R-藤Pair Copula模型下的投资组合最优套期保值比例研究
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摘要
目前我国证券市场尚未成熟,风险对冲手段单一,因此构建一个期货对多资产进行套期保值策略对于投资组合的风险管理尤为重要.本文构建了基于线性规划的最小CVaR (Conditional Value at Risk)套期保值模型,同时运用R-藤Pair CopulaGARCH模型结合蒙特卡洛模拟生成投资组合中各资产收益率的情景和概率,将结果用于基于线性规划的最小CVaR套期保值模型,可确定投资组合的最优套期保值比例.针对沪深300指数和5支沪深300成分股的实证研究表明,相对改良后的正态假定模型,经本文模型套期保值后的投资组合在风险和收益上均有更好的表现.
At present,Chinese security market is not mature and risk hedging tools are limited.Therefore,the use of one futures hedging on multiple assets is an important strategy in portfolio risk management.This paper first constructs a minimum CVaR(Conditional Value at Risk)hedging model based on linear programming and then applies the R-vine Pair Copula-GARCH model combined with Monte Carlo simulation to generate the joint distribution of returns and scenarios that fit the simulated distribution,which is the inputs to the minimum CVaR model to obtain the optimal hedging ratio.Empirical researches based on CSI 300 stock index futures and five stocks have shown that portfolios hedged by using the proposed model in this paper achieve better performance in both return and risk control when compared with the improved hedging model under normal distribution assumption.
At present,Chinese security market is not mature and risk hedging tools are limited.Therefore,the use of one futures hedging on multiple assets is an important strategy in portfolio risk management.This paper first constructs a minimum CVaR(Conditional Value at Risk)hedging model based on linear programming and then applies the R-vine Pair Copula-GARCH model combined with Monte Carlo simulation to generate the joint distribution of returns and scenarios that fit the simulated distribution,which is the inputs to the minimum CVaR model to obtain the optimal hedging ratio.Empirical researches based on CSI 300 stock index futures and five stocks have shown that portfolios hedged by using the proposed model in this paper achieve better performance in both return and risk control when compared with the improved hedging model under normal distribution assumption.
引文
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[4]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(1):27-33Chi G T,Zhao G J,Yang Z Y.Futures optimal hedge ratio model based on CVaR and its application[J].Journal of Systems&Management,2009,18(1):27-33
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[6]Cao Z G,Harris D F R,Shen J.Hedging and value at risk:a semi-parametric approach[J].Journal of Futures Markets,2010,30(8):780-794
[7]费广平,孙燕红.最小CVaR股指期货套期保值比率的实证研究[J].统计与决策,2013,(08):156-159Fei G P,Sun Y H.An empirical study on hedge ratio of stock index futures based on minimum CVaR[J].Statistics&Decision,2013,(08):156-159
[8]吴文娣,程希骏,刘峰.基于k-means聚类情景生成和广义熵约束的CVaR投资组合模型研究[J].中国科学院大学学报,2016,33(1):31-36Wu W D,Cheng X J,Liu F.CVaR portfolio model based on k-means clustering with the constraint of generalized entropy[J].Journal of University of Chinese Academy of Sciences,2016,33(1):31-36
[9]Krokhmal P,Palmquist J,Uryasev S.Portfolio optimization with conditional value-at-risk objective and constraints[J].The Journal of Risk,2002,4(2):124-129
[10]Nelsen R B.An Introduction to Copulas[M].New York:Springer,1999:21-23
[11]Bedford T,Cooke R M.Vine-a new graphical model for dependent random variables[J].The Annals of Statistics,2002,30(4):1031-1068
[12]Diffmann J,Brechmann E C,Czado C,et al.Selecting and estimating regular vine copulae and application to financial returns[J].Computational Statistics&Data Analysis,2013,59(2):52-69
[13]Aas K,Czado C,Frigessi A,et al.Pair-copula construction of multiple dependence[J].Insurance:Mathematics and Economics,2009,44(2):182-198
[14]胡根华,吴恒煜,邱甲贤.碳排放权市场结构相依特征研究:规则藤方法[J].中国人口·资源与环境,2015,(5):44-52Hu G H,Wu H Y,Qiu J X.Dependence structure of carbon emission markets:regular vine approach[J].China Population,Resources and Environment,2015,(5):44-52
[15]Darling D A.The Kolmogorov-Smirnov,Cramer-von mises tests[J].Annals of Mathematical Statistics,1957,28(4):823-838
[16]Efron B.Bootstrap methods:another look at the jackknife[J].The Annals of Statistics,1979,7(1):1-26
[2]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):1-10Wang Y G,Chi G T,Yang W W.Minimum variance hedge ratio based on Copula[J].System EngineeringTheory&Practice,2009,29(8):1-10
[3]马超群,王宝兵.基于Copula-GARCH模型的外汇期货最优套期保值比率研究[J].统计与决策,2011,(12):124-128Ma C Q,Wang B B.A study on optimal hedging ratio of foreign exchange futures based on Copula-GARCHmodel[J].Statistics&Decision,2011,(12):124-128
[4]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(1):27-33Chi G T,Zhao G J,Yang Z Y.Futures optimal hedge ratio model based on CVaR and its application[J].Journal of Systems&Management,2009,18(1):27-33
[5]Harris D F R,Shen J.Hedging and value at risk[J].Journal of Futures Markets,2006,26(4):369-390
[6]Cao Z G,Harris D F R,Shen J.Hedging and value at risk:a semi-parametric approach[J].Journal of Futures Markets,2010,30(8):780-794
[7]费广平,孙燕红.最小CVaR股指期货套期保值比率的实证研究[J].统计与决策,2013,(08):156-159Fei G P,Sun Y H.An empirical study on hedge ratio of stock index futures based on minimum CVaR[J].Statistics&Decision,2013,(08):156-159
[8]吴文娣,程希骏,刘峰.基于k-means聚类情景生成和广义熵约束的CVaR投资组合模型研究[J].中国科学院大学学报,2016,33(1):31-36Wu W D,Cheng X J,Liu F.CVaR portfolio model based on k-means clustering with the constraint of generalized entropy[J].Journal of University of Chinese Academy of Sciences,2016,33(1):31-36
[9]Krokhmal P,Palmquist J,Uryasev S.Portfolio optimization with conditional value-at-risk objective and constraints[J].The Journal of Risk,2002,4(2):124-129
[10]Nelsen R B.An Introduction to Copulas[M].New York:Springer,1999:21-23
[11]Bedford T,Cooke R M.Vine-a new graphical model for dependent random variables[J].The Annals of Statistics,2002,30(4):1031-1068
[12]Diffmann J,Brechmann E C,Czado C,et al.Selecting and estimating regular vine copulae and application to financial returns[J].Computational Statistics&Data Analysis,2013,59(2):52-69
[13]Aas K,Czado C,Frigessi A,et al.Pair-copula construction of multiple dependence[J].Insurance:Mathematics and Economics,2009,44(2):182-198
[14]胡根华,吴恒煜,邱甲贤.碳排放权市场结构相依特征研究:规则藤方法[J].中国人口·资源与环境,2015,(5):44-52Hu G H,Wu H Y,Qiu J X.Dependence structure of carbon emission markets:regular vine approach[J].China Population,Resources and Environment,2015,(5):44-52
[15]Darling D A.The Kolmogorov-Smirnov,Cramer-von mises tests[J].Annals of Mathematical Statistics,1957,28(4):823-838
[16]Efron B.Bootstrap methods:another look at the jackknife[J].The Annals of Statistics,1979,7(1):1-26