股指期货动态套期保值率研究——基于DCC-MVGARCH模型

本文利用传统的回归模型(OLS)、双变量向量自回归模型(VAR)、双变量向量误差修正模型(VECM)和动态条件自相关双变量GARCH模型(DCC-MVGARCH)对恒生指数期货、标准普尔500指数期货、日经225指数期货、我国的沪深300指数期货的最优套期保值比率进行了估计,并采用基于风险最小化的方法对4种模型的套期保值有效性进行了比较。结果双变量向量误差修正模型估计出的最优套期保值比率更大,对4种模型的套期保值有效性的检验表明,采用动态条件自相关双变量GARCH模型(DCC-MVGARCH)估计得到的最优套期保值比率进行套期保值的效果,并非优于采用传统回归模型、双变量向量自回归模型、双变量向量误差修正模型估计得到的套期保值比率进行套期保值的效果。     

HEDGING AND PORTFOLIO OPTIMIZATION UNDER TRANSACTION COSTS: A MARTINGALE APPROACH12

We derive a formula for the minimal initial wealth needed to hedge an arbitrary contingent claim in a continuous-time model with proportional transaction costs; the expression obtained can be interpreted as the supremum of expected discounted values of the claim, over all (pairs of) probability measures under which the “wealth process” is a supermartingale. Next, we prove the existence of an optimal solution to the portfolio optimization problem of maximizing utility from terminal wealth in the same model, we also characterize this solution via a transformation to a hedging problem: the optimal portfolio is the one that hedges the inverse of marginal utility evaluated at the shadow state-price density solving the corresponding dual problem, if such exists. We can then use the optimal shadow state-price density for pricing contingent claims in this market. the mathematical tools are those of continuous-time martingales, convex analysis, functional analysis, and duality theory.     

DISCRETE TIME HEDGING OF THE AMERICAN OPTION

In a complete financial market we consider the discrete time hedging of the American option with a convex payoff. It is well known that for the perfect hedging the writer of the option must trade continuously in time, which is impossible in practice. In reality, the writer hedges only at some discrete time instants. The perfect hedging requires the knowledge of the partial derivative of the value function of the American option in the underlying asset, the explicit form of which is unknown in most cases of practical importance. Several approximation methods have been developed for the calculation of the value function of the American option. We claim in this paper that having at hand any uniform approximation of the American option value function at equidistant discrete rebalancing times it is possible to construct a discrete time hedging portfolio, the value process of which uniformly approximates the value process of the continuous time perfect delta‐hedging portfolio. We are able to estimate the corresponding discrete time hedging error that leads to a complete justification of our hedging method for nonincreasing convex payoff functions including the important case of the American put. This method is essentially based on a new type square integral estimate for the derivative of an arbitrary convex function recently found by Shashiashvili.     

Determinants of corporate hedging and derivatives: A revisit

Although the primary purpose of hedging is to reduce earnings volatility, corporate hedging may also increase firm value. Using publicly-available data, we found that hedging reduces the probability of financial distress, reduces the agency costs of debt, and reduces some agency costs of equity. However, we found no support for the hypothesis that hedging increases firm value by reducing expected tax liability. In addition, we suggest that corporate ownership structure may affect the desirability of hedging. We also found that large firms have a stronger tendency to hedge, firms with a larger percentage of value derived from growth opportunities are more likely to hedge, and convertible debt serves as a substitute for corporate hedging. With a dummy variable for multinational corporations as a proxy for operational hedging, we found that operational hedging and derivative hedging are complements rather than substitutes.     

How to hedge if the payment date is uncertain?

This paper investigates how firms should hedge price risk when payment dates are uncertain. We derive variance-minimizing strategies and show that the instrument choice is essential for this problem, similar to the choice between a strip and a stack hedge. The first setting concentrates on futures hedges, whereas the second allows for nonlinear derivatives. In both settings, firms should take positions in derivatives with different maturities simultaneously. We present an empirical analysis for commodities and exchange rates, showing that in both settings the optimal strategy clearly outperforms the commonly used heuristic strategies which consider only one hedging instrument at a time.     

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.     

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     

Effects of nondiscretionary trading on futures prices

This paper examines the effects of the nondiscretionary trading demands of volatility index (VIX) exchange-traded products (ETPs) issuers on the prices and volumes in the VIX futures. We find that the ETPs' informationless, mechanical rebalancing of futures positions to maintain the constant maturity of the index and the promised leverage ratios of the VIX ETPs have significantly positive predictive power for end-of-day futures returns. We also show that the impact on price has diminished through time from increased liquidity provided by hedge funds, and the “natural” hedging of the issuers' inverse products.     

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     

Use of high-frequency data to evaluate the performance of dynamic hedging strategies

The hedging performance results of generalized autoregressive conditional heteroskedasticity models are mixed; we address this herein by adopting an asymptotic setting to determine the relative performance of competing hedge ratios. The proxy variable is constructed through precise realized measures rather than through noisy squared returns because the substitution of the latent true hedged portfolio variance with a noisy proxy renders the loss function incapable of ranking forecasts consistently. The merits of allowing some features in modeling the spot–futures distribution are assessed. Empirical comparisons suggest that hedgers may favor the wrong model when the quality of the proxy variable deteriorates.     

Optimal Futures Hedging Under Multichain Markov Regime Switching

Most of the existing Markov regime switching GARCH‐hedging models assume a common switching dynamic for spot and futures returns. In this study, we release this assumption and suggest a multichain Markov regime switching GARCH (MCSG) model for estimating state‐dependent time‐varying minimum variance hedge ratios. Empirical results from commodity futures hedging show that MCSG creates hedging gains, compared with single‐state‐variable regime‐switching GARCH models. Moreover, we find an average of 24% cross‐regime probability, indicating the importance of modeling cross‐regime dynamic in developing optimal futures hedging strategies. © 2012 Wiley Periodicals, Inc. Jrl Fut Mark 34:173–202, 2014     

OPTIMAL STATIC–DYNAMIC HEDGES FOR BARRIER OPTIONS

We study optimal hedging of barrier options, using a combination of a static position in vanilla options and dynamic trading of the underlying asset. The problem reduces to computing the Fenchel–Legendre transform of the utility-indifference price as a function of the number of vanilla options used to hedge. Using the well-known duality between exponential utility and relative entropy, we provide a new characterization of the indifference price in terms of the minimal entropy measure, and give conditions guaranteeing differentiability and strict convexity in the hedging quantity, and hence a unique solution to the hedging problem. We discuss computational approaches within the context of Markovian stochastic volatility models.     

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     

The Characteristics of Foreign Exchange Hedging: A Comparative Analysis

The hedging of foreign exchange exposure is an important aspect of financial management. This article examines what firm foreign exchange hedging practices actually are and compares these to firm characteristics via a comparison of New Zealand firms with U.S., Asian, and European studies. Using survey evidence and a carefully updated methodology, we gained a fairly detailed understanding of hedging methods from a limited question set. Overall, we found evidence of focus on accounting objectives rather than financial objectives, and a possible small-country hedging style which differs from that of U.S., U.K., or German firms. We also found that firms from small countries have a widespread use of forwards, options, and nonderivative hedging methods, even for quite small firms. We also found that some firms that claimed to hedge their exposure display no obvious method of doing so.     

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.     

Hedging and value at risk: A semi‐parametric approach

The non‐normality of financial asset returns has important implications for hedging. In particular, in contrast with the unambiguous effect that minimum‐variance hedging has on the standard deviation, it can actually increase the negative skewness and kurtosis of hedge portfolio returns. Thus, the reduction in Value at Risk (VaR) and Conditional Value at Risk (CVaR) that minimum‐variance hedging generates can be significantly lower than the reduction in standard deviation. In this study, we provide a new, semi‐parametric method of estimating minimum‐VaR and minimum‐CVaR hedge ratios based on the Cornish‐Fisher expansion of the quantile of the hedged portfolio return distribution. Using spot and futures returns for the FTSE 100, FTSE 250, and FTSE Small Cap equity indices, the Euro/US Dollar exchange rate, and Brent crude oil, we find that the semiparametric approach is superior to the standard minimum‐variance approach, and to the nonparametric approach of Harris and Shen (2006). In particular, it provides a greater reduction in both negative skewness and excess kurtosis, and consequently generates hedge portfolios that in most cases have lower VaR and CVaR. © 2009 Wiley Periodicals, Inc. Jrl Fut Mark 30:780–794, 2010     

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     

Dealing with downside risk in a multi‐commodity setting: A case for a “Texas hedge”?

This study analyzes the problem of multi‐commodity hedging from the downside risk perspective. The lower partial moments (LPM₂)‐minimizing hedge ratios for the stylized hedging problem of a typical Texas panhandle feedlot operator are calculated and compared with hedge ratios implied by the conventional minimum‐variance (MV) criterion. A kernel copula is used to model the joint distributions of cash and futures prices for commodities included in the model. The results are consistent with the findings in the single‐commodity case in that the MV approach leads to over‐hedging relative to the LPM₂‐based hedge. An interesting and somewhat unexpected result is that minimization of a downside risk criterion in a multi‐commodity setting may lead to a “Texas hedge” (i.e. speculation) being an optimal strategy for at least one commodity. © 2009 Wiley Periodicals, Inc. Jrl Fut Mark 30:290–304, 2010     

中国黄金期货与现货市场的相关性及其套期保值研究

通过构建VAR-DCC-MVGARCH模型,检验2008—2011年中国黄金期货与现货市场的相关性,并分析最小化资产组合风险的最优套期保值率及其绩效,结果表明:黄金市场仅存在着现货收益率对期货收益率的单向影响;收益率的波动间具有高度正相关的时变特征;动态套期保值组合能够有效地规避黄金现货的投资风险。