基于Copula函数-Asymmetric Laplace分布的金融市场风险度量与套期保值研究
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摘要
随着金融全球一体化的发展，金融市场的复杂程度日益提高，防范金融风险已成为全社会的共识。加强金融系统风险防范和管理能力，提高市场转移及消化吸收风险的能力，将是我国金融市场健康成长和发展的重要保障。金融秩序和金融运行环境的不断改变，金融风险的产生、传播、控制与管理等都日趋复杂，对金融市场风险的度量与管理的研究也更加重要和复杂。金融市场风险是最常见也是我国金融机构面临的主要风险，但是对其的研究，一些传统的基于正态、线性或波动性对称等模型的研究已不再适用，很难充分地捕获市场风险信息。这就需要不断探索研究，给出更多适应现阶段风险管理要求的理论模型研究及实证研究。
本文在分析现代金融风险管理理论的基础上，总结了市场风险度量及期货套期保值等方面的研究，指出了现有研究的不足，针对金融市场风险的复杂性，建立了基于非正态分布方法及非线性相关性模型的风险度量模型和套期保值策略模型，对金融市场风险的度量与套期保值进行了研究。主要从以下四个方面展开了主体部分的研究：
（1）本文建立了基于Asymmetric Laplace（AL）分布的市场风险VaR与CVaR的度量模型。构建了市场风险VaR和CVaR度量的AL参数法和AL-MC法，并进行了比较研究。选取上证指数、日经225指数及S&P500指数为研究对象，结合各股市的风险特征，给出了VaR和CVaR度量及其返回检验和准确性评价。结果表明，基于AL分布的风险度量模型能更好刻画市场风险特征，能很好地度量市场风险。
（2）本文建立了动态风险VaR和CVaR度量的ARMA-GJR-AL模型。从相关性、波动性及残差分布特征三方面考虑，研究了基于ARMA-GJR-AL模型的动态风险VaR和CVaR的度量。通过实证研究，给出了上海股市与纽约股市的市场风险预测及准确性检验，研究了模型的有效性。结果表明，基于AL分布的动态风险度量模型更具合理性和适用性，能有效地度量风险。
（3）本文运用Copula函数技术来描述资产间的相关性结构，建立了金融资产组合的市场风险VaR和CVaR的度量和分配的Copula-AL模型，并对常用的基于多元统计分布的度量方法及基于OLS模型的风险分配方法进行了比较研究。选取上证指数和深圳成指的组合为例，计算了组合风险及其分配。结果表明，基于t-Copula-AL模型的VaR、CVaR法计算简单准确，且能方便地进行风险分配。
（4）本文采用参数和非参数分布法来刻画边际分布特征，结合Copula函数技术来描述期现市场间的相关性，以CVaR最小化为目标函数，建立了基于静态和动态Copula-CVaR的最优套保比率度量模型，并对各模型进行了比较研究。以沪深300指数现货和期货为研究对象，建立了静态和动态Copula-CVaR模型及OLS模型，在给定套保期限内，分析了各模型的套保费用，并给出了修正成本套保效率的比较分析。实证结果表明，考虑套保费用时，应选择简单易行的静态套保策略，即使市场条件相同，也应据自身的费用情况选择最优套保策略。
本文的研究促进了金融市场风险度量、期货套期保值、AL分布及Copula函数理论等方面的研究，具有很好的理论意义，同时对投资决策、经济资本管理及风险管理等实践活动也起到很好的帮助和借鉴作用。
With the development of financial globalization and the increasing complexity offinancial markets, and to prevent financial risk had become the consensus of the wholesociety. To strengthen the risk prevention and management capabilities of the financialsystem and to improve the ability of market transfer, digestion and absorption of risk, wereimportant guarantee for the healthy growth and development of our financial market. Withthe continuing changing of financial operating mechanism and environment, the financialrisk's generation, dissemination, control and management have become increasinglycomplex. And the study on financial market risk measurement and management hasbecome more important and complex. Market risk was the most common and the mainrisk faced by financial institutions. However, traditional research methods based on themodel of normality, linearity or symmetry of volatility were no longer applicable. Becausethese were difficult to fully capture the market risk information, which needed moreconstantly researches, and given more theoretical and empirical researches to adaptmorden risk management requirement.
This paper mainly studied the financial market risk measurement and management.Based on analysing the modern theory of financial risk management, it summarized theresearch of market risk measurement and futures hedging, and pointed out the lack ofexisting research. For the complexity of financial market risk, it established riskmeasurement models and hedging strategies models which were based on the non-normaldistribution method and non-linear correlation model, then studied the method of financialmarket risk measurement and hedging. The main parts of the research carried out mainlyfrom the following four aspects:
(1) In this paper, Asymmetric Laplace distribution was used to fit the data of assetreturns and described the features of market risk. Then, it provided AL parametric method and AL-MC method of measuring VaR and CVaR. Selected the Shanghai Composite Index,Nikkei225Stock Index and S&P500Index, it given the calculation of VaR and CVaRconsidering the actual stocks risk features, and also given the back testing and accuracyassessment of risk. The results showed that the risk measurement model based onAsymmetric Laplace distribution was reasonable and applicable, and can effectivelyestimated the market risk.
(2) In this paper, the ARMA-GJR-AL model was established to describe the featuresof market risk considering the correlation, volatility and innovation distribution. Based onthe financial risk measurement toll VaR/CVaR and the theories of mathematical statistics,it studied the dynamic VaR and CVaR of market risk under Asymmetric Laplacedistribution and given the tests of accurate measurement. Selected the ShanghaiComposite Index and New York Composite Index from the year of2005to2009asobserved samples, it established ARMA (1,1)-GJR (1,1)-AL and ARMA (1,1)-GJR(1,1)-N model to capture the markets' risk characteristics, got the model parametersestimation by using Matlab software program and given the prediction and test of dailyVaR and CVaR for the year of2010. The results showed that the dynamic riskmeasurement model based on AL distribution was more reasonable and applicable, andcan effectively predicted risk. Finally, it further analyzed the stock market risk.
(3) This paper used AL distribution to describe the marginal distributions’ features,combined with Copula function technique to describe the relationship between assets andstudied the VaR and CVaR of market portfolio and their allocation. At the same time, itgiven the comparative study on commonly used measurement method based onmultivariate statistical distribution and risk allocation method based on OLS model. Theauthor calculated the portfolio risk and their allocation with portfolio of ShanghaiComposite Index and Shenzhen Component Index. The results showed that the methods ofVaR and CVaR which based on t-Copula-AL model are more simple and precise, and itcould easily calculate risk allocation.
(4) Used parametric and non-parametric distribution to describe the marginaldistributions’ features and combined Copula function technique to describe the correlationbetween them, this paper took CVaR risk minimization as the objective function andestablished an optimal hedging ratio model based on constant and dynamic Copula-CVaR.Selected the recent spot and futures of IS300as samples，it established constant anddynamic Copula-CVaR and OLS model, then analyzed the hedging cost and givencomparative analysis of the amendment-cost-hedging-efficiency for each model in acertain hedging term. When considering the hedging cost, the results showed that investorsshould choose a simple static hedging strategy and should select the optimal hedgingstrategy based on their actual cost conditions even under the same market conditions.
This paper had great theoretical significance and practical value. It promoted theresearch of financial market risk measurement, futures hedging, AL distribution andCopula function theory and so on. At the same time, it would play great help and referencein practice activities, such as the investment decision-making, economic capitalmanagement and risk management and so on.
本文在分析现代金融风险管理理论的基础上，总结了市场风险度量及期货套期保值等方面的研究，指出了现有研究的不足，针对金融市场风险的复杂性，建立了基于非正态分布方法及非线性相关性模型的风险度量模型和套期保值策略模型，对金融市场风险的度量与套期保值进行了研究。主要从以下四个方面展开了主体部分的研究：
（1）本文建立了基于Asymmetric Laplace（AL）分布的市场风险VaR与CVaR的度量模型。构建了市场风险VaR和CVaR度量的AL参数法和AL-MC法，并进行了比较研究。选取上证指数、日经225指数及S&P500指数为研究对象，结合各股市的风险特征，给出了VaR和CVaR度量及其返回检验和准确性评价。结果表明，基于AL分布的风险度量模型能更好刻画市场风险特征，能很好地度量市场风险。
（2）本文建立了动态风险VaR和CVaR度量的ARMA-GJR-AL模型。从相关性、波动性及残差分布特征三方面考虑，研究了基于ARMA-GJR-AL模型的动态风险VaR和CVaR的度量。通过实证研究，给出了上海股市与纽约股市的市场风险预测及准确性检验，研究了模型的有效性。结果表明，基于AL分布的动态风险度量模型更具合理性和适用性，能有效地度量风险。
（3）本文运用Copula函数技术来描述资产间的相关性结构，建立了金融资产组合的市场风险VaR和CVaR的度量和分配的Copula-AL模型，并对常用的基于多元统计分布的度量方法及基于OLS模型的风险分配方法进行了比较研究。选取上证指数和深圳成指的组合为例，计算了组合风险及其分配。结果表明，基于t-Copula-AL模型的VaR、CVaR法计算简单准确，且能方便地进行风险分配。
（4）本文采用参数和非参数分布法来刻画边际分布特征，结合Copula函数技术来描述期现市场间的相关性，以CVaR最小化为目标函数，建立了基于静态和动态Copula-CVaR的最优套保比率度量模型，并对各模型进行了比较研究。以沪深300指数现货和期货为研究对象，建立了静态和动态Copula-CVaR模型及OLS模型，在给定套保期限内，分析了各模型的套保费用，并给出了修正成本套保效率的比较分析。实证结果表明，考虑套保费用时，应选择简单易行的静态套保策略，即使市场条件相同，也应据自身的费用情况选择最优套保策略。
本文的研究促进了金融市场风险度量、期货套期保值、AL分布及Copula函数理论等方面的研究，具有很好的理论意义，同时对投资决策、经济资本管理及风险管理等实践活动也起到很好的帮助和借鉴作用。
With the development of financial globalization and the increasing complexity offinancial markets, and to prevent financial risk had become the consensus of the wholesociety. To strengthen the risk prevention and management capabilities of the financialsystem and to improve the ability of market transfer, digestion and absorption of risk, wereimportant guarantee for the healthy growth and development of our financial market. Withthe continuing changing of financial operating mechanism and environment, the financialrisk's generation, dissemination, control and management have become increasinglycomplex. And the study on financial market risk measurement and management hasbecome more important and complex. Market risk was the most common and the mainrisk faced by financial institutions. However, traditional research methods based on themodel of normality, linearity or symmetry of volatility were no longer applicable. Becausethese were difficult to fully capture the market risk information, which needed moreconstantly researches, and given more theoretical and empirical researches to adaptmorden risk management requirement.
This paper mainly studied the financial market risk measurement and management.Based on analysing the modern theory of financial risk management, it summarized theresearch of market risk measurement and futures hedging, and pointed out the lack ofexisting research. For the complexity of financial market risk, it established riskmeasurement models and hedging strategies models which were based on the non-normaldistribution method and non-linear correlation model, then studied the method of financialmarket risk measurement and hedging. The main parts of the research carried out mainlyfrom the following four aspects:
(1) In this paper, Asymmetric Laplace distribution was used to fit the data of assetreturns and described the features of market risk. Then, it provided AL parametric method and AL-MC method of measuring VaR and CVaR. Selected the Shanghai Composite Index,Nikkei225Stock Index and S&P500Index, it given the calculation of VaR and CVaRconsidering the actual stocks risk features, and also given the back testing and accuracyassessment of risk. The results showed that the risk measurement model based onAsymmetric Laplace distribution was reasonable and applicable, and can effectivelyestimated the market risk.
(2) In this paper, the ARMA-GJR-AL model was established to describe the featuresof market risk considering the correlation, volatility and innovation distribution. Based onthe financial risk measurement toll VaR/CVaR and the theories of mathematical statistics,it studied the dynamic VaR and CVaR of market risk under Asymmetric Laplacedistribution and given the tests of accurate measurement. Selected the ShanghaiComposite Index and New York Composite Index from the year of2005to2009asobserved samples, it established ARMA (1,1)-GJR (1,1)-AL and ARMA (1,1)-GJR(1,1)-N model to capture the markets' risk characteristics, got the model parametersestimation by using Matlab software program and given the prediction and test of dailyVaR and CVaR for the year of2010. The results showed that the dynamic riskmeasurement model based on AL distribution was more reasonable and applicable, andcan effectively predicted risk. Finally, it further analyzed the stock market risk.
(3) This paper used AL distribution to describe the marginal distributions’ features,combined with Copula function technique to describe the relationship between assets andstudied the VaR and CVaR of market portfolio and their allocation. At the same time, itgiven the comparative study on commonly used measurement method based onmultivariate statistical distribution and risk allocation method based on OLS model. Theauthor calculated the portfolio risk and their allocation with portfolio of ShanghaiComposite Index and Shenzhen Component Index. The results showed that the methods ofVaR and CVaR which based on t-Copula-AL model are more simple and precise, and itcould easily calculate risk allocation.
(4) Used parametric and non-parametric distribution to describe the marginaldistributions’ features and combined Copula function technique to describe the correlationbetween them, this paper took CVaR risk minimization as the objective function andestablished an optimal hedging ratio model based on constant and dynamic Copula-CVaR.Selected the recent spot and futures of IS300as samples，it established constant anddynamic Copula-CVaR and OLS model, then analyzed the hedging cost and givencomparative analysis of the amendment-cost-hedging-efficiency for each model in acertain hedging term. When considering the hedging cost, the results showed that investorsshould choose a simple static hedging strategy and should select the optimal hedgingstrategy based on their actual cost conditions even under the same market conditions.
This paper had great theoretical significance and practical value. It promoted theresearch of financial market risk measurement, futures hedging, AL distribution andCopula function theory and so on. At the same time, it would play great help and referencein practice activities, such as the investment decision-making, economic capitalmanagement and risk management and so on.
引文
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