a dynamic position in one asset and static (buy‐and‐hold) positions in other assets. We give general representations of the optimal strategy and the hedging error under the criterion of variance optimality and provide tractable formulas using Fourier integration in case of the Heston model. We also consider the problem of optimally selecting a sparse semistatic hedging strategy, i.e., a strategy that only uses a small subset of available hedging assets and discuss parallels to the variable‐selection problem in linear regression. The methods developed are illustrated in an extended numerical example where we compute a sparse semistatic hedge for a variance swap using European options as static hedging assets.     

A Leland model for delta hedging in central risk books

Using a tractable extension of the model of Leland (1985), we study how a delta-hedging strategy can realistically be implemented using market and limit orders in a centralized, automated market-making desk that integrates trading and liquidity provision for both options and their underlyings. In the continuous-time limit, the optimal limit-order exposure can be computed explicitly by a pointwise maximization. It is determined by the relative magnitudes of adverse selection, bid–ask spreads, and volatilities. The corresponding option price—from which the option can be replicated using market and limit orders—is characterized via a nonlinear PDE. Our results highlight the benefit of tactical liquidity provision for contrarian trading strategies, even for a trading desk that is not a competitive market maker. More generally, the paper also showcases how reduced-form models are competitive with “brute force” numerical approaches to market microstructure. Both the estimation of microstructure parameters and the simulation of the optimal trading strategy are made concrete and reconciled with real-life high frequency data.     

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     

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     

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     

Regime‐switching in stock index and Treasury futures returns and measures of stock market stress

We investigate bivariate regime‐switching in daily futures‐contract returns for the US stock index and ten‐year Treasury notes over the crisis‐rich 1997–2005 period. We allow the return means, volatilities, and correlation to all vary across regimes. We document a striking contrast between regimes, with a high‐stress regime that exhibits a much higher stock volatility, a much lower stock–bond correlation, and a higher mean bond return. The high‐stress regime is associated with higher average values of stock‐implied volatility, stock illiquidity, and stock and bond futures trading volume. The lagged implied volatility from equity‐index options is useful in modeling the time‐varying transition probabilities of the regime‐switching process. Our findings support the notions that: (1) stock market stress can have a material influence on Treasury bond pricing, and (2) the diversification benefits of combined stock–bond holdings tend to be greater during times with relatively high stock market stress. © 2009 Wiley Periodicals, Inc. Jrl Fut Mark 30:753–779, 2010     

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     

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     

A Markov regime‐switching ARMA approach for hedging stock indices

This study considers the hedging effectiveness of applying the N‐state Markov regime‐switching autoregressive moving‐average (MRS‐ARMA) model to the S&P‐500 and FTSE‐100 markets. The distinguishingfeature of this study is to incorporate the observations of serially correlated stockreturns into the hedging analysis. To resolve the problem of N^T possible routes induced by the presence of MA parameters associated with the algorithm of Hamilton JD ( 1989 ) and a sample of size T, we propose an algorithm by combining the ideas of Hamilton JD ( 1989 ) and Gray SF ( 1996 ). We find that the hedging performances of the three proposed MRS‐MA(1) strategies herein are superior to their corresponding MRS counterparts considered in Alizadeh A and Nomikos N ( 2004 ) over the out‐of‐sample periods, even when we realistically track the transaction costs generated from rebalancing the hedged portfolios. © 2010 Wiley Periodicals, Inc. Jrl Fut Mark 31:165–191, 2011     

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     

Exports and hedging exchange rate risks: the multi‐country case

This article examines the optimal production, export allocation, and hedging decisions of a risk‐averse international firm that exports to several foreign markets with different currencies. The firm faces multiple exchange rate risks. Optimal decisions are analyzed under two scenarios. In the first, there is a forward market for one currency only. Then, the export allocation to different markets is separable from the firm's preferences and the joint distribution of the exchange rates. In contrast, total production is not separable except for a special case. In the second scenario, there is a forward market for each currency. Then, both production and export allocation are separable. Hedging with forward contracts depends on risk premia and on the joint distribution of the exchange rates. If tradable exchange rate risk is a linear function of untradable exchange rate risk plus noise, there is a conflict between cross hedging and taking a basis risk. If, alternatively, the untradable exchange rate risk is a linear function of the tradable exchange rate risk and noise, there is no such conflict. A speculative position in a biased forward market for one currency can be cross hedged using an unbiased forward market for another currency. © 2000 John Wiley & Sons, Inc. Jrl Fut Mark 20:843–864, 2000.     

A note on the relationships between some risk‐adjusted performance measures

Assuming portfolio returns are normally distributed, it is shown that both Sortino ratio (SR) and upside potential ratio (UPR) are monotonically increasing functions of the Sharpe ratio. As a result, all three risk‐adjusted performance measures provide identical ranking among investment alternatives. The effects of skewness and kurtosis are then evaluated within the Edgeworth‐Sargan density family. For the Sortino ratio, the above conclusion remains valid in the presence of negative skewness or excessive kurtosis. Similar results apply to the UPR with modifications. For all other cases, both SR and UPR provide exactly opposite ranking among investment alternatives to that suggested by the Sharpe ratio when the Sharpe ratio is large. Applications to futures hedging are discussed. Specifically, it is found that the Sharpe ratio may frequently lead to a smaller futures position than the other two ratios. © 2002 Wiley Periodicals, Inc. Jrl Fut Mark 22:483–495, 2002     

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     

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