Optimal hedging in an extended binomial market under transaction costs

We develop an approach to optimal hedging of a contingent claim under proportional transaction costs in a discrete time financial market model which extends the binomial market model with transaction costs. Our model relaxes the binomial assumption on the stock price ratios to the case where the stock price ratio distribution has bounded support. Non-self-financing hedging strategies are studied to construct an optimal hedge for an investor who takes a short position in a European contingent claim settled by delivery. We develop the theoretical basis for our optimal hedging approach, extending results obtained in our previous work. Specifically, we derive a no-arbitrage option price interval and establish properties of the non-self-financing strategies and their residuals. Based on the theoretical foundation, we develop a computational algorithm for optimizing an investor relevant criterion over the set of admissible non-self-financing hedging strategies. We demonstrate the applicability of our approach using both simulated data and real market data.     

Optimal static quadratic hedging

We propose a flexible framework for hedging a contingent claim by holding static positions in vanilla European calls, puts, bonds and forwards. A model-free expression is derived for the optimal static hedging strategy that minimizes the expected squared hedging error subject to a cost constraint. The optimal hedge involves computing a number of expectations that reflect the dependence among the contingent claim and the hedging assets. We provide a general method for approximating these expectations analytically in a general Markov diffusion market. To illustrate the versatility of our approach, we present several numerical examples, including hedging path-dependent options and options written on a correlated asset.     

Commodity futures hedging,risk aversion and the hedging horizon

This paper examines the impact of management preferences on optimal futures hedging strategy and associated performance. Applying an expected utility hedging objective, the optimal futures hedge ratio is determined for a range of preferences on risk aversion, hedging horizon and expected returns. Empirical results reveal substantial hedge ratio variation across distinct management preferences and are supportive of the hedging policies of real firms. Hedging performance is further shown to be strongly dependent on underlying preferences. In particular, hedgers with high risk aversion and short horizon reduce hedge portfolio risk but achieve inferior utility in comparison to those with low aversion.     

Coherent hedging in incomplete markets

In incomplete financial markets, not every contingent claim can be perfectly replicated by a self-financing strategy. In this paper, we minimize the risk that the value of the hedging portfolio falls below the payoff of the claim at time T. We use a coherent risk measure, introduced by Artzner et al., to measure the risk of the shortfall. The dynamic optimization problem of finding a self-financing strategy that minimizes the coherent risk of the shortfall can be split into a static optimization problem and a representation problem. We will deduce necessary and sufficient optimality conditions for the static problem using convex duality methods. The solution of the static optimization problem turns out to be a randomized test with a typical 0–1 structure. Our results improve those obtained by Nakano. The optimal hedging strategy consists of superhedging a modified claim that is the product of the original payoff and the solution to the static problem.     

HEDGING INTEREST RATE RISK UNDER TERM STRUCTURE EFFECTS: AN APPLICATION TO FINANCIAL INSTITUTIONS

In this paper we investigate the use of the structured full rank model for hedging the balance sheet of a financial institution. Simulation results suggest that the optimal hedge is insensitive to changes in parameter estimates. In addition, we hedge a portfolio of Treasury bills using both the full information covariance matrix and the structured covariance matrix. We then contrast these results with those obtained from a duration-based model. Empirical results suggest that the structured full rank model is generally more effective in hedging applications than either the full information model or duration-based model.     

DCC-GARCH、M-Copula-GARCH和Copula-SV在商品期货对冲中的应用研究

中国商品期货市场已经成为全球期货市场不可或缺的重要组成部分。文章比较研究了DCC-GARCH、M-Copula-GARCH和Copula-SV三种模型对我国最重要的期货合约——铜和棉花的对冲比率的影响。结果表明:Copula-SV是最优的对冲模型,文章还发现:二月期的铜期货合约和三月期的棉花期货合约对冲现货的效率最高。     

Dynamic Hedging Effectiveness in South Korean Index Futures and the Impact of the Asian Financial Crisis

This paper focuses on the impact of the 1997 Asian financial market crisis upon hedging effectiveness within the KOSPI 200 stock index and index futures markets. The paper utilizes the inter-temporal relationship between the two markets to examine the characteristics of several minimum variance hedge ratios. It also examines the performances of alternative hedging strategies for dynamic portfolio management in the presence of cointegrated time-varying risks. The results show a decline in the persistence of conditional volatility within market prices after the crisis. This decline leads to the relative performance of utilizing constant hedge ratios to increase, though not significantly so to guarantee a superior performance over more sophisticated time-varying hedge ratio strategies.     

THE DETERMINANTS OF SELECTIVE EXCHANGE RISK MANAGEMENT–EVIDENCE FROM GERMAN NON-FINANCIAL CORPORATIONS

Survey studies of both corporate exchange risk management and the corporate use of derivatives in general have shown considerable variation in managerial practices. Some firms do not hedge open positions at all, and some hedge their exposures completely. Most companies, however, hedge only those positions on which they expect a currency loss, while leaving open positions on which they expect a currency gain—a practice known as “selective hedging.” Finally, there is a small minority of firms that engage in outright speculation, deliberately creating risk exposures in addition to those arising from their normal business operations. Such findings are consistent with survey studies that suggest that a majority of corporate financial managers appear to believe that they are able to “beat the market”—a belief that, of course, is inconsistent with efficient markets theory. So why do some companies follow selective risk management strategies while other firms hedge open positions without recourse to exchange rate forecasts? In an attempt to answer this question, the author surveyed 74 German non‐financial companies about their exchange risk management practices. He found that highly levered firms were less likely to take bets in the currency markets, while bank‐controlled firms were more likely to use a selective risk management strategy. There was a negative relationship between profitability and the use of selective hedging—a finding that could be interpreted as suggesting that selective hedging does not generally benefit the firm's shareholders. Finally, there was a weak tendency for larger firms to be more inclined to use forecasts in their foreign exchange risk management.     

Convex costs and the hedging paradox

Financial theory suggests that hedging can increase shareholder value in the presence of capital market imperfections, including direct and indirect costs of financial distress, costly external financing, and convex tax exposure. The influence of these costs, which are high when profits are low and low or negligible when profits are large, on the extent of firm hedging has not been consistently addressed in the finance literature. In Brown and Toft's (2002) model, more convex costs imply that a firm will decrease the extent of hedging. At the same time, one version of Smith and Stulz's (1985) tax hypothesis implies that a given firm is expected to increase the extent of hedging under a more convex tax exposure. I address this ambiguity in the literature by showing that, in incomplete markets, value-maximizing firms that stand to gain the most from hedging may in fact hedge less than otherwise identical firms with less to gain from hedging. This hedging paradox can partly account for the lack of conclusive evidence to suggest that convex costs can influence both a firm's decision to hedge and the extent of the firm's hedging. Finally, I introduce a new interpretation of empirical relations between potential hedging gains and the extent of hedging.     

Hedging effectiveness of the Athens stock index futures contracts

This paper examines the hedging effectiveness of the FTSE/ATHEX-20 and FTSE/ATHEX Mid-40 stock index futures contracts in the relatively new and fairly unresearched futures market of Greece. Both in-sample and out-of-sample hedging performances using weekly and daily data are examined, considering both constant and time-varying hedge ratios. Results indicate that time-varying hedging strategies provide incremental risk-reduction benefits in-sample, but under-perform simple constant hedging strategies out-of-sample. Moreover, futures contracts serve effectively their risk management role and compare favourably with results in other international stock index futures markets. Estimation of investor utility functions and corresponding optimal utility maximising hedge ratios yields similar results, in terms of model selection. For the FTSE/ATHEX Mid-40 contracts we identify the existence of speculative components, which lead to utility-maximising hedge ratios, that are different to the minimum variance hedge ratio solutions.     

Hedging and competition

We consider firms that, all else equal, wish to minimize variability in their internal capital (due to convex costs of raising external funds). The firms can hedge the cash flow risk of the project, but not that of winning or losing the auction. We characterize optimal hedging and bidding strategies in this competition framework. We show that access to financial markets makes firms bid more aggressively, possibly even above their valuation for the project. In addition, hedging increases the variance of bids and makes firm values more dispersed. Further, with hedging, the covariance of internal capital changes with the risk factor is negative, and is more negative, the higher the correlation of the hedging instrument with the risk factor.     

Corporate Hedging: The Relevance of Contract Specifications and Banking Relationships

This article examines the contribution of hedging to firm value and the cost of hedging in a unified framework. Optimal hedging and firm value are explicitly linked to firm risk, the type of debt covenants and the relative priority of the hedging contract. It is shown that in some cases hedging is possible only if the counterparty to the forward contract also holds a significant portion of the debt. Also, the spread in the hedging contract reduces the optimal amount of hedging to less than the minimum-variance hedge ratio. Among other results this article elucidates why some firms hedge using forward contracts while other firms hedge in the futures markets, as well as why higher priority forward contracts are more efficient hedging vehicles.     

Why and How UK Firms Hedge

This paper attempts to differentiate among the theories of hedging by using disclosures in the annual reports of 400 UK companies and data collected via a survey. I find, unlike many previous US studies, strong evidence linking the decision to hedge and the expected costs of financial distress. The tests show that this is mainly because my definition of hedging includes all hedgers and not just derivative users. However, when the tests employ the same hedging definition as previous US studies, financial distress cost factors still appear to be more important for this sample than samples of US firms. Therefore, a secondary explanation for the strong financial distress results might be due to differences in the bankruptcy codes in the two countries, which result in higher expected costs of financial distress for UK firms. The paper also examines the determinants of the choice of hedging method distinguishing between non‐derivative and derivatives hedging. My evidence shows that larger firms, firms with more cash, firms with a greater probability of financial distress, firms with exports or imports and firms with more short‐term debt are more likely to hedge with derivatives. Thus, differences in opportunities, in incentives for reducing risk and in the types of financial price exposure play an important role in how firms hedge their risks.     

套期会计原则缺失问题研究——IASB套期会计征求意见稿评述

IASB 2010年12月发布的套期会计征求意见稿首次提出了套期会计目标,简化了套期会计适用条件,增加了套期工具和被套期项目种类,充分体现了财务报告编制者对增加套期会计适用性的要求。本文分析了套期会计原则缺失导致的套期会计方法与目标不一致问题,并通过对我国企业衍生金融工具交易实践的分析说明,套期会计方法可能会产生与套期会计目标背离的会计结果。提出应建立明晰的套期会计原则,实现套期会计方法与目标的统一,保证套期会计能够传达套期工具的实质,使报表使用者能够清楚地了解企业使用套期工具的真实目的和实际效果。     

Do Firms Hedge in Response to Tax Incentives?

There are two tax incentives for corporations to hedge: to increase debt capacity and interest tax deductions, and to reduce expected tax liability if the tax function is convex. We test whether these incentives affect the extent of corporate hedging with derivatives. Using an explicit measure of tax function convexity, we find no evidence that firms hedge in response to tax convexity. Our analysis does, however, indicate that firms hedge to increase debt capacity, with increased tax benefits averaging 1.1 percent of firm value. Our results also indicate that firms hedge because of expected financial distress costs and firm size.     

Optimal international hedging in commodity and currency forward markets

This paper derives optimal hedging and production rules for an exporting firm which faces both commodity-price and foreign- exchange-rate uncertainty. The size of the commodity hedge is independent of the properties of the foreign-exchange market. However, the optimal foreign-exchange hedge depends on the commodity hedge and the properties of the commodity forward market. The firm's production decision is independent of its objective function if both forward markets exist, but depends on the consumption beta of the unhedgeable risks in the absence of one or both of the markets.     

BASIS VOLATILITY: IMPLICATIONS FOR HEDGING

Most hedges placed in futures markets must be lifted before contract expiration, which necessitates incurring “basis risk.” The focus of this paper is on quantifying such risk as a function of the timing of a hedge, its duration, distance from contract expiration, hedge life, and other market-observable variables. The development of basis-risk profiles provides a hedger with estimates of hedging risks that reasonably can be expected before the actual placement of hedges, thus serving as a useful input in the hedging decision.     

Vertical integration as an input price hedge: The case of Delta Air Lines and trainer refinery

In April 2012, Delta Air Lines (Delta) purchased a mothballed oil refinery. We use this case to illustrate when, how, and why vertical integration (VI) can hedge input price risk. First, we show that stockholders and creditors expected the move to create wealth. Consistent with their predictions, Delta's exposure to refining margins, cash flow volatility, cost of debt, and default probability all decreased, relative to peers, postacquisition. Our evidence is consistent with the refinery influencing Delta's operating strategies, especially in its most affected markets. The case demonstrates how asset specificity and financial hedging frictions can justify VI.     

THE ROLE OF CAPITAL ADEQUACY REGULATION IN THE HEDGING DECISIONS OF FINANCIAL INTERMEDIARIES

This paper identifies the effect of capital adequacy requirements, which have been ignored to date in the hedging literature, on the forward hedging decisions of financial intermediaries. Using a more general framework than has been used in the literature on intermediary behavior in forward markets, cases are developed where capital and forward contracting are substitutes as well as where increasing the capital requirement increases the volume of desired forward contracting. The model shows that the most important factors in determining the equilibrium rate and the equilibrium position of intermediaries are the statistical association between the level of the forward rate and the spread between interest rates, the level of the capital-to-assets ratio, and the degree of risk aversion of intermediaries and other participants in the forward market. To characterize whether the intermediary's optimal forward position is long or short, one must have knowledge of at least the sign of the association between the level and spread for the particular intermediary, the intermediary's capital position, and whether the forward market equilibrium corresponds to a positive or negative premium. The model also demonstrates that a full hedge of assets is always sub-optimal, and a universally applicable expression for the optimal hedge ratio when hedging is costless is derived.