金融市场风险的尾部估计和极值度量
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摘要
经典的风险理论通常是根据收益率序列的样本数据估计资产组合损失分布函数,然后得出一定置信水平下的可能损失。但近年来,人们越来越发现根据总体损失数据得到的损失分布模型在高频率低损失的中心区域拟合效果比较好,但在低频率大损失的尾部拟合效果往往表现欠佳。而恰恰是位于损失分布尾部的极端风险事件,对相当数量的机构和个人投资者而言,由于缺乏有效预判和充足的风险准备,后果经常是灾难性的。因此,尾部风险的度量已成为金融风险领域研究的重要内容。本文在金融危机的影响尚未消散,各国及全球金融市场仍处于恢复、调整期,甚至有可能面临二次危机的严峻形势下,把目光汇聚于极端情况下金融市场风险的度量与管理,通过理论探讨和实证分析研究行之有效的方法,为识别和管理风险创造良好条件,无疑具有很强的现实意义。
极值模型和压力测试是重要的极端风险事件分析工具,近年来,人们将其引入VaR模型,用以进行金融市场尾部风险测度,取得了比较好的效果。但是,极值模型和压力测试在应用过程中仍然面临一些问题,理论研究者和风险管理实践者仍在不断研究其改进方法。本文正是从这些问题中选取了部分对模型有效性有重要影响的问题开展研究和讨论,包括阈值如何选取、样本数据的尾部相关性和极值指数的估计、满足一致性要求的压力测试风险度量模型等问题,得到了一些令人满意的结果。同时,在研究资产组合个体风险测度模型的基础上,本文还重点讨论了极端情况下的系统性风险管理,并从宏观审慎性监管的视角,提出了完善我国金融监管体制架构的建议。
本文的主要研究工作及成果可归纳如下:第一章介绍了论文研究的理论与现实意义,以文献综述的形式介绍了国内外关于极值理论、压力测试等方面的研究成果,概述了论文的研究内容、研究方法和主要创新。第二章主要是介绍极值分布的基本理论,重点介绍了极值模型的研究对象和极值型定理,广义极值分布和广义Pareto模型形式及原理,以及GEV模型中形状参数的估计问题。第三章基于变点理论探讨了GPD模型中的阈值选取问题,所得模型克服了传统阈值选取方法存在的局限性。第四章重点研究了样本数据的尾部相关性和极值指数的估计问题,对上证综指(SHCI)和标准普尔500指数(S&P500)收益率数据进行了尾指数的实际计算与比较。之后,依次回顾了分块估计方法、倒数串估计法、串估计法以及Ferro-Segers方法计算极值指数的过程及原理,并分别计算了SHCI和S&P500收益率数据用上述方法得到的极值指数。最后,提出了一种新的计算极值指数的计量方法,并证明了其有效性。第五章讨论了一致性框架下的压力测试风险度量模型,将极值分布作为压力测试情景的具体分布形式,在SHCI收益率样本数据中引入压力测试情景(模拟损失),应用历史模拟法、EGARCH(1,1)-M模型进行了实证检验。第六章从分析金融危机爆发以来各主要经济体采取的应对措施入手,讨论了极端情况下的系统性风险管理问题,分析了宏观审慎监管的原则、框架以及与微观审慎监管的区别与联系,提出了相关建议。
本文采取理论研究为主,实证分析为辅的研究方法,以定量研究为主要手段,以定性分析为补充。创新之处体现在理论和应用两个方面:
理论创新包括,给出了基于变点理论的GPD模型阈值估计和样本区间分割方法,从理论和实证方面证明了二阶差分变点阈值选取方法的有效性;提出了极值指数的计量估计方法,讨论了此种方法的估计原理,并将实证分析结果与原有的极值指数估计方法进行了比较;将GPD模型作为压力测试情景的具体分布形式,构建了压力测试的一致性框架;从分析金融危机爆发以来各主要经济体采取的应对措施入手,讨论了极端情况下的系统性风险管理,并从宏观审慎监管视角,提出了完善我国金融监管体制架构的建议。
应用创新包括,将从理论上探讨出的二阶差分变点阈值选取方法应用于VaR的估计中,对目前文献中的相关方法只能粗略估计阈值的状况进行了改进,并实际估计了上证综合指数收益率在不同置信水平下的VaR值;分析比较了SHCI和S&p500收益率数据的尾指数,得出了上证综指收益率服从的边际分布右尾较S&P500厚,但无法识别SHCI与S&P500收益率服从的边际分布左尾厚度差异性的结论;应用分块估计方法、倒数串估计法、串估计法以及Ferro-Segers方法计算了上证综合指数和S&P500收益率数据的极值指数,并将计算结果应用于VaR的实际计算,得到了不同置信水平下的VaR值;应用极值指数的计量估计方法实际计算了上证综合指数和S&P500收益率数据的极值指数,得到了与原有估计方法较为相近的结果;对引入压力测试情景的样本数据应用EGARCH(1,1)—M模型估计了动态VaR和ES值,结果表明压力测试情景对估计结果的影响较为显著,在95%置信水平下,将EGARCH(1,1)—M模型估计的动态VaR进行了Kupiec检验,证明了其能够较为准确地测度SHCI收益率的动态风险。
Classical Theories for risk measurement estimate loss CDF of asset portfolios by sample data of profit-loss series, then get the probable loss in a given confidential level. But in recent years, people found that CDF on the basis of loss data worked better in central area equivalent of high frequency and low loss data, but performed poorly in tails consisting of low frequency and high loss data. In general, just the extreme events in distribution’s tails are able to cause catastrophic effect for quite a number of institution and individual investors because lacking effective prediction and adequate reserve fund of risks. So tail risk measurement has already been the crucial topic in the field of financial risks. This paper focuses on financial risks measurement and management on extreme values, and can provide some effective methods to theoretical investigation and empirical analysis. It is undoubtedly meaningful to risk identification and management when the influences of financial crisis still exist, financial market is also in the regulatory period, and the crisis in second round might be truth.
Extreme value theory and stress testing are important analysis tools to extreme events, and had been involved in VaR model in recent years. People got some satisfactory results when used these two tools to tail risk measurement. But there are still some problems in applications of extreme model and stress testing. Researchers and practitioners of risk management are making great efforts to improve them. This paper discussed some problems which have major sense to model effectiveness. Such problems involved threshold selection, tail dependence of sample data and estimation of extremal index, risk measurement of coherent stress testing, etc. We got some satisfactory results. Meanwhile, on the basis of researches on risk measurement for asset portfolio, we also discussed topics of systematic risk management, from the standpoint of macro-prudential regulations, presented some suggestions.
The main contents and conclusions are summarized as follows: the first chapter introduces theoretical and practical sense, present some research achievements about extreme value theory and stress testing, summarize contents, methods and innovations of this paper. The second chapter introduces foundations of extreme value theory such as research objects and Fisher-Tippett theorem, GEV and GPD model, estimation on shape parameter in GEV. The third chapter discusses threshold selection basing on change point theory. The forth chapter studies estimations on tail dependence and extremal index, calculates tail index of SHCI and S&P500, compares the results. Then we review blocks method, reciprocal cluster method, run method and Ferro-Segers method on extremal index calculations, and get results in all methods. Finally we present a new econometric way to get extremal index, and prove its effectiveness. The fifth chapter discusses risk measurement in a coherent stress testing framework, makes GPD be the specific distribution of stress testing, involved stress scenario in sample data, uses historical simulation, EGARCH(1,1)-M model in empirical test. The sixth chapter starts on reactions of major economic entities on the financial crisis, discusses systematic risk management in extreme conditions, analyzed principle and framework of macro-prudential regulation, and its difference and connection to micro-prudential regulation. We also give some advices.
This paper is mainly for theory and supports by empirical analysis. Its key tools are quantitative researches, supplement by qualitative analyses. The primary innovations include as theoretical and practical sides.
Theoretical innovations are as follows: presents a new method for threshold selection basing on change point theory; presents a econometric way to calculate extremal index, discusses principle of this method; introduce GPD as stress scenario distribution, constructs a coherent stress testing framework; discusses systematical risk management in extreme conditions, gives some advices about macro-prudential regulations.
Empirical innovations are as follows: uses second-order difference method of threshold selection in VaR model, improves existing methods, and calculate SHCI’s VaR in different confidence levels; compares the tail indexes between SHCI and S&P500; calculates the extremal indexes of SHCI and S&P500 by blocks method, reciprocal cluster method, run method and Ferro-Segers method, uses the results to VaR calculation; get extremal indexes of SHCI and S&P500 in econometric way, and this result is close to the original ones; apply EGARCH(1,1)-M model to estimate dynamic VaR and ES, the consequence shows that stress scenario has prominent influence to VaR estimation, in 95% level, dynamic VaR estimated by EGARCH(1,1)-M model can meet Kupiec test.
极值模型和压力测试是重要的极端风险事件分析工具,近年来,人们将其引入VaR模型,用以进行金融市场尾部风险测度,取得了比较好的效果。但是,极值模型和压力测试在应用过程中仍然面临一些问题,理论研究者和风险管理实践者仍在不断研究其改进方法。本文正是从这些问题中选取了部分对模型有效性有重要影响的问题开展研究和讨论,包括阈值如何选取、样本数据的尾部相关性和极值指数的估计、满足一致性要求的压力测试风险度量模型等问题,得到了一些令人满意的结果。同时,在研究资产组合个体风险测度模型的基础上,本文还重点讨论了极端情况下的系统性风险管理,并从宏观审慎性监管的视角,提出了完善我国金融监管体制架构的建议。
本文的主要研究工作及成果可归纳如下:第一章介绍了论文研究的理论与现实意义,以文献综述的形式介绍了国内外关于极值理论、压力测试等方面的研究成果,概述了论文的研究内容、研究方法和主要创新。第二章主要是介绍极值分布的基本理论,重点介绍了极值模型的研究对象和极值型定理,广义极值分布和广义Pareto模型形式及原理,以及GEV模型中形状参数的估计问题。第三章基于变点理论探讨了GPD模型中的阈值选取问题,所得模型克服了传统阈值选取方法存在的局限性。第四章重点研究了样本数据的尾部相关性和极值指数的估计问题,对上证综指(SHCI)和标准普尔500指数(S&P500)收益率数据进行了尾指数的实际计算与比较。之后,依次回顾了分块估计方法、倒数串估计法、串估计法以及Ferro-Segers方法计算极值指数的过程及原理,并分别计算了SHCI和S&P500收益率数据用上述方法得到的极值指数。最后,提出了一种新的计算极值指数的计量方法,并证明了其有效性。第五章讨论了一致性框架下的压力测试风险度量模型,将极值分布作为压力测试情景的具体分布形式,在SHCI收益率样本数据中引入压力测试情景(模拟损失),应用历史模拟法、EGARCH(1,1)-M模型进行了实证检验。第六章从分析金融危机爆发以来各主要经济体采取的应对措施入手,讨论了极端情况下的系统性风险管理问题,分析了宏观审慎监管的原则、框架以及与微观审慎监管的区别与联系,提出了相关建议。
本文采取理论研究为主,实证分析为辅的研究方法,以定量研究为主要手段,以定性分析为补充。创新之处体现在理论和应用两个方面:
理论创新包括,给出了基于变点理论的GPD模型阈值估计和样本区间分割方法,从理论和实证方面证明了二阶差分变点阈值选取方法的有效性;提出了极值指数的计量估计方法,讨论了此种方法的估计原理,并将实证分析结果与原有的极值指数估计方法进行了比较;将GPD模型作为压力测试情景的具体分布形式,构建了压力测试的一致性框架;从分析金融危机爆发以来各主要经济体采取的应对措施入手,讨论了极端情况下的系统性风险管理,并从宏观审慎监管视角,提出了完善我国金融监管体制架构的建议。
应用创新包括,将从理论上探讨出的二阶差分变点阈值选取方法应用于VaR的估计中,对目前文献中的相关方法只能粗略估计阈值的状况进行了改进,并实际估计了上证综合指数收益率在不同置信水平下的VaR值;分析比较了SHCI和S&p500收益率数据的尾指数,得出了上证综指收益率服从的边际分布右尾较S&P500厚,但无法识别SHCI与S&P500收益率服从的边际分布左尾厚度差异性的结论;应用分块估计方法、倒数串估计法、串估计法以及Ferro-Segers方法计算了上证综合指数和S&P500收益率数据的极值指数,并将计算结果应用于VaR的实际计算,得到了不同置信水平下的VaR值;应用极值指数的计量估计方法实际计算了上证综合指数和S&P500收益率数据的极值指数,得到了与原有估计方法较为相近的结果;对引入压力测试情景的样本数据应用EGARCH(1,1)—M模型估计了动态VaR和ES值,结果表明压力测试情景对估计结果的影响较为显著,在95%置信水平下,将EGARCH(1,1)—M模型估计的动态VaR进行了Kupiec检验,证明了其能够较为准确地测度SHCI收益率的动态风险。
Classical Theories for risk measurement estimate loss CDF of asset portfolios by sample data of profit-loss series, then get the probable loss in a given confidential level. But in recent years, people found that CDF on the basis of loss data worked better in central area equivalent of high frequency and low loss data, but performed poorly in tails consisting of low frequency and high loss data. In general, just the extreme events in distribution’s tails are able to cause catastrophic effect for quite a number of institution and individual investors because lacking effective prediction and adequate reserve fund of risks. So tail risk measurement has already been the crucial topic in the field of financial risks. This paper focuses on financial risks measurement and management on extreme values, and can provide some effective methods to theoretical investigation and empirical analysis. It is undoubtedly meaningful to risk identification and management when the influences of financial crisis still exist, financial market is also in the regulatory period, and the crisis in second round might be truth.
Extreme value theory and stress testing are important analysis tools to extreme events, and had been involved in VaR model in recent years. People got some satisfactory results when used these two tools to tail risk measurement. But there are still some problems in applications of extreme model and stress testing. Researchers and practitioners of risk management are making great efforts to improve them. This paper discussed some problems which have major sense to model effectiveness. Such problems involved threshold selection, tail dependence of sample data and estimation of extremal index, risk measurement of coherent stress testing, etc. We got some satisfactory results. Meanwhile, on the basis of researches on risk measurement for asset portfolio, we also discussed topics of systematic risk management, from the standpoint of macro-prudential regulations, presented some suggestions.
The main contents and conclusions are summarized as follows: the first chapter introduces theoretical and practical sense, present some research achievements about extreme value theory and stress testing, summarize contents, methods and innovations of this paper. The second chapter introduces foundations of extreme value theory such as research objects and Fisher-Tippett theorem, GEV and GPD model, estimation on shape parameter in GEV. The third chapter discusses threshold selection basing on change point theory. The forth chapter studies estimations on tail dependence and extremal index, calculates tail index of SHCI and S&P500, compares the results. Then we review blocks method, reciprocal cluster method, run method and Ferro-Segers method on extremal index calculations, and get results in all methods. Finally we present a new econometric way to get extremal index, and prove its effectiveness. The fifth chapter discusses risk measurement in a coherent stress testing framework, makes GPD be the specific distribution of stress testing, involved stress scenario in sample data, uses historical simulation, EGARCH(1,1)-M model in empirical test. The sixth chapter starts on reactions of major economic entities on the financial crisis, discusses systematic risk management in extreme conditions, analyzed principle and framework of macro-prudential regulation, and its difference and connection to micro-prudential regulation. We also give some advices.
This paper is mainly for theory and supports by empirical analysis. Its key tools are quantitative researches, supplement by qualitative analyses. The primary innovations include as theoretical and practical sides.
Theoretical innovations are as follows: presents a new method for threshold selection basing on change point theory; presents a econometric way to calculate extremal index, discusses principle of this method; introduce GPD as stress scenario distribution, constructs a coherent stress testing framework; discusses systematical risk management in extreme conditions, gives some advices about macro-prudential regulations.
Empirical innovations are as follows: uses second-order difference method of threshold selection in VaR model, improves existing methods, and calculate SHCI’s VaR in different confidence levels; compares the tail indexes between SHCI and S&P500; calculates the extremal indexes of SHCI and S&P500 by blocks method, reciprocal cluster method, run method and Ferro-Segers method, uses the results to VaR calculation; get extremal indexes of SHCI and S&P500 in econometric way, and this result is close to the original ones; apply EGARCH(1,1)-M model to estimate dynamic VaR and ES, the consequence shows that stress scenario has prominent influence to VaR estimation, in 95% level, dynamic VaR estimated by EGARCH(1,1)-M model can meet Kupiec test.
引文
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