极值理论在中国股市风险度量中的应用研究
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摘要
金融体系具有内在的脆弱性(Financial Fragility),近些年来,这种内在的脆弱性非但没有随着金融业的迅速发展而有所消弱,反而在一些新兴的、甚至是成熟的市场经济体中表现日益严重,导致了金融危机频繁爆发。而金融危机显著的系统性(Systematicness)则进一步引起了危机在区域性或世界性范围内的蔓延,加剧了金融危机影响的广度与深度,对经济体系造成了严重的打击。爆发于2007年并至今仍在肆虐世界经济的美国次级住房抵押贷款危机(Subprime Mortgage Crisis)就是一个典型的事例。
鉴于金融风险内源性及影响的系统性,对一个经济主体来说,如何抵御、防范及化解金融风险无疑具有非常重大的意义。而有效抵御、防范与化解金融风险的基础与核心正在于对金融风险的准确度量,这也一直是金融理论研究中的一个非常重要的课题。
目前,国际上度量风险的最主要工具是在险价值(Value at Risk,VaR),其实质上是通过对资产收益率分布的估计,刻画一定置信水平下资产在未来一段时期内所可能遭受到的最大可能损失。VaR以损益额衡量风险,通过置信水平概念将预期损失与该损失发生概率结合起来,并可直接测算出投资组合的风险值。然而与其它类型资产不同,实际中大多数金融资产收益率序列具有显著的厚尾特征。这意味着VaR在度量金融风险时,存在资产收益率正态性假设的瑕疵,即对极值事件(Rare Event)考虑不足,导致了极端风险(Extreme Risk)的低估。
极值事件发生的概率虽然很低,但其引发的极端风险却损害巨大,有时甚至是灾难性的灾难。故对金融风险管理者来说,极值事件尤为值得关注。J.B.Philippe(2000)也曾指出,金融领域中关心的就是这些极端风险,首先要控制的也是这些极端风险。近些年,国际金融业监管当局也一直在试图制定一些规则以限制金融机构暴露在这些极端风险面前。
极值理论(Extreme Value Theory,EVT)是研究随机过程的极值分布及其特征的模型技术,对随机过程中的厚尾现象具有突出的针对性,并可在总体分布未知情况下,依靠样本数据外推得到总体极值的变化性质,克服了传统统计方法不能超越样本数据进行分析的局限。将EVT应用到金融风险管理领域可以弥补VaR对极值事件关注的不足,有利于更精确地度量金融极端风险。
另外,我国正处在经济转型期,虽已初步建立起以国有商业银行为主体的商业性金融体系,但金融体制的市场改革依然远远滞后于其它经济部门,整体行业受政策影响较大,市场运行机制经常发生变化,金融体系风险非但没有降低,反而不断积聚,金融市场动荡加剧,作为市场经济晴雨表的沪深股票市场频频的巨幅涨跌即清楚地表示了金融体系的震荡状况。故对处于经济转型期中的我国金融业来说,利用EVT研究金融市场极端风险度量无疑更是具有针对性与非常重要的现实意义。
本文即基于EVT研究金融极端风险的度量问题,并在相关研究结论之上对我国沪深股票市场的极端风险进行实证分析。
本文主要研究内容有:极值渐近分布的类型及性质;基于广义极值分布(GEV)和广义Pareto分布(GPD)的BMM模型与POT模型,并将极值BMM与POT模型引入到尾部高分位数的估计中;金融时间序列相关性对极值模型的影响及其减消处置;极值模型的回测技术选择与验证标准。特别是,在BMM模型中充分地考虑了子区间极值一般极限分布与极值序列极限分布之间的关系,测度了受子区间长度影响的极值VaR;在POT模型中运用参数估计量稳定性法弥补了目前普遍采用的样本平均超出量函数e (u )法的不足,针对一些图解法无法适用的问题,实现了峰度法对阈值的定量选取,并对指数回归模型法、子样本自助法、序贯法等定量法进行了分析探讨。
本文以我国沪深股票市场为研究对象,考虑到沪深股市实行涨跌停板制度(Raising limit),分段选取沪深股市基准日至1996年12月26日、以及1996年12月26日至2008年3月12日之间的综合指数收益率为数据,测度并比较分析了涨跌停板制度前后沪深股市的极端风险。在实证中,尤其重点考察了涨跌停板制度对沪深股市收益率序列尾分布的影响,即涨跌停板制度对极值数据异质性的抑制作用,以及由此导致的极值模型的测度效果和极值风险有效指标。
本文基于EVT研究金融极端风险的度量,学术与实践意义在于为金融市场投资者、市场监管机构防范与抵御金融极端风险提供理论与方法支持。
In recent years, financial fragility inherently has become increasingly more serious in some emerging, or even mature market economies, instead of being weakened with the rapid development of the financial sector, which has resulted in the more frequent crisis. Financial risks are also systematic, likely to bring national, regional or worldwide economic system disorders, recession or even collapse such as the Subprime Mortgage Crisis which broke out in U.S. in 2007 and have been raging economic system worldwidely.
In view of the endogenous and systematic of financial risks, undoubtedly, to resist and prevent financial risks is of great significance to the economy of one country. The foundation and core of effective resistance and prevention is the accurate measurement of financial risks, which has become a very important issue in the research of financial theory. At present, as internationally the most important tool of measuring risks, VaR describes the most possible loss in the future given a certain degree of confidence. VaR measures risk through measuring profit and loss by introducing the concept of confidence level, it combines expected loss and its probability, and directly measures the value of portfolio's risk. However, different from other types of assets, the sequence of returns on most financial assets practically bares significant characteristics of the fat-tail, which means that there exists a flawed assumption of the normal distribution of assets’returns, and that the tail extreme risk is underestimated because of the ignorance of rare events.
Though the probability of the occurrence of extreme risk is very low, the occurrence will definitely cause great damage, and the consequences are often disastrous. Therefore, in order to manage financial risks, events of extreme value are particularly worthy of our attention. J.B.Philippe (2000) also pointed out that in financial sector what should be concerned is nothing but extreme risks, and what should firstly be controlled are also extreme risks. In recent years, the international regulators of financial industry have kept trying to develop a number of provisions to restrict banks to be exposed to these extreme risks.
Extreme Value Theory (Extreme Value Theory, EVT) is the modeling technique focusing on the distribution and characteristics of the extreme value of random processes, the most prominent feature of which is that the flat-tail in random processes could be better solved, and in the case of population distribution unknown, the changing nature of population’s extreme value could be deduced from sample data, which could overcome the limitations of traditional statistical methods which cannot make analysis beyond sample data. Applying EVT to financial risk management can make up for the lack of VaR methodology, therefore could estimate the financial extreme events caused by the extreme risk more accurately.
In addition, China is in the socio-economic transition period. Though the commercial financial system has been initially established with the subject of state-owned commercial banks, the reform of financial system market is still lagging far behind other sectors of the economy. The industry as a whole is more influenced by policies. The market operating mechanism frequently changes. Risks in financial system continue to accumulate instead of lowering. Financial market vibrates, such as the frequent great fluctuations recently. Thus, how to accurately measure the extreme risk of financial market based on EVT has become an urgent task for the financial sector experiencing the socio-economic transformation.
Focusing the measurement of financial risk of extreme, this study empirically investigated the extreme risks of Chinese stock market based the theoretical researches of extreme value and relevant conclusions.
This dissertation made an in-depth study on the type and nature of the asymptotic distribution of extreme value. It studied BMM and POT model based on GEV and GPD separately, and introduced the two models into the estimation of tail high quantile. It examined the impact of the correlation of financial time series on EVT model and its eliminating disposal. It also studied standards of selection and validation of Back Testing techniques of EVT model. Particularly, in the BMM model, it took into account the relationship between the distribution of the extreme value limit of subinterval and that of sequence, and measured the extreme value of VaR affected by the length of the subinterval. In POT model, it used the technique of parameter estimator stability, making up for the limits of the currently popularly-used Mean Excess Function e (u ), and the threshold quantitatively selected by Kurtosis Method has also been achieved, and solving the problem the illustration method couldn’t be applied to. It also discussed other quantitative methods, such as Exponential Regression Model Method, Subsample Bootstrap Method, Sequential Method and so on.
Taking into account the factor of raising limit in Chinese stock markets, we sub-selected data of composite indices of returns on days between benchmark day to December 26, 1996, and December 26, 1996 to March 12, 2008, measured and compared the extreme risk in Chinese stock markets before and after the raising limit. In the empirical part, we particularly investigated the impact of raising limit on the distribution of tail sequence of returns data from Chinese stock markets, that is, the inhibit effect of raising limit on the heterogeneity of data with extreme value, as well as the efficiency of results of EVT Model and the effective indicators of extreme risk.
Based on EVT, this dissertation focused on the measurement of extreme financial risks, the academic and practical significance of which is to provide both theoretical and methodological support for financial market investors and market regulators to guard against extreme financial risks.
鉴于金融风险内源性及影响的系统性,对一个经济主体来说,如何抵御、防范及化解金融风险无疑具有非常重大的意义。而有效抵御、防范与化解金融风险的基础与核心正在于对金融风险的准确度量,这也一直是金融理论研究中的一个非常重要的课题。
目前,国际上度量风险的最主要工具是在险价值(Value at Risk,VaR),其实质上是通过对资产收益率分布的估计,刻画一定置信水平下资产在未来一段时期内所可能遭受到的最大可能损失。VaR以损益额衡量风险,通过置信水平概念将预期损失与该损失发生概率结合起来,并可直接测算出投资组合的风险值。然而与其它类型资产不同,实际中大多数金融资产收益率序列具有显著的厚尾特征。这意味着VaR在度量金融风险时,存在资产收益率正态性假设的瑕疵,即对极值事件(Rare Event)考虑不足,导致了极端风险(Extreme Risk)的低估。
极值事件发生的概率虽然很低,但其引发的极端风险却损害巨大,有时甚至是灾难性的灾难。故对金融风险管理者来说,极值事件尤为值得关注。J.B.Philippe(2000)也曾指出,金融领域中关心的就是这些极端风险,首先要控制的也是这些极端风险。近些年,国际金融业监管当局也一直在试图制定一些规则以限制金融机构暴露在这些极端风险面前。
极值理论(Extreme Value Theory,EVT)是研究随机过程的极值分布及其特征的模型技术,对随机过程中的厚尾现象具有突出的针对性,并可在总体分布未知情况下,依靠样本数据外推得到总体极值的变化性质,克服了传统统计方法不能超越样本数据进行分析的局限。将EVT应用到金融风险管理领域可以弥补VaR对极值事件关注的不足,有利于更精确地度量金融极端风险。
另外,我国正处在经济转型期,虽已初步建立起以国有商业银行为主体的商业性金融体系,但金融体制的市场改革依然远远滞后于其它经济部门,整体行业受政策影响较大,市场运行机制经常发生变化,金融体系风险非但没有降低,反而不断积聚,金融市场动荡加剧,作为市场经济晴雨表的沪深股票市场频频的巨幅涨跌即清楚地表示了金融体系的震荡状况。故对处于经济转型期中的我国金融业来说,利用EVT研究金融市场极端风险度量无疑更是具有针对性与非常重要的现实意义。
本文即基于EVT研究金融极端风险的度量问题,并在相关研究结论之上对我国沪深股票市场的极端风险进行实证分析。
本文主要研究内容有:极值渐近分布的类型及性质;基于广义极值分布(GEV)和广义Pareto分布(GPD)的BMM模型与POT模型,并将极值BMM与POT模型引入到尾部高分位数的估计中;金融时间序列相关性对极值模型的影响及其减消处置;极值模型的回测技术选择与验证标准。特别是,在BMM模型中充分地考虑了子区间极值一般极限分布与极值序列极限分布之间的关系,测度了受子区间长度影响的极值VaR;在POT模型中运用参数估计量稳定性法弥补了目前普遍采用的样本平均超出量函数e (u )法的不足,针对一些图解法无法适用的问题,实现了峰度法对阈值的定量选取,并对指数回归模型法、子样本自助法、序贯法等定量法进行了分析探讨。
本文以我国沪深股票市场为研究对象,考虑到沪深股市实行涨跌停板制度(Raising limit),分段选取沪深股市基准日至1996年12月26日、以及1996年12月26日至2008年3月12日之间的综合指数收益率为数据,测度并比较分析了涨跌停板制度前后沪深股市的极端风险。在实证中,尤其重点考察了涨跌停板制度对沪深股市收益率序列尾分布的影响,即涨跌停板制度对极值数据异质性的抑制作用,以及由此导致的极值模型的测度效果和极值风险有效指标。
本文基于EVT研究金融极端风险的度量,学术与实践意义在于为金融市场投资者、市场监管机构防范与抵御金融极端风险提供理论与方法支持。
In recent years, financial fragility inherently has become increasingly more serious in some emerging, or even mature market economies, instead of being weakened with the rapid development of the financial sector, which has resulted in the more frequent crisis. Financial risks are also systematic, likely to bring national, regional or worldwide economic system disorders, recession or even collapse such as the Subprime Mortgage Crisis which broke out in U.S. in 2007 and have been raging economic system worldwidely.
In view of the endogenous and systematic of financial risks, undoubtedly, to resist and prevent financial risks is of great significance to the economy of one country. The foundation and core of effective resistance and prevention is the accurate measurement of financial risks, which has become a very important issue in the research of financial theory. At present, as internationally the most important tool of measuring risks, VaR describes the most possible loss in the future given a certain degree of confidence. VaR measures risk through measuring profit and loss by introducing the concept of confidence level, it combines expected loss and its probability, and directly measures the value of portfolio's risk. However, different from other types of assets, the sequence of returns on most financial assets practically bares significant characteristics of the fat-tail, which means that there exists a flawed assumption of the normal distribution of assets’returns, and that the tail extreme risk is underestimated because of the ignorance of rare events.
Though the probability of the occurrence of extreme risk is very low, the occurrence will definitely cause great damage, and the consequences are often disastrous. Therefore, in order to manage financial risks, events of extreme value are particularly worthy of our attention. J.B.Philippe (2000) also pointed out that in financial sector what should be concerned is nothing but extreme risks, and what should firstly be controlled are also extreme risks. In recent years, the international regulators of financial industry have kept trying to develop a number of provisions to restrict banks to be exposed to these extreme risks.
Extreme Value Theory (Extreme Value Theory, EVT) is the modeling technique focusing on the distribution and characteristics of the extreme value of random processes, the most prominent feature of which is that the flat-tail in random processes could be better solved, and in the case of population distribution unknown, the changing nature of population’s extreme value could be deduced from sample data, which could overcome the limitations of traditional statistical methods which cannot make analysis beyond sample data. Applying EVT to financial risk management can make up for the lack of VaR methodology, therefore could estimate the financial extreme events caused by the extreme risk more accurately.
In addition, China is in the socio-economic transition period. Though the commercial financial system has been initially established with the subject of state-owned commercial banks, the reform of financial system market is still lagging far behind other sectors of the economy. The industry as a whole is more influenced by policies. The market operating mechanism frequently changes. Risks in financial system continue to accumulate instead of lowering. Financial market vibrates, such as the frequent great fluctuations recently. Thus, how to accurately measure the extreme risk of financial market based on EVT has become an urgent task for the financial sector experiencing the socio-economic transformation.
Focusing the measurement of financial risk of extreme, this study empirically investigated the extreme risks of Chinese stock market based the theoretical researches of extreme value and relevant conclusions.
This dissertation made an in-depth study on the type and nature of the asymptotic distribution of extreme value. It studied BMM and POT model based on GEV and GPD separately, and introduced the two models into the estimation of tail high quantile. It examined the impact of the correlation of financial time series on EVT model and its eliminating disposal. It also studied standards of selection and validation of Back Testing techniques of EVT model. Particularly, in the BMM model, it took into account the relationship between the distribution of the extreme value limit of subinterval and that of sequence, and measured the extreme value of VaR affected by the length of the subinterval. In POT model, it used the technique of parameter estimator stability, making up for the limits of the currently popularly-used Mean Excess Function e (u ), and the threshold quantitatively selected by Kurtosis Method has also been achieved, and solving the problem the illustration method couldn’t be applied to. It also discussed other quantitative methods, such as Exponential Regression Model Method, Subsample Bootstrap Method, Sequential Method and so on.
Taking into account the factor of raising limit in Chinese stock markets, we sub-selected data of composite indices of returns on days between benchmark day to December 26, 1996, and December 26, 1996 to March 12, 2008, measured and compared the extreme risk in Chinese stock markets before and after the raising limit. In the empirical part, we particularly investigated the impact of raising limit on the distribution of tail sequence of returns data from Chinese stock markets, that is, the inhibit effect of raising limit on the heterogeneity of data with extreme value, as well as the efficiency of results of EVT Model and the effective indicators of extreme risk.
Based on EVT, this dissertation focused on the measurement of extreme financial risks, the academic and practical significance of which is to provide both theoretical and methodological support for financial market investors and market regulators to guard against extreme financial risks.
引文
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