基于高阶矩和逐日盯市风险的套期保值模型研究
|
摘要
近年来，以石油、铁矿石等为代表的资源性大宗商品价格大幅度波动，使得企业采用期货等金融衍生品进行套期保值以规避价格风险的需求迅速增加。但是，随着江铜等企业频频失手套期保值、出现巨额亏损，很多企业谈“套期保值”色变。在这样的背景下，如何合理运用期货等金融衍生品进行套期保值就成为理论界和实务界研究的热点问题。然而，现有的套期保值研究忽视了两个重要的风险：高阶矩风险和逐日盯市风险。高阶矩风险的存在使得套期保值过程中发生极值亏损事件发生的概率大大增加；而逐日盯市风险的存在，则可能使投资者面临强行平仓风险。针对这两个问题，本文结合期货本身的特点，建立了考虑逐日盯市风险和高阶矩风险的套期保值模型，并通过实证研究说明所建立的模型的适用性。具体来说，本文的主要工作与创新归纳如下：
（1）引入高阶矩，建立高阶矩期货套期保值模型
已有的套期保值研究忽视了高阶矩风险对于套期保值的影响，从而低估了套期保值组合的风险。本文通过负指数效用函数，通过泰勒展开引入偏度风险和峰度风险，建立了考虑偏度风险和峰度风险的非线性套期保值模型；本文也采用多目标方法引入三阶矩风险，建立了资金约束下考虑三阶矩风险的多目标套期保值模型，并给出了模型的解析解。最后，通过原油和铜的空头套期保值等例子，对建立的两个模型与已有模型进行了比较，结果表明高阶矩风险对于套期保值策略有较大影响。
（2）考虑逐日盯市风险，建立了规避逐日盯市风险的单阶段套期保值模型
已有的研究忽视了期货市场两个特有制度——保证金制度和逐日盯市制度可能产生的逐日盯市风险。本文分析了逐日盯市风险对于套期保值策略的影响，建立了规避逐日盯市风险的单阶段套期保值模型：建立了自有资金和借入资金两种情况下规避逐日盯市风险的期货套期保值模型；建立了逐日盯市风险下考虑保证金利息和机会成本的套期保值模型；建立了逐日盯市风险下的复合交叉套期保值模型。同时，给出了这些模型的最优套期保值比率。最后，通过铜和热轧板材的套期保值等例子，说明这些模型的适用性。结果表明，建立的模型可以较好地规避逐日盯市风险。
（3）建立了逐日盯市风险下的两阶段组合套期保值模型
已有的研究主要关注单种商品的套期保值，较少关注多种商品的套期保值。本文针对生产商所面临的原材料和商品双重价格风险，引入逐日盯市风险，建立了逐日盯市风险下的两阶段组合套期保值模型，从而拓展了已有的单商品套期保值模型。然后，考虑保证金利息和机会成本对于套期保值的影响，建立了逐日盯市风险下考虑保证金利息和机会成本的组合套期保值模型。另外，本文也给出了求解该模型的lemke算法。最后，以豆油生产企业为例说明了建立的模型的有效性。
（4）资金约束下的多阶段套期保值模型
已有的多期套期保值研究较少考虑资金约束对于套期保值的影响。本文采用动态规划方法，建立了资金约束下的成堆套期保值模型；同时，考虑资金约束对于多种现货投资的影响，建立了资金约束下单种期货对冲多种现货的多阶段套期保值模型。最后通过模型转换和逆推方法得到了这两个模型的最优解。
In recent years, big fluctuations are common for the commodities, such as oil and iron.These cause a great demand for futures hedging. However, many companies failed to hedgetheir risk exposure with futures, which makes them be afraid to manage the risk exposure withfutures. Under such circumstances, the issue of how to reasonly hedge the risk exposure withfutures has been an active research topic in recent years. However, the existing studies ignoretwo important risks in determining the optimal hedge strategy: higher moments risk andmark-to-market risk. If the optimal hedge strategies do not consider higher moment’s risk, theprobability of extreme loss will greatly increase. If mark-to-market risk is completely ignoredin determining the optimal hedge strategy, the position taked by the hedger will be closed outby the exchange, which leads to the failure of hedging strategy. Based on two important risks,this thesis proposes future hedging models under higher moments risk and mark-to-marketrisk and gives some empirical cases to illustrate the proposed models. The main results andinnovations in this thesis are listed as follows:
First, this thesis introduces the higher moments risk into the conventional futureshedging framework.
The existing studies ignore the impact of higher moments risk on the hedging strategies.This thesis takes the negative exponential utility function for decision-making function andproposes nonlinear futures hedging model under higher moments. Using the multi-objectivedecision-making approaches, this thesis also proposes futures hedging model under the thirdmoments and gives the optimal hedge ratio. Finally, the cases of hedging oil and copper aregiven to illustrate futures hedging models under higher moments risk. The empirical resultsshow that higher moments have a big impact on the hedge strategy.
Second, this thesis incorporates mark-to-market risk into futures hedging models.
The existing studies do not consider the mark-to-market risk that is caused by the depositsystem and mark-to-market system. This thesis analyses the effect of mark-to-market risk onthe hedging strategy and proposes three static hedging models under mark-to-market risk:futures hedging models in the cases of own funds and borrowing money; futures hedgingmodel with the interests income and the opportunity cost of the deposit; compositecross-hedging models under mark-to-market risk. We also give the optimal hedge ratios ofthese models. The cases of hedging copper and hot rolled coils are employed to examine thefeasibility of the proposed model. The empirical results show that the proposed models caneliminate mark-to-market risk very well.
Third, a new theoretical model is presented to manage the risk exposure of the portfolioincluding raw materials and the commodity under mark-to-market risk.
The existing studies are concerned with single commodity hedge. This thesis considersthe hedging problem of a portfolio composed of raw materials and the commodity undermark-to-market risk and extends the conventional single commodity hedging models. Thisthesis also sets up the portfolio hedging model with the income and the opportunity cost of thedeposit. The Lemke algorithm is employed to select the optimal hedging strategy. Finally, thecases of the soybean oil manufacturer are given to illustrate the portfolio hedging modelsunder mark-to-market risk.
Four, this thesis proposes multiperiod hedging models with capital constraint.
The existing studies ignore the effect of capital constraint on the hedging strategy. Usingdynamic programming, this thesis proposes multiperiod stack-and-roll hedging models withcapital constraint. Considering the inpact of capital constraint on investing the cash, this thesisalso presents multiperiod models for hedging spot assets with one futures when there existscapital constraint. The optimal solutions of the proposed models are obtained by the modeltransformation and backward induction.
（1）引入高阶矩，建立高阶矩期货套期保值模型
已有的套期保值研究忽视了高阶矩风险对于套期保值的影响，从而低估了套期保值组合的风险。本文通过负指数效用函数，通过泰勒展开引入偏度风险和峰度风险，建立了考虑偏度风险和峰度风险的非线性套期保值模型；本文也采用多目标方法引入三阶矩风险，建立了资金约束下考虑三阶矩风险的多目标套期保值模型，并给出了模型的解析解。最后，通过原油和铜的空头套期保值等例子，对建立的两个模型与已有模型进行了比较，结果表明高阶矩风险对于套期保值策略有较大影响。
（2）考虑逐日盯市风险，建立了规避逐日盯市风险的单阶段套期保值模型
已有的研究忽视了期货市场两个特有制度——保证金制度和逐日盯市制度可能产生的逐日盯市风险。本文分析了逐日盯市风险对于套期保值策略的影响，建立了规避逐日盯市风险的单阶段套期保值模型：建立了自有资金和借入资金两种情况下规避逐日盯市风险的期货套期保值模型；建立了逐日盯市风险下考虑保证金利息和机会成本的套期保值模型；建立了逐日盯市风险下的复合交叉套期保值模型。同时，给出了这些模型的最优套期保值比率。最后，通过铜和热轧板材的套期保值等例子，说明这些模型的适用性。结果表明，建立的模型可以较好地规避逐日盯市风险。
（3）建立了逐日盯市风险下的两阶段组合套期保值模型
已有的研究主要关注单种商品的套期保值，较少关注多种商品的套期保值。本文针对生产商所面临的原材料和商品双重价格风险，引入逐日盯市风险，建立了逐日盯市风险下的两阶段组合套期保值模型，从而拓展了已有的单商品套期保值模型。然后，考虑保证金利息和机会成本对于套期保值的影响，建立了逐日盯市风险下考虑保证金利息和机会成本的组合套期保值模型。另外，本文也给出了求解该模型的lemke算法。最后，以豆油生产企业为例说明了建立的模型的有效性。
（4）资金约束下的多阶段套期保值模型
已有的多期套期保值研究较少考虑资金约束对于套期保值的影响。本文采用动态规划方法，建立了资金约束下的成堆套期保值模型；同时，考虑资金约束对于多种现货投资的影响，建立了资金约束下单种期货对冲多种现货的多阶段套期保值模型。最后通过模型转换和逆推方法得到了这两个模型的最优解。
In recent years, big fluctuations are common for the commodities, such as oil and iron.These cause a great demand for futures hedging. However, many companies failed to hedgetheir risk exposure with futures, which makes them be afraid to manage the risk exposure withfutures. Under such circumstances, the issue of how to reasonly hedge the risk exposure withfutures has been an active research topic in recent years. However, the existing studies ignoretwo important risks in determining the optimal hedge strategy: higher moments risk andmark-to-market risk. If the optimal hedge strategies do not consider higher moment’s risk, theprobability of extreme loss will greatly increase. If mark-to-market risk is completely ignoredin determining the optimal hedge strategy, the position taked by the hedger will be closed outby the exchange, which leads to the failure of hedging strategy. Based on two important risks,this thesis proposes future hedging models under higher moments risk and mark-to-marketrisk and gives some empirical cases to illustrate the proposed models. The main results andinnovations in this thesis are listed as follows:
First, this thesis introduces the higher moments risk into the conventional futureshedging framework.
The existing studies ignore the impact of higher moments risk on the hedging strategies.This thesis takes the negative exponential utility function for decision-making function andproposes nonlinear futures hedging model under higher moments. Using the multi-objectivedecision-making approaches, this thesis also proposes futures hedging model under the thirdmoments and gives the optimal hedge ratio. Finally, the cases of hedging oil and copper aregiven to illustrate futures hedging models under higher moments risk. The empirical resultsshow that higher moments have a big impact on the hedge strategy.
Second, this thesis incorporates mark-to-market risk into futures hedging models.
The existing studies do not consider the mark-to-market risk that is caused by the depositsystem and mark-to-market system. This thesis analyses the effect of mark-to-market risk onthe hedging strategy and proposes three static hedging models under mark-to-market risk:futures hedging models in the cases of own funds and borrowing money; futures hedgingmodel with the interests income and the opportunity cost of the deposit; compositecross-hedging models under mark-to-market risk. We also give the optimal hedge ratios ofthese models. The cases of hedging copper and hot rolled coils are employed to examine thefeasibility of the proposed model. The empirical results show that the proposed models caneliminate mark-to-market risk very well.
Third, a new theoretical model is presented to manage the risk exposure of the portfolioincluding raw materials and the commodity under mark-to-market risk.
The existing studies are concerned with single commodity hedge. This thesis considersthe hedging problem of a portfolio composed of raw materials and the commodity undermark-to-market risk and extends the conventional single commodity hedging models. Thisthesis also sets up the portfolio hedging model with the income and the opportunity cost of thedeposit. The Lemke algorithm is employed to select the optimal hedging strategy. Finally, thecases of the soybean oil manufacturer are given to illustrate the portfolio hedging modelsunder mark-to-market risk.
Four, this thesis proposes multiperiod hedging models with capital constraint.
The existing studies ignore the effect of capital constraint on the hedging strategy. Usingdynamic programming, this thesis proposes multiperiod stack-and-roll hedging models withcapital constraint. Considering the inpact of capital constraint on investing the cash, this thesisalso presents multiperiod models for hedging spot assets with one futures when there existscapital constraint. The optimal solutions of the proposed models are obtained by the modeltransformation and backward induction.
引文
[1] Johnson L. The theory of hedging and speculation in commodity futures [J]. Reviewof Economic Studies,1960,27(3):139-151.
[2] Ederington L. The hedging performance of the new futures markets [J]. Journal ofFinance,1979,34(1):157-170.
[3]吴冲锋，钱宏伟，吴文锋．期货套期保值理论与实证研究(I)[J].系统工程理论方法应用,1998,7(4):20-26.
[4]张学东,徐成贤,李栓劳,张芳.考虑交易成本的股价指数期货最优套期保值策略模型[J].西安交通大学学报,2002,36(12):1317-1319.
[5]迟国泰,张梅,杨磊.基于持有成本理论的期货套期保值决策模型[J].运筹与管理,2010,19(6):104-116.
[6] Lioui A, Poncet P. The minimum variance hedge ratio under stochastic interest rates[J]. Management Science,2000,46(5):658-668.
[7] Terry. Minimum-variance futures hedging under alternative return specifications [J].The Journal of Futures Markets,2005,25(6):537-552.
[8]杨中原,迟国泰,赵光军.基于最小模糊方差的最优交叉套期保值模型[J].运筹与管理,2008,17(6):113-126.
[9] Ederington L H, Salas J M. Minimum variance hedging when spot price changes arepartially predictable [J]. Journal of Banking&Finance,2008,32:654–663.
[10]杨国梁,张新新,杨敏慧.基于支持向量机的套期保值技术研究[J].中央财经大学学报,2010,(3):28-32.
[11]马永开,唐小我.组合套期保值策略及其理论研究[J].预测,1999,18(4):48-51.
[12]林孝贵.组合套期保值的投影分析[J].预测,2001,20(5):58-60.
[13] Lien D. A note on estimating the benefit of a composite hedge [J]. Journal of FuturesMarkets,2008,28(7):711-716.
[14]杨中原,迟国泰,赵光军.基于整体风险控制的组合套期保值优化模型[J].系统工程学报,2009,24(5):515-522.
[15]迟国泰,于超,杨万武.多种期货对多种现货的最优套期保值决策模型[J].系统工程学报,2010,25(1):50-54.
[16] De Jong A, De Roon F, Veld C. Out-of-sample hedging effectiveness of currencyfutures for alternative models and hedging strategies [J]. Journal of Futures Markets,1997,17(7):817–837.
[17] Turvey C G, Nayak G. The semivariance-minimizing hedge ratio [J]. Journal ofAgricultura1and Resource Economics,2003,28(1):100-115.
[18] Lien D, Tse Y K. Hedging downside risk: futures vs. options [J]. International Reviewof Economics and finance,2001,10(2):159-169.
[19] Mattos F, Garcia P, Nelson C. Relaxing standard hedging assumptions in the presenceof downside risk [J]. Quarterly Review of Economics and Finance,2008,48(1):78-93.
[20]陈蓉,蔡宗武,陈妙琼.最小下偏矩套期保值比率估计研究——基于混合copula方法[J].厦门大学学报(哲学社会科学版),2009,(3):35-40.
[21] Lien D, Tse Y K. Hedging time-varying downside risk [J]. Journal of Futures Markets,1998,18(6):705-722.
[22] Demirer R, Lien D. Downside risk for short and long hedgers [J]. InternationalReview of Economics and Finance,2003,12(1):25-44.
[23]安俊英,蒋祥林,张卫国.基于下方风险的期货套期保值[J].系统工程,2007,25(10):46-50.
[24] Eftekhari B. Lower partial moment hedge ratios [J]. Applied Financial Economics,1998,8(6):645-652.
[25] Lien D, Tse Y K. Hedging Downside Risk with Futures Contracts [J]. AppliedFinancial Economics,2000,10(2):163-170.
[26] Duarte J A M. optimal value at risk hedge using simulation methods [J]. DerivativesQuarterly,1998,5(2):67-75.
[27] Huang J C, Chiu C L, Lee M C. Hedging with zero-value at risk hedge ratio [J].Applied Financial Economics,2006,16(3):259-269.
[28]薛宏刚,徐成贤,徐凤敏.股票指数期货-投资、套利与套期保值[M].北京:科学出版社,2008:220-221.
[29]甘斌.最小平均VaR套期保值比率计算模型及实证研究[J].经济管理,2010,32(9):133-138.
[30] Harris R D F, Shen J. Hedging and value at risk [J]. Journal of Futures Markets,2006,26(4):369-390.
[31]林孝贵. t分布下期货套期保值VaR风险的敏感度分析[J].商业研究,2008,(9):26-29.
[32]迟国泰,余方平,刘轶芳.基于VaR的期货最优套期保值模型及应用研究[J].系统工程学报,2008,23(4):33-36.
[33]王元斌.基于几何谱风险测度的期货套期保值模型研究[D].大连:大连理工大学,2008.
[34]迟国泰,赵光军,杨中原.基于CVaR的期货最优套期保值比率模型及应用[J].系统管理学报,2009,18(l):27-33.
[35]林孝贵.期货套期保值CVaR风险的敏感度分析[J].数学的认识与实践,2009,39(4):36-41.
[36] Cao Z G, Harris R D F, Shen J. Hedging and value at risk: A semi-parametricapproach [J]. Journal of Futures Markets,2010,30(8):780-794.
[37]赵光军,迟国泰,杨中原.基于极端风险控制的多品种期货套期保值模型[J].系统工程学报,2010,25(2):228-234.
[38] Cheung C S, Kwan C C Y, Yip P C Y. The hedging effectiveness of options andfutures: A mean-Gini approach [J]. Journal of Futures Markets,1990,10(1):61-74.
[39] Kolb R W, Okunev J. Utility maximizing hedge ratios in the extended mean Giniframework [J]. Journal of Futures Markets,1993,13(6):597-609.
[40] Shalit H. Mean-Gini hedging in futures markets [J]. Journal of Futures Markets,1995,15(6):617-635.
[41] Lien D, Luo X. Estimating the extended mean-Gini coefficient for futures hedging [J].Journal of Futures Markets,1993,13(6):665-676.
[42] Lien D, Shaffer D R. A note on estimating the minimum extended Gini hedge ratio [J].Journal of Futures Markets,1999,19(1):101-113.
[43] Shaffer D R, Demaskey A. Currency hedging using the mean-Gini framework [J].Review of Quantitative Finance and Accounting,2005,25(2):125-137.
[44] Howard C T, D'Antonio L J. A risk-return measure of hedging effectiveness [J].Journal of Financial and Quantitative Analysis,1984,19(1):101-112.
[45] Satyanarayan S. A note on a risk-return measure of hedging effectiveness [J]. Journalof Futures Markets,1998,18(7):867-870.
[46] Chen S S, Lee C F, Shrestha K. On a mean-generalized semivariance approach todetermining the hedge ratio [J]. Journal of Futures Markets,2001,21(6):581-598.
[47] Lien D.A note on the relationships between some risk-adjusted performance measures[J]. Journal of Futures Markets,2002,22(5):483-495.
[48]杨万武,迟国泰,余方平.基于资金限制的单品种期货最优套期比模型[J].系统管理学报,2007,16(4):345-350.
[49]迟国泰,杨万武,余方平.基于资金限制的Sharp-ARIMA期货套期保值决策模型[J].预测,2007,26(3):72-80.
[50]林孝贵.基于收益与风险比率的期货套期保值策略[J].系统工程,2004,22(1):74-77.
[51]李国荣,吴大为,余方平.基于差异系数σ/μ的期货套期保值优化策略[J].系统工程,2005,23(8):78-81.
[52]安俊英,张卫国,蒋祥林,张睿.基于收益率与风险比率的期货套期保值策略研究[J].2008,30(4):357-361.
[53]于超.基于存量与增量组合的最优套期保值决策模型[D].大连:大连理工大学,2007.
[54] Kahl K H. Determination of the Recommended Hedging Ratio [J]. American Journalof Agricultural Economics,1983,65(3):603-605.
[55] Anderson R W, Danthine J P. Hedger Diversity in futures Market [J]. The EconomicJournal,1985,93:370-389.
[56] David H. Risk, Futures Pricing, and the Organization of Production in CommodityMarkets [J]. Journal of Political Economy,1988,96(6):1206-1120.
[57] Hsin C W, Kuo J, Lee C F. A new measure to compare the hedging effectiveness offoreign currency futures versus options [J]. Journal of Futures Markets,1994,14(6):685-707.
[58]谢赤.组合投资β调整与效用最大化的套期比的选择[J].运筹与管理,2002,11(5):87-92.
[59]徐成贤,王昭.全时段最优套期保值模型及实证研究[J].运筹学学报,2010,14(3):101-108.
[60] Hsu P, Liao S. The portfolio strategy and hedging: A spectrum perspective onmean–variance theory [J]. International Review of Economics and Finance,2012,22(1):129-140.
[61]黄长征.期货套期保值决策模型研究[J].数量经济技术经济研究,2004,(7):96-102.
[62]伍海军,马永开.期货市场套期保值非线性风险-收益策略[J].系统管理学报,2007,16(6):618-621.
[63]吴冲锋,钱宏伟,吴文锋.期货套期保值理论与实证研究[J].系统工程理论方法应用,1998,7(4):20-31.
[64] Lien D. Optimal futures hedging: Quadratic versus exponential utility functions [J].Journal of Futures Markets,2007,28(2):208-211.
[65] Kolb R W, Okunev J. Utility Maximizing Hedge Ratios in the Extended Mean-GiniFramework [J]. Journal of Futures Markets,1993,13(6):597-609.
[66] Chen S S, Lee C F, Shrestha K. On A Mean-Generalized Semi variance Approach toDetermining the Hedge Ratio [J]. Journal of Futures Markets,2001,21(6):581-598.
[67]袁象.价格密度函数不确定情形下的套期保值策略[J].大连海事大学学报(社会科学版),2009,8(1):48-50.
[68] Adam-Müller A F A, Nolte I. Cross hedging under multiplicative basis risk [J]. Journal,of Banking&Finance,2011,35(11):2956-2964.
[69] Adam-Müller A F A, Wong K P. The impact of delivery risk on optimal productionand futures hedging [J]. European Finance Review,2003,7(3):459-477.
[70] Lien D, Wang Y. Cross-hedging with futures and options: The effects ofdisappointment aversion [J]. Journal of Multinational Financial Management,2006,16(1):16–26.
[71] Mattos F, Garcia P, Pennings J M E. Probability weighting and loss aversion infutures hedging [J]. Journal of Financial Markets,2008,11(4):433-452.
[72] Lien D, Luo X. Estimating Extended Mean-Gini Coefficient for Futures Hedging [J].Journal of Futures Markets,1993,13(6):665-676.
[73] Balke N S, Fomby T B. Threshold Cointegration [J]. International Economic Review,1997,38:627-645.
[74] Lien D, Tse Y K. Fractional Cointegration and Futures Hedging [J]. Journal of FuturesMarkets,1999,19(4):457-474.
[75] Broll U, Chow K. W, Wong K P. Hedging and Nonlinear Risk Exposure [J]. OxfordEconomic Papers,2001,53(2):281-296.
[76] Sim A B, Zurbruegg R. Optimal Hedge Ratios and Alternative Hedging Strategies inthe Presence of Cointegrated Time-Varying Risks [J]. The European Journal ofFinance,2001,7(3):269-283.
[77]袁象,曹范愚.协整关系对期货套期保值策略的影响[J].数理统计与管理,2003,22(2):44-47.
[78]胡利琴,李殊琦.基于协整的最优套期保值比率的估计[J].武汉理工大学学报,2007,29(8):201-204.
[79] Baillie R T, Myers R J. Bavariate Garch estimation of the optimal commodity futureshedge [J]. Journal of Applied Ecnomitrucs.1991,6(2):109-124.
[80] Lien D, Tse Y K, Tsui A K C. Evaluating the Hedging Performance of theConstant-Correlation GARCH Models [J]. Applied Financial Economics,2002,12(11):791-798.
[81] McMillan D G. Time-varying hedge ratios for non-ferrous metals prices [J]. ResourcesPolicy,2005,30(3):186-193.
[82]吕江林,胡治山.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[J].数量经济技术经济研究,2006,(10):150-160.
[83] Fleming J, Kirby C. The specification of GARCH models with stochastic covariates[J]. Journal of Futures Markets,2008,28(10):911-934.
[84] Tse Y K, Tsui A K C. A multivariate generalized autoregressive conditionalheteroscedasticity model with time-varying correlations [J]. Journal of Business andEconomic Statistics,2002,20(3):351-362.
[85] Lien D, Yang L. Hedging with Chinese metal futures [J]. Global Finance Journal,2008,19(2):123-138.
[86]袁象,余思勤.存在时变方差的股指期货最佳套期保值比率计算[J].大连海事大学学报(社会科学版),2008,7(1):52-55.
[87]赵倩,杨德权,刘旸.基于DCC模型的外汇期货交叉套期保值比率估计[J].预测,2009,28(3):51-56.
[88]佟孟华.沪深300股指期货动态套期保值比率模型估计及比较——基于修正的ECM-BGARCH (1,1)模型的实证研究[J].数量经济技术经济研究,2011,(4):137-149.
[89] Sephton P S. Hedging wheat and canola at the Winnipeg commodity exchange [J].Applied Financial Economics,1993,3(1):67–72.
[90]迟国泰,杨万武,王玉刚.基于资金限制的多品种期货套期保值决策模型[J].系统工程理论与实践,2008,28(6):45-58.
[91]迟国泰,王玉刚,杨万武.多种期货对一种现货非线性组合套期保值模型[J].预测,2009,28(6):53-59.
[92] Kroner K F, Sultan J. Time-varying distributions and dynamic hedging with foreigncurrency futures [J]. Journal of Financial and Quantitative Analysis,1993,28(4):535-551.
[93]冯春山,蒋馥,吴家春.石油期货套期保值比选取的研究[J].系统工程理论方法应,2005,14(2):190-192.
[94]彭红枫,叶永刚.基于修正的ECM-GARCH模型的动态最优套期保值比率估计及比较研究[J].中国管理科学,2007,15(5):29-35.
[95] Hsu C C, Tseng C P, Wang Y H. Dynamic Hedging with Futures: A Copula-basedGARCH Model [J]. The Journal of Futures Markets,2008,28(11):1095-1116.
[96]姚荣辉,王书平,张蜀林.动态非线性套期保值策略研究[J].工业技术经济,28(7):126-130.
[97]张高勋,田益祥,李秋敏.基于Copula-ECM-GARCH模型的动态最优套期保值比率估计及比较[J].系统工程,2011,29(8):56-64.
[98]梁建峰,陈健平,刘京军.基于copula-GARCH方法的LPM套期保值研究[J].系统工程学报,2011,26(5):636-641.
[99]周怡.以VaR为目标函数的期货最优套期保值比率估计[J].统计与决策,2008,(18):157-159.
[100] Lee H-T, Yoder J. Optimal hedging with a regime-switching time-varying correlationGARCH model [J]. Journal of Futures Markets,2007,27(5):495-516.
[101] Alizadeh A H, Nomikos N K, Pouliasis, P K. A Markov regime switching approachfor hedging energy commodities [J]. Journal of Banking and Finance,2008,32(9):1970-1983.
[102] Lee H. Optimal futures hedging under jump switching dynamics [J]. Journal ofEmpirical Finance,2009,16(3):446-456.
[103] Lee H. Regime switching correlation hedging [J]. Journal of Banking and Finance,2010,34(11):2728-2741.
[104]刘兰燕,吴琼兰.基于Laplace分布的DCC-MVGARCH的铜期货动态套期保值率研究[J].时代金融,2011,(11):19-21.
[105] Harvey A C, Ruiz E, Shephard N. Multivariate Stochastic Variance Models [J].Review of Economic Studies,1994,61(2):247-264.
[106] Uhlig H. Bayesian Vector Autoregressions with Stochastic Volatility [J].Econometrica,1997,65(1):59-73.
[107] Danielsson J. Multivariate Stochastic Volatility Models: Estimation and a Comparisonwith VGARCH Models [J]. Journal of Empirical Finance,1998,5(2):155-173.
[108] Lien D, Wilson B. Multiperiod Hedging in the Presence of Stochastic Volatility [J].International Review of Financial Analysis,2001,10(4):395-406.
[109]张凤霞,王宝森.基于植入SV的VaR模型的股指期货风险度量[J].河北工程大学学报（自然科学版）2006,23(1):80-85.
[110] Baesel J, Grant D. Optimal Sequential Futures Trading [J]. The Journal of Financialand Quantitative Analysis,1982,17(5):683-695.
[111] McCabe G M, Franckle C T. The Effectiveness of Rolling the Hedge Forward in theTreasury Bill Futures Market [J]. Financial Management,1983,(1):21-29.
[112] Grant. Rolling the Hedge Forward: An Extension [J]. Financial Management.1984,13(4):195-220.
[113] Gardner B. Rollover Hedging and Missing Long-Term Futures Markets [J]. AmericanJournal of Agricultural Economics,1989,71(2):311-318.
[114] Mathews K H, Holthausen D M. A Simple Multiperiod Minimum Risk Hedge Model[J]. American Journal of Agricultural Economics,1997,73(4):1020-1026.
[115] Schwartz E S. The stochastic behavior of commodity prices: Implications forvaluation and hedging [J]. Journal of Finance,1997,52(3):923-973.
[116] Ross S A. Hedging long run commitmentsa: exercises in incomplete market pricing[J]. Economic Notes,1997,26(1):385-419.
[117] Hilliard J E. Analytics Underlying the Metallgesellschaft Hedge: Short Term Futuresin a Multi-Period Environment [J]. Review of Quantitative Finance and Accounting,1999,12(3):195–219.
[118] Lien D, Shaffer D R. Hedging Multi-period Forward Commitments: The Case ofPeriod-by-Period Quantity Uncertainty [J]. Review of Quantitative Finance andAccounting,2001,16(2):171-181.
[119] Veld-Merkoulova Y V, De Roon F A. Hedging long-term commodity risk [J]. TheJournal of Futures Markets,2003,23(2):109-133.
[120]伍海军,马永开.展期套期保值策略研究[J].电子科技大学学报(自然科学版),2004,33(1):109-112.
[121] Bühler W, Korn O, Sch bel R. Hedging Long-Term Forwards with Short-TermFutures: A Two-Regime Approach [J]. Review of Derivatives Research,2004,7(3):185-212.
[122] Hilliard J E, Huang P. An empirical analysis of multi-period hedges: Applications tocommercial and investment assets [J]. Journal of Futures Markets,2005,6(25):587-606.
[123]阳晓晖.多阶段展期套期保值策略研究[J].重庆工商大学学报(社会科学版),2005,22(6):51-54.
[124] Lien D, Shrestha K. An empirical analysis of the relationship between hedge ratio andhedging horizon using wavelet analysis [J]. Journal of Futures Markets,2007,27(2):127-150.
[125] Fernandez V. Multi-period hedge ratios for a multi-asset portfolio when accounting forreturns co-movement [J]. Journal of Futures Markets,2008,28(2):182-207.
[126] Bertus M, Godbey J, Hilliard J E. minimum variance cross hedging undermean-reverting spreads, stochastic convenience yields, and jumps: application to theairline industry.[J]. Journal of Futures Markets,2009,29(8):736-756.
[127] Culp C L, Miller M H. Metallgesellschaft and the Economics of Synthetic Storage [J].Journal of Applied Corporate Finance,1995,7(4):62-76.
[128] Neuberger A. Hedging Long Run Term Exposures with Multiple Short Term FuturesContracts [J]. Review of Financial Studies,1999,12(3):429-459.
[129] Collins R A. The risk management effectiveness of multivariate hedging models in theU. S. soy-complex [J]. Journal of Futures Markets,2000,20(2):189-204.
[130] Lien D, Shaffer D R. Multi-period Strip Hedging of Forward Commitments [J].Review of Quantitative Finance and Accounting,2002,18(4):345-358.
[131] Low A, Muthuswamy J, Sakar S, etal. Multiperiod hedging with futures contracts [J].Journal of Futures Markets,2002,22(12):1179-1203.
[132] Larcher G, Leobacher G. An optimal strategy for hedging with short-term futurescontracts [J]. Mathematical Finance,2003,13(2):331-344.
[133] Lien D, Kwak S. Provisional liquidation of futures hedge programs [J]. EnergyEconomics,2006,(28):266-273.
[134] Godbey J M, Hilliard J E. Adjusting stacked-hedge ratios for stochastic convenienceyield: a minimum variance approach [J]. Quantitative Finance,2007,7(3):289-300.
[135]伍海军,马永开.期货市场多阶段展期套期保值的基本理论探讨[J].系统工程,2007,25(4):83-87.
[136]阳晓晖,伍海军.多阶段展期套期保值策略研究[J].统计与决策,2007,(4):51-54.
[137] Leobacher G. On a class of optimization problems emerging when hedging with shortterm futures contracts [J]. Mathematical Methods of Operations Research,2008,67(1):65-90.
[138]迟国泰,杨中原.基于最小方差的系列展期套期保值优化模型[J].系统工程理论与实践,2009,29(12):163-174.
[139] Carbonez K A E, Nguyen V T T, Sercu P. Hedging with Two Futures Contracts:Simplicity Pays [J]. European Financial Management,2011,17(5):806-834.
[140]王征,樊治平,张权.期货套期保值多目标规划模型[J].系统工程,1997,15(2):50-53.
[141] Bera A K, Garcia P, Roh J S. Estimation of Time-Varying Hedging Ratios for Cornand Soybeans: BGARCH and Random Coefcient Approaches [J]. Sankhya,1997,59:346-368.
[142] Jo lle M. Conditional OLS minimum variance hedge ratios [J]. Journal of FuturesMarkets,2004,24(10):945-964.
[143] Kuwornu J K M, Kuiper W. E, Pennings J M E, Meulenberg M T G. Time-varyingHedge Ratios: A Principal-agent Approach [J]. Journal of Agricultural Economics,2005,56(3):417-432.
[144] Alizadeh A, Nomikos N. A Markov regime switching approach for hedging stockindices [J]. Journal of Futures Markets,2004,24(7):649-674.
[145] Lee H, Yoder J K, Mittelhammer R C, McCluskey J J. A random coefficientautoregressive Markov regime switching model for dynamic futures hedging [J].Journal of Futures Markets,2006,26(2):103-129.
[146]付剑茹,张宗成,龚金林.基于MCMC模拟的期货最优套保比贝叶斯分析[J].管理工程学报,2009,23(3):120-126.
[147] Haigh M S, Holt M T. Hedging multiple price uncertainty in international grain trade[J]. American Journal of Agricultural Economics,2000,82(4):881-896.
[148]王玉刚,迟国泰,杨万武.基于Copula的最小方差套期保值比率[J].系统工程理论与实践,2009,29(8):1-10.
[149]迟国泰,余方平,王玉刚.基于动态规划多期期货套期保值优化模型研究[J].中国管理科学,2010,18(3):17-24.
[150]邹庆忠,李金林,王贝贝.基于时变相关Coupla的最小方差套期保值研究[J].北京理工大学学报,2011,31(11):1384-1387.
[151]付剑茹,张宗成.时变最优套期保值比估计及比较研究——基于卡尔曼滤波在状态空间模型中的应用[J].管理科学学报,2010,13(12):69-73+82.
[152]陶琲,王献立.期货经济学教程[M].北京:商务印书馆,2003.
[153] Cotter J, Hanly J. Reevaluating hedging performance [J]. Journal of Futures Markets,2006,26(7):677-702.
[154]王学民.应用概率统计[M].上海:上海财经大学出版社,2005.
[155]徐成贤,薛宏刚.金融工程--计算技术与方法[M].北京:科学出版社,2007.
[156]傅俊辉,张卫国,杜倩,孔文涛.规避逐日盯市风险的期货套期保值模型[J].管理科学,2011,24(3):86-93.
[157] Blank S C. Determing futures hedging reserve capital requirements [J]. Journal ofFutures Markes,1990,10(2):169-177.
[158] Lien D. The effect of liquidity constraints on futures hedging [J]. Journal of FuturesMarkets,2003,23(6):603-613.
[159] Mirmirani S, Li H C. Gold price, neural networks and Genetic algorithm [J].Computational Economics,2004,23(2):193-204.
[160]翟育明,邹亚平,周俊文,冯旖旎.自适应遗传神经网络的基金走势预测模型研究[J].武汉理工大学学报,2010,32(1):107-111.
[161]高琴.人工神经网络在股市预测模型中的应用[J].微电子学与计算机,2007,24(11):147-151.
[162]郝华宁,刘阳.基于遗传神经网络的个股价格短期预测[J].西安石油大学学报(自然科学版),2010,25(2):88-91.
[163]史峰,王小川,郁磊,李洋. MATLAB神经网络30个案例分析[M].北京:北京航空航天大学出版社,2010.
[164]阳明盛,罗长童.最优化原理、方法及求解软件[M].北京:科学出版社,2006.
[165] Reid R W, Citron S J. On Noninferior Performance Index Vector [J]. Journal ofOptimization Theory and Applications1971,7(1):11-28.
[2] Ederington L. The hedging performance of the new futures markets [J]. Journal ofFinance,1979,34(1):157-170.
[3]吴冲锋，钱宏伟，吴文锋．期货套期保值理论与实证研究(I)[J].系统工程理论方法应用,1998,7(4):20-26.
[4]张学东,徐成贤,李栓劳,张芳.考虑交易成本的股价指数期货最优套期保值策略模型[J].西安交通大学学报,2002,36(12):1317-1319.
[5]迟国泰,张梅,杨磊.基于持有成本理论的期货套期保值决策模型[J].运筹与管理,2010,19(6):104-116.
[6] Lioui A, Poncet P. The minimum variance hedge ratio under stochastic interest rates[J]. Management Science,2000,46(5):658-668.
[7] Terry. Minimum-variance futures hedging under alternative return specifications [J].The Journal of Futures Markets,2005,25(6):537-552.
[8]杨中原,迟国泰,赵光军.基于最小模糊方差的最优交叉套期保值模型[J].运筹与管理,2008,17(6):113-126.
[9] Ederington L H, Salas J M. Minimum variance hedging when spot price changes arepartially predictable [J]. Journal of Banking&Finance,2008,32:654–663.
[10]杨国梁,张新新,杨敏慧.基于支持向量机的套期保值技术研究[J].中央财经大学学报,2010,(3):28-32.
[11]马永开,唐小我.组合套期保值策略及其理论研究[J].预测,1999,18(4):48-51.
[12]林孝贵.组合套期保值的投影分析[J].预测,2001,20(5):58-60.
[13] Lien D. A note on estimating the benefit of a composite hedge [J]. Journal of FuturesMarkets,2008,28(7):711-716.
[14]杨中原,迟国泰,赵光军.基于整体风险控制的组合套期保值优化模型[J].系统工程学报,2009,24(5):515-522.
[15]迟国泰,于超,杨万武.多种期货对多种现货的最优套期保值决策模型[J].系统工程学报,2010,25(1):50-54.
[16] De Jong A, De Roon F, Veld C. Out-of-sample hedging effectiveness of currencyfutures for alternative models and hedging strategies [J]. Journal of Futures Markets,1997,17(7):817–837.
[17] Turvey C G, Nayak G. The semivariance-minimizing hedge ratio [J]. Journal ofAgricultura1and Resource Economics,2003,28(1):100-115.
[18] Lien D, Tse Y K. Hedging downside risk: futures vs. options [J]. International Reviewof Economics and finance,2001,10(2):159-169.
[19] Mattos F, Garcia P, Nelson C. Relaxing standard hedging assumptions in the presenceof downside risk [J]. Quarterly Review of Economics and Finance,2008,48(1):78-93.
[20]陈蓉,蔡宗武,陈妙琼.最小下偏矩套期保值比率估计研究——基于混合copula方法[J].厦门大学学报(哲学社会科学版),2009,(3):35-40.
[21] Lien D, Tse Y K. Hedging time-varying downside risk [J]. Journal of Futures Markets,1998,18(6):705-722.
[22] Demirer R, Lien D. Downside risk for short and long hedgers [J]. InternationalReview of Economics and Finance,2003,12(1):25-44.
[23]安俊英,蒋祥林,张卫国.基于下方风险的期货套期保值[J].系统工程,2007,25(10):46-50.
[24] Eftekhari B. Lower partial moment hedge ratios [J]. Applied Financial Economics,1998,8(6):645-652.
[25] Lien D, Tse Y K. Hedging Downside Risk with Futures Contracts [J]. AppliedFinancial Economics,2000,10(2):163-170.
[26] Duarte J A M. optimal value at risk hedge using simulation methods [J]. DerivativesQuarterly,1998,5(2):67-75.
[27] Huang J C, Chiu C L, Lee M C. Hedging with zero-value at risk hedge ratio [J].Applied Financial Economics,2006,16(3):259-269.
[28]薛宏刚,徐成贤,徐凤敏.股票指数期货-投资、套利与套期保值[M].北京:科学出版社,2008:220-221.
[29]甘斌.最小平均VaR套期保值比率计算模型及实证研究[J].经济管理,2010,32(9):133-138.
[30] Harris R D F, Shen J. Hedging and value at risk [J]. Journal of Futures Markets,2006,26(4):369-390.
[31]林孝贵. t分布下期货套期保值VaR风险的敏感度分析[J].商业研究,2008,(9):26-29.
[32]迟国泰,余方平,刘轶芳.基于VaR的期货最优套期保值模型及应用研究[J].系统工程学报,2008,23(4):33-36.
[33]王元斌.基于几何谱风险测度的期货套期保值模型研究[D].大连:大连理工大学,2008.
[34]迟国泰,赵光军,杨中原.基于CVaR的期货最优套期保值比率模型及应用[J].系统管理学报,2009,18(l):27-33.
[35]林孝贵.期货套期保值CVaR风险的敏感度分析[J].数学的认识与实践,2009,39(4):36-41.
[36] Cao Z G, Harris R D F, Shen J. Hedging and value at risk: A semi-parametricapproach [J]. Journal of Futures Markets,2010,30(8):780-794.
[37]赵光军,迟国泰,杨中原.基于极端风险控制的多品种期货套期保值模型[J].系统工程学报,2010,25(2):228-234.
[38] Cheung C S, Kwan C C Y, Yip P C Y. The hedging effectiveness of options andfutures: A mean-Gini approach [J]. Journal of Futures Markets,1990,10(1):61-74.
[39] Kolb R W, Okunev J. Utility maximizing hedge ratios in the extended mean Giniframework [J]. Journal of Futures Markets,1993,13(6):597-609.
[40] Shalit H. Mean-Gini hedging in futures markets [J]. Journal of Futures Markets,1995,15(6):617-635.
[41] Lien D, Luo X. Estimating the extended mean-Gini coefficient for futures hedging [J].Journal of Futures Markets,1993,13(6):665-676.
[42] Lien D, Shaffer D R. A note on estimating the minimum extended Gini hedge ratio [J].Journal of Futures Markets,1999,19(1):101-113.
[43] Shaffer D R, Demaskey A. Currency hedging using the mean-Gini framework [J].Review of Quantitative Finance and Accounting,2005,25(2):125-137.
[44] Howard C T, D'Antonio L J. A risk-return measure of hedging effectiveness [J].Journal of Financial and Quantitative Analysis,1984,19(1):101-112.
[45] Satyanarayan S. A note on a risk-return measure of hedging effectiveness [J]. Journalof Futures Markets,1998,18(7):867-870.
[46] Chen S S, Lee C F, Shrestha K. On a mean-generalized semivariance approach todetermining the hedge ratio [J]. Journal of Futures Markets,2001,21(6):581-598.
[47] Lien D.A note on the relationships between some risk-adjusted performance measures[J]. Journal of Futures Markets,2002,22(5):483-495.
[48]杨万武,迟国泰,余方平.基于资金限制的单品种期货最优套期比模型[J].系统管理学报,2007,16(4):345-350.
[49]迟国泰,杨万武,余方平.基于资金限制的Sharp-ARIMA期货套期保值决策模型[J].预测,2007,26(3):72-80.
[50]林孝贵.基于收益与风险比率的期货套期保值策略[J].系统工程,2004,22(1):74-77.
[51]李国荣,吴大为,余方平.基于差异系数σ/μ的期货套期保值优化策略[J].系统工程,2005,23(8):78-81.
[52]安俊英,张卫国,蒋祥林,张睿.基于收益率与风险比率的期货套期保值策略研究[J].2008,30(4):357-361.
[53]于超.基于存量与增量组合的最优套期保值决策模型[D].大连:大连理工大学,2007.
[54] Kahl K H. Determination of the Recommended Hedging Ratio [J]. American Journalof Agricultural Economics,1983,65(3):603-605.
[55] Anderson R W, Danthine J P. Hedger Diversity in futures Market [J]. The EconomicJournal,1985,93:370-389.
[56] David H. Risk, Futures Pricing, and the Organization of Production in CommodityMarkets [J]. Journal of Political Economy,1988,96(6):1206-1120.
[57] Hsin C W, Kuo J, Lee C F. A new measure to compare the hedging effectiveness offoreign currency futures versus options [J]. Journal of Futures Markets,1994,14(6):685-707.
[58]谢赤.组合投资β调整与效用最大化的套期比的选择[J].运筹与管理,2002,11(5):87-92.
[59]徐成贤,王昭.全时段最优套期保值模型及实证研究[J].运筹学学报,2010,14(3):101-108.
[60] Hsu P, Liao S. The portfolio strategy and hedging: A spectrum perspective onmean–variance theory [J]. International Review of Economics and Finance,2012,22(1):129-140.
[61]黄长征.期货套期保值决策模型研究[J].数量经济技术经济研究,2004,(7):96-102.
[62]伍海军,马永开.期货市场套期保值非线性风险-收益策略[J].系统管理学报,2007,16(6):618-621.
[63]吴冲锋,钱宏伟,吴文锋.期货套期保值理论与实证研究[J].系统工程理论方法应用,1998,7(4):20-31.
[64] Lien D. Optimal futures hedging: Quadratic versus exponential utility functions [J].Journal of Futures Markets,2007,28(2):208-211.
[65] Kolb R W, Okunev J. Utility Maximizing Hedge Ratios in the Extended Mean-GiniFramework [J]. Journal of Futures Markets,1993,13(6):597-609.
[66] Chen S S, Lee C F, Shrestha K. On A Mean-Generalized Semi variance Approach toDetermining the Hedge Ratio [J]. Journal of Futures Markets,2001,21(6):581-598.
[67]袁象.价格密度函数不确定情形下的套期保值策略[J].大连海事大学学报(社会科学版),2009,8(1):48-50.
[68] Adam-Müller A F A, Nolte I. Cross hedging under multiplicative basis risk [J]. Journal,of Banking&Finance,2011,35(11):2956-2964.
[69] Adam-Müller A F A, Wong K P. The impact of delivery risk on optimal productionand futures hedging [J]. European Finance Review,2003,7(3):459-477.
[70] Lien D, Wang Y. Cross-hedging with futures and options: The effects ofdisappointment aversion [J]. Journal of Multinational Financial Management,2006,16(1):16–26.
[71] Mattos F, Garcia P, Pennings J M E. Probability weighting and loss aversion infutures hedging [J]. Journal of Financial Markets,2008,11(4):433-452.
[72] Lien D, Luo X. Estimating Extended Mean-Gini Coefficient for Futures Hedging [J].Journal of Futures Markets,1993,13(6):665-676.
[73] Balke N S, Fomby T B. Threshold Cointegration [J]. International Economic Review,1997,38:627-645.
[74] Lien D, Tse Y K. Fractional Cointegration and Futures Hedging [J]. Journal of FuturesMarkets,1999,19(4):457-474.
[75] Broll U, Chow K. W, Wong K P. Hedging and Nonlinear Risk Exposure [J]. OxfordEconomic Papers,2001,53(2):281-296.
[76] Sim A B, Zurbruegg R. Optimal Hedge Ratios and Alternative Hedging Strategies inthe Presence of Cointegrated Time-Varying Risks [J]. The European Journal ofFinance,2001,7(3):269-283.
[77]袁象,曹范愚.协整关系对期货套期保值策略的影响[J].数理统计与管理,2003,22(2):44-47.
[78]胡利琴,李殊琦.基于协整的最优套期保值比率的估计[J].武汉理工大学学报,2007,29(8):201-204.
[79] Baillie R T, Myers R J. Bavariate Garch estimation of the optimal commodity futureshedge [J]. Journal of Applied Ecnomitrucs.1991,6(2):109-124.
[80] Lien D, Tse Y K, Tsui A K C. Evaluating the Hedging Performance of theConstant-Correlation GARCH Models [J]. Applied Financial Economics,2002,12(11):791-798.
[81] McMillan D G. Time-varying hedge ratios for non-ferrous metals prices [J]. ResourcesPolicy,2005,30(3):186-193.
[82]吕江林,胡治山.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[J].数量经济技术经济研究,2006,(10):150-160.
[83] Fleming J, Kirby C. The specification of GARCH models with stochastic covariates[J]. Journal of Futures Markets,2008,28(10):911-934.
[84] Tse Y K, Tsui A K C. A multivariate generalized autoregressive conditionalheteroscedasticity model with time-varying correlations [J]. Journal of Business andEconomic Statistics,2002,20(3):351-362.
[85] Lien D, Yang L. Hedging with Chinese metal futures [J]. Global Finance Journal,2008,19(2):123-138.
[86]袁象,余思勤.存在时变方差的股指期货最佳套期保值比率计算[J].大连海事大学学报(社会科学版),2008,7(1):52-55.
[87]赵倩,杨德权,刘旸.基于DCC模型的外汇期货交叉套期保值比率估计[J].预测,2009,28(3):51-56.
[88]佟孟华.沪深300股指期货动态套期保值比率模型估计及比较——基于修正的ECM-BGARCH (1,1)模型的实证研究[J].数量经济技术经济研究,2011,(4):137-149.
[89] Sephton P S. Hedging wheat and canola at the Winnipeg commodity exchange [J].Applied Financial Economics,1993,3(1):67–72.
[90]迟国泰,杨万武,王玉刚.基于资金限制的多品种期货套期保值决策模型[J].系统工程理论与实践,2008,28(6):45-58.
[91]迟国泰,王玉刚,杨万武.多种期货对一种现货非线性组合套期保值模型[J].预测,2009,28(6):53-59.
[92] Kroner K F, Sultan J. Time-varying distributions and dynamic hedging with foreigncurrency futures [J]. Journal of Financial and Quantitative Analysis,1993,28(4):535-551.
[93]冯春山,蒋馥,吴家春.石油期货套期保值比选取的研究[J].系统工程理论方法应,2005,14(2):190-192.
[94]彭红枫,叶永刚.基于修正的ECM-GARCH模型的动态最优套期保值比率估计及比较研究[J].中国管理科学,2007,15(5):29-35.
[95] Hsu C C, Tseng C P, Wang Y H. Dynamic Hedging with Futures: A Copula-basedGARCH Model [J]. The Journal of Futures Markets,2008,28(11):1095-1116.
[96]姚荣辉,王书平,张蜀林.动态非线性套期保值策略研究[J].工业技术经济,28(7):126-130.
[97]张高勋,田益祥,李秋敏.基于Copula-ECM-GARCH模型的动态最优套期保值比率估计及比较[J].系统工程,2011,29(8):56-64.
[98]梁建峰,陈健平,刘京军.基于copula-GARCH方法的LPM套期保值研究[J].系统工程学报,2011,26(5):636-641.
[99]周怡.以VaR为目标函数的期货最优套期保值比率估计[J].统计与决策,2008,(18):157-159.
[100] Lee H-T, Yoder J. Optimal hedging with a regime-switching time-varying correlationGARCH model [J]. Journal of Futures Markets,2007,27(5):495-516.
[101] Alizadeh A H, Nomikos N K, Pouliasis, P K. A Markov regime switching approachfor hedging energy commodities [J]. Journal of Banking and Finance,2008,32(9):1970-1983.
[102] Lee H. Optimal futures hedging under jump switching dynamics [J]. Journal ofEmpirical Finance,2009,16(3):446-456.
[103] Lee H. Regime switching correlation hedging [J]. Journal of Banking and Finance,2010,34(11):2728-2741.
[104]刘兰燕,吴琼兰.基于Laplace分布的DCC-MVGARCH的铜期货动态套期保值率研究[J].时代金融,2011,(11):19-21.
[105] Harvey A C, Ruiz E, Shephard N. Multivariate Stochastic Variance Models [J].Review of Economic Studies,1994,61(2):247-264.
[106] Uhlig H. Bayesian Vector Autoregressions with Stochastic Volatility [J].Econometrica,1997,65(1):59-73.
[107] Danielsson J. Multivariate Stochastic Volatility Models: Estimation and a Comparisonwith VGARCH Models [J]. Journal of Empirical Finance,1998,5(2):155-173.
[108] Lien D, Wilson B. Multiperiod Hedging in the Presence of Stochastic Volatility [J].International Review of Financial Analysis,2001,10(4):395-406.
[109]张凤霞,王宝森.基于植入SV的VaR模型的股指期货风险度量[J].河北工程大学学报（自然科学版）2006,23(1):80-85.
[110] Baesel J, Grant D. Optimal Sequential Futures Trading [J]. The Journal of Financialand Quantitative Analysis,1982,17(5):683-695.
[111] McCabe G M, Franckle C T. The Effectiveness of Rolling the Hedge Forward in theTreasury Bill Futures Market [J]. Financial Management,1983,(1):21-29.
[112] Grant. Rolling the Hedge Forward: An Extension [J]. Financial Management.1984,13(4):195-220.
[113] Gardner B. Rollover Hedging and Missing Long-Term Futures Markets [J]. AmericanJournal of Agricultural Economics,1989,71(2):311-318.
[114] Mathews K H, Holthausen D M. A Simple Multiperiod Minimum Risk Hedge Model[J]. American Journal of Agricultural Economics,1997,73(4):1020-1026.
[115] Schwartz E S. The stochastic behavior of commodity prices: Implications forvaluation and hedging [J]. Journal of Finance,1997,52(3):923-973.
[116] Ross S A. Hedging long run commitmentsa: exercises in incomplete market pricing[J]. Economic Notes,1997,26(1):385-419.
[117] Hilliard J E. Analytics Underlying the Metallgesellschaft Hedge: Short Term Futuresin a Multi-Period Environment [J]. Review of Quantitative Finance and Accounting,1999,12(3):195–219.
[118] Lien D, Shaffer D R. Hedging Multi-period Forward Commitments: The Case ofPeriod-by-Period Quantity Uncertainty [J]. Review of Quantitative Finance andAccounting,2001,16(2):171-181.
[119] Veld-Merkoulova Y V, De Roon F A. Hedging long-term commodity risk [J]. TheJournal of Futures Markets,2003,23(2):109-133.
[120]伍海军,马永开.展期套期保值策略研究[J].电子科技大学学报(自然科学版),2004,33(1):109-112.
[121] Bühler W, Korn O, Sch bel R. Hedging Long-Term Forwards with Short-TermFutures: A Two-Regime Approach [J]. Review of Derivatives Research,2004,7(3):185-212.
[122] Hilliard J E, Huang P. An empirical analysis of multi-period hedges: Applications tocommercial and investment assets [J]. Journal of Futures Markets,2005,6(25):587-606.
[123]阳晓晖.多阶段展期套期保值策略研究[J].重庆工商大学学报(社会科学版),2005,22(6):51-54.
[124] Lien D, Shrestha K. An empirical analysis of the relationship between hedge ratio andhedging horizon using wavelet analysis [J]. Journal of Futures Markets,2007,27(2):127-150.
[125] Fernandez V. Multi-period hedge ratios for a multi-asset portfolio when accounting forreturns co-movement [J]. Journal of Futures Markets,2008,28(2):182-207.
[126] Bertus M, Godbey J, Hilliard J E. minimum variance cross hedging undermean-reverting spreads, stochastic convenience yields, and jumps: application to theairline industry.[J]. Journal of Futures Markets,2009,29(8):736-756.
[127] Culp C L, Miller M H. Metallgesellschaft and the Economics of Synthetic Storage [J].Journal of Applied Corporate Finance,1995,7(4):62-76.
[128] Neuberger A. Hedging Long Run Term Exposures with Multiple Short Term FuturesContracts [J]. Review of Financial Studies,1999,12(3):429-459.
[129] Collins R A. The risk management effectiveness of multivariate hedging models in theU. S. soy-complex [J]. Journal of Futures Markets,2000,20(2):189-204.
[130] Lien D, Shaffer D R. Multi-period Strip Hedging of Forward Commitments [J].Review of Quantitative Finance and Accounting,2002,18(4):345-358.
[131] Low A, Muthuswamy J, Sakar S, etal. Multiperiod hedging with futures contracts [J].Journal of Futures Markets,2002,22(12):1179-1203.
[132] Larcher G, Leobacher G. An optimal strategy for hedging with short-term futurescontracts [J]. Mathematical Finance,2003,13(2):331-344.
[133] Lien D, Kwak S. Provisional liquidation of futures hedge programs [J]. EnergyEconomics,2006,(28):266-273.
[134] Godbey J M, Hilliard J E. Adjusting stacked-hedge ratios for stochastic convenienceyield: a minimum variance approach [J]. Quantitative Finance,2007,7(3):289-300.
[135]伍海军,马永开.期货市场多阶段展期套期保值的基本理论探讨[J].系统工程,2007,25(4):83-87.
[136]阳晓晖,伍海军.多阶段展期套期保值策略研究[J].统计与决策,2007,(4):51-54.
[137] Leobacher G. On a class of optimization problems emerging when hedging with shortterm futures contracts [J]. Mathematical Methods of Operations Research,2008,67(1):65-90.
[138]迟国泰,杨中原.基于最小方差的系列展期套期保值优化模型[J].系统工程理论与实践,2009,29(12):163-174.
[139] Carbonez K A E, Nguyen V T T, Sercu P. Hedging with Two Futures Contracts:Simplicity Pays [J]. European Financial Management,2011,17(5):806-834.
[140]王征,樊治平,张权.期货套期保值多目标规划模型[J].系统工程,1997,15(2):50-53.
[141] Bera A K, Garcia P, Roh J S. Estimation of Time-Varying Hedging Ratios for Cornand Soybeans: BGARCH and Random Coefcient Approaches [J]. Sankhya,1997,59:346-368.
[142] Jo lle M. Conditional OLS minimum variance hedge ratios [J]. Journal of FuturesMarkets,2004,24(10):945-964.
[143] Kuwornu J K M, Kuiper W. E, Pennings J M E, Meulenberg M T G. Time-varyingHedge Ratios: A Principal-agent Approach [J]. Journal of Agricultural Economics,2005,56(3):417-432.
[144] Alizadeh A, Nomikos N. A Markov regime switching approach for hedging stockindices [J]. Journal of Futures Markets,2004,24(7):649-674.
[145] Lee H, Yoder J K, Mittelhammer R C, McCluskey J J. A random coefficientautoregressive Markov regime switching model for dynamic futures hedging [J].Journal of Futures Markets,2006,26(2):103-129.
[146]付剑茹,张宗成,龚金林.基于MCMC模拟的期货最优套保比贝叶斯分析[J].管理工程学报,2009,23(3):120-126.
[147] Haigh M S, Holt M T. Hedging multiple price uncertainty in international grain trade[J]. American Journal of Agricultural Economics,2000,82(4):881-896.
[148]王玉刚,迟国泰,杨万武.基于Copula的最小方差套期保值比率[J].系统工程理论与实践,2009,29(8):1-10.
[149]迟国泰,余方平,王玉刚.基于动态规划多期期货套期保值优化模型研究[J].中国管理科学,2010,18(3):17-24.
[150]邹庆忠,李金林,王贝贝.基于时变相关Coupla的最小方差套期保值研究[J].北京理工大学学报,2011,31(11):1384-1387.
[151]付剑茹,张宗成.时变最优套期保值比估计及比较研究——基于卡尔曼滤波在状态空间模型中的应用[J].管理科学学报,2010,13(12):69-73+82.
[152]陶琲,王献立.期货经济学教程[M].北京:商务印书馆,2003.
[153] Cotter J, Hanly J. Reevaluating hedging performance [J]. Journal of Futures Markets,2006,26(7):677-702.
[154]王学民.应用概率统计[M].上海:上海财经大学出版社,2005.
[155]徐成贤,薛宏刚.金融工程--计算技术与方法[M].北京:科学出版社,2007.
[156]傅俊辉,张卫国,杜倩,孔文涛.规避逐日盯市风险的期货套期保值模型[J].管理科学,2011,24(3):86-93.
[157] Blank S C. Determing futures hedging reserve capital requirements [J]. Journal ofFutures Markes,1990,10(2):169-177.
[158] Lien D. The effect of liquidity constraints on futures hedging [J]. Journal of FuturesMarkets,2003,23(6):603-613.
[159] Mirmirani S, Li H C. Gold price, neural networks and Genetic algorithm [J].Computational Economics,2004,23(2):193-204.
[160]翟育明,邹亚平,周俊文,冯旖旎.自适应遗传神经网络的基金走势预测模型研究[J].武汉理工大学学报,2010,32(1):107-111.
[161]高琴.人工神经网络在股市预测模型中的应用[J].微电子学与计算机,2007,24(11):147-151.
[162]郝华宁,刘阳.基于遗传神经网络的个股价格短期预测[J].西安石油大学学报(自然科学版),2010,25(2):88-91.
[163]史峰,王小川,郁磊,李洋. MATLAB神经网络30个案例分析[M].北京:北京航空航天大学出版社,2010.
[164]阳明盛,罗长童.最优化原理、方法及求解软件[M].北京:科学出版社,2006.
[165] Reid R W, Citron S J. On Noninferior Performance Index Vector [J]. Journal ofOptimization Theory and Applications1971,7(1):11-28.