A note on output hedging with cost uncertainty

Using a general framework and a multiple‐input technology, we thoroughly investigate the hedging and production decisions under cost uncertainty. In doing so, we show the impact of the cost risk on the optimal output, hedge and hedge ratio. Copyright © 2006 John Wiley & Sons, Ltd.     

The Use of Forward Contracts for Hedging Currency Risk

This paper derives an optimal rule for hedging currency risk in a general utility framework. Ex ante hedging performance of the forward markets is examined using the optimal hedge ratio derived from the utility model and an optimal rule derived from another model (excess return per unit risk) suggested in the hedging literature. Results of this study indicate a naive (one-to-one) hedge performs similarly to the optimal hedge ratios under either model. An implication of this study is that financial managers of multinational firms should simply follow a one-to-one rule when hedging foreign exchange risk in the forward markets.     

Do cryptocurrencies provide better hedging? Evidence from major equity markets during COVID-19 pandemic

Using the five-minute interval price data of two cryptocurrencies and eight stock market indices, we examine the risk spillover and hedging effectiveness between these two assets. Our approach provides a comparative assessment encompassing the pre-COVID-19 and COVID-19 sample periods. We employ copula models to assess the dependence and risk spillover from Bitcoin and Ethereum to stock market returns during both the pre-COVID-19 and COVID-19 periods. Notably, the COVID-19 pandemic has increased the risk spillover from Bitcoin and Ethereum to stock market returns. The findings vis-à-vis portfolio weights and hedge effectiveness highlight hedging gains; however, optimal investments in Bitcoin and Ethereum have reduced during the COVID-19 pandemic, while the cost of hedging has increased during this period. The findings also confirm that cryptocurrencies cannot provide incremental gains by hedging stock market risk during the COVID-19 pandemic.     

Cross-hedging minimum return guarantees: Basis and liquidity risks

We reveal pitfalls in the hedging of insurance contracts with a minimum return guarantee on the underlying investment, e.g. an external mutual fund. We analyze basis risk entailed by hedging the guarantee with a dynamic portfolio of proxy assets for the funds. We also take account of liquidity risk which arises since the insurer may need to advance funds for performing the hedge. Based on a least-squares Monte Carlo simulation, we study the economic implications of basis and liquidity risks. We demonstrate that both risks may be surprisingly high and show how the design of the contract and the hedging strategy may help to alleviate them.     

一个考虑基差收敛性的最适保值比率模型——上期所铜期货卖空保值实证分析

本文针对商品期货市场在基差持续朝一个方向变动的情况下卖空保值风险大、成本高的重大现实问题，基于商品期货的持有成本理论，推导出具有普遍实用价值的考虑基差收敛性的动态最适保值比率模型。然后，综合应用时间序列分析和截面分析方法，在现货价格与到期期间恒定的利率调整基差间构建BV-GARCH模型，并利用BEKK形式的BV-GARCH模型，以上海期货交易所铜期货为实证对象，检验和比较了考虑与未考虑基差收敛性的最适保值比率模型的保值绩效，得出了有意义的具体结论。     

Mean-variance hedging for interest rate models¶with stochastic volatility

The mean-variance hedging approach for pricing and hedging claims in incomplete markets was originally introduced for risky assets. The aim of this paper is to apply this approach to interest rate models in the presence of stochastic volatility, seen as a consequence of incomplete information. We fix a finite number of bonds such that the volatility matrix is invertible and provide an explicit formula for the density of the variance-optimal measure which is independent of the chosen times of maturity. Finally, we compute the mean-variance hedging strategy for a caplet and compare it with the optimal stategy according to the local risk minimizing approach. Received: 14 July 2000 / Accepted: 10 April 2001     

Selective hedging with market views and risk limits: the case of Hydro-Quebec

This study presents how Hydro-Quebec manages its short-term financial risks. The quantitative hedging model is articulated over forward and volatility premia and constrained by a yearly risk limit provided by the firm's Finance Committee. The hedging solutions provide the optimal linear hedging parameters and option strike levels. The second part of the paper is devoted to a theoretical analysis of the sensitivity of the optimal solutions to changes in the premia, by means of the general implicit function theorem.     

Optimal portfolios when variances and covariances can jump

We analyze the optimal portfolio choice in a multi-asset Wishart-model in which return variances and correlations are stochastic and subject to jump risk. The optimal portfolio is characterized by the positions in stock diffusion risk, variance-covariance diffusion risk, and jump risk. We find that including jumps in the second moments changes the optimal positions and particularly variance-covariance hedging demands significantly. Erroneously omitting these jumps gives rise to substantial model risk. Furthermore, variance-covariance jump risk can have a significant impact on potential utility gains when the market is completed by adding derivatives. As a robustness check, we compare our results to those obtained for other parametrizations of Wishart-models from the literature as well as to various single-asset models.     

Tax asymmetry and futures hedging under liquidity constraints

This paper examines the optimal futures hedging decision of a firm facing uncertain income that is subject to asymmetric taxation with no loss‐offset provisions. All futures contracts are marked to market and require interim cash settlement of gains and losses. The firm is liquidity constrained in that it is forced to prematurely close its futures position on which the interim loss incurred exceeds a threshold level. The liquidity risk created by the interim funding requirement of a futures hedge is shown to proffer the firm perverse incentives, thereby making an under‐hedge optimal. This under‐hedging result holds irrespective of whether the firm is risk neutral or risk averse. Copyright © 2005 John Wiley & Sons, Ltd.     

Corporate hedging and input price risk

Input price variability is an important source of risk for corporations that process raw commodities. Models of optimal input hedging are developed in this paper based on the maximization of managerial expected utility. The relationship between hedging strategies and output decisions is examined to assess the impact of the ability to set output prices on futures market participation. As a firm's ability to set output prices diminishes in the short run, input futures positions increase although the optimal hedge ratio may either increase or decrease. For a perfectly competitive firm, however, shifts in output price caused by input price changes provide a natural cash market hedge of input price risk and reduce the firm's optimal input futures position.     

The costs of suboptimal dynamic asset allocation: General results and applications to interest rate risk, stock volatility risk, and growth/value tilts

The recent theoretical asset allocation literature has derived optimal dynamic investment strategies in various advanced models of asset returns. But how sensitive is investor welfare to deviations from the theoretically optimal strategy? Will unsophisticated investors do almost as well as sophisticated investors? This paper develops a general theoretical framework for answering such questions and applies it to three specific models of interest rate risk, stochastic stock volatility, and mean reversion and growth/value tilts of stock portfolios. Among other things, we find that growth/value tilts are highly valuable, but the hedging of time-varying stock risk premia is less important.     

Explicit formulas for the minimal variance hedging strategy in a martingale case

We explicitly compute closed formulas for the minimal variance hedging strategy in discrete time of a European option and for the variance of the corresponding hedging error under the hypothesis that the underlying asset is a martingale following a geometric Brownian motion. The formulas are easy to implement, hence the optimal hedge ratio can be employed as a valid substitute of the standard Black–Scholes delta, and the knowledge of the variance of the total error can be a useful tool for measuring and managing the hedging risk.     

International tenders and futures hedging

This paper examines the optimal bidding and hedging decisions of a risk‐averse firm that takes part in an international tender. The firm faces multiple sources of uncertainty: exchange rate risk, risk of an unsuccessful tender, and business risk. The firm is allowed to trade unbiased currency futures contracts to imperfectly hedge its contingent foreign exchange risk exposure. We show that the firm shorts less (more) of the unbiased futures contracts when its marginal utility function is convex (concave) as compared with the case that the marginal utility function is linear. We further show that the curvature of the marginal utility function plays a decisive role in determining the impact of currency futures hedging on the firm's bidding behavior. Sufficient conditions that ensure the firm bids more or less aggressively than in the case without hedging opportunities are derived. Copyright © 2006 John Wiley & Sons, Ltd.     

Option hedging theory under transaction costs

The problem of option hedging in the presence of proportional transaction costs can be formulated as a singular stochastic control problem. Hodges and Neuberger [1989. Optimal replication of contingent claims under transactions costs. Review of Futures Markets 8, 222–239] introduced an approach that is based on maximization of the expected utility of terminal wealth. We develop a new algorithm to solve the corresponding singular stochastic control problem and introduce a new approach to option hedging which is closer in spirit to the pathwise replication of Black and Scholes [1973. The pricing of options and corporate liabilities. Journal of Political Economy 81, 637–654]. This new approach is based on minimization of a Black–Scholes-type measure of pathwise risk, defined in terms of a market delta, subject to an upper bound on the hedging cost. We provide an efficient backward induction algorithm for the problem of cost-constrained risk minimization, whose associated singular stochastic control problem is shown to be equivalent to an optimal stopping problem. This algorithm is then modified to solve the singular stochastic control problem associated with utility maximization, which cannot be reduced to an optimal stopping problem. We propose to choose an optimal parameter (risk-aversion coefficient or Lagrange multiplier) in either approach by minimizing the mean squared hedging error and demonstrate that with this “best” choice of the parameter, both approaches have similar performance. We also discuss the different notions of risk in both approaches and propose a volatility adjustment for the risk-minimization approach, which is analogous to that introduced by Zakamouline [2006. European option pricing and hedging with both fixed and proportional transaction costs. Journal of Economic Dynamics and Control 30, 1–25] for the utility maximization approach, thereby providing a unified treatment of both approaches.     

Understanding saving and portfolio choices with predictable changes in assets returns

We consider an expected-utility-maximizing consumer living two periods who can invest in two assets, one of which is risk free. We do not restrict relative risk aversion to be constant. We first examine the effect that a change in the opportunity set in the second period has on the optimal saving in the first period. We show that an increase in the future risk free rate (keeping the equity premium unchanged) reduces savings if relative risk aversion is uniformly larger than unity. An increase in the equity premium or a reduction in the volatility of the risky asset raises savings if the index of cautiousness, i.e., the derivative of absolute risk tolerance, is smaller than unity. In a second stage, we use these results to determine the sign of the hedging demand for the risky asset for the following three types of predictability: predictable changes in the interest rate, mean-reversion in stock returns, and predictable changes in volatility. Depending upon the type of predictability under scrutiny, what matters to sign the hedging demand is whether relative risk aversion or cautiousness is smaller or larger than unity.     

Hedging and the competitive firm under correlated price and background risk

This paper examines the behavior of the competitive firm under correlated price and background risk when a futures market exists for hedging purposes. We show that imposing the background risk, be it additive or multiplicative, on the firm has no effect on the separation theorem. The full-hedging theorem, however, holds if the background risk is independent of the price risk. In the general case of the correlated price and background risk, we adopt the concept of expectation dependence to describe the bivariate dependence structure. When the background risk is additive, the firm finds it optimal to opt for an over-hedge or an under-hedge, depending on whether the price risk is positively or negatively expectation dependent on the background risk, respectively. When the background risk is multiplicative, both the concept of expectation dependence and the Arrow–Pratt measure of relative risk aversion are called for to determine the firm’s optimal futures position.     

Variance trading and market price of variance risk

This paper develops a new approach for variance trading. We show that the discretely-sampled realized variance can be robustly replicated under very general conditions, including when the price can jump. The replication strategy specifies the exact timing for rebalancing in the underlying. The deviations from the optimal schedule can lead to surprisingly large hedging errors. In the empirical application, we synthesize the prices of the variance contract on S&P 500 index over the period from 01/1990 to 12/2009. We find that the market variance risk is priced, its risk premium is negative and economically very large. The variance risk premium cannot be explained by the known risk factors and option returns.     

Option pricing and replication with transaction costs and dividends

This paper derives optimal perfect hedging portfolios in the presence of transaction costs within the binomial model of stock returns, for a market maker that establishes bid and ask prices for American call options on stocks paying dividends prior to expiration. It is shown that, while the option holder's optimal exercise policy at the ex-dividend date varies according to the stock price, there are intervals of values for such a price where the optimal policy would depend on the holder's preferences. Nonetheless, the perfect hedging assumption still allows the derivation of optimal hedging portfolios for both long and short positions of a market maker on the option.     

股指期货的最优套期保值率实证研究——基于沪深300指数期货仿真交易视角

在分析和比较常用的几种股指期货最优套期保值比率确定模型的基础上,基于风险最小化模型框架,利用沪深300指数期货合约模拟运行以来的样本数据,通过最小二乘回归模型、向量自回归模型、误差修正模型以及广义自回归条件异方差模型四种估计方法,对其最优套期保值比率进行了实证测算和绩效比较,提出了相应的政策建议和投资策略。     

Corporate risk management and asymmetric information

We discuss the effect of information on corporate risk management decisions when the information is asymmetric between the insider and the market. We suggest an explanation for previous contradiction between existing theories and empirical findings, which state that fewer small firms choose to hedge. We consider two different scenarios of information revelation to the market, and find hedging cost is not the main reason preventing firms from hedging. Rather asymmetric information plays the decisive role in a firm's risk management policy. One of the empirical implications we find is that cash flows with high variances may discourage firms from hedging even when they face high financial distress costs.