极值理论在操作风险模型中的应用
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摘要
近年来,金融机构,特别是银行业操作风险事件的频频发生,商业银行操作风险管理引起了银行业界、监管当局以及学术界的重点关注。与有着较为成熟的信用风险和市场风险管理的理论和技术相比,操作风险管理的研究还处于初级阶段。2004年6月《巴塞尔新资本协议》的发布,它把操作风险纳入了最低资本充足要求的管理框架内,体现了国际银行业监管的最新理念和风险管理的最新成果。对于中国银行业而言,如何提高我国银行业的操作风险管理水平已经成为日渐重要的议题。2007年5月中国银监会印发了《商业银行操作风险管理指引》,推动我国银行业在加强操作风险管理方面向前迈进了一步。
极值理论是次序统计学的一门分支,传统上被用来预测海啸、地震、洪水等自然灾害,近年来已被广泛地应用于金融风险的管理中。它注重分布的尾部,比较有效地解决了在缺少样本的客观条件下如何预测和防范金融风险的问题,因此,越来越多的人认识到极值理论在极端事件风险管理中的巨大潜力,所以也可以应用于操作风险度量的模型中。
基于以上考虑,首先,论文分析了国内外操作风险管理的现状,进而提出了加强操作风险度量的必要性,总结了操作风险的度量模型,分析了各种模型优缺点；其次,详细的阐述了极值分布的基本理论,并利用阈顶点模型(POT)对操作风险进行了数学建模,在此过程中,给出了厚尾判断、参数估计、阈值的选取以及模型的检验方法等；最后,给出了我国商业银行选择操作风险度量模型的建议。
In recent years, with the frequent occurrence of the operational risk events in financial institutions, especially in banks, how to manage the operational risk attracts the attention of the banking industry, regulatory authorities and the academe. Compared with the theory and skills of credit and market risk management, research on operational risk management is less consummate and still in its initial stage. The "New Basel Capital Accord" in June 2004 brought operational risk into minimum capital adequacy requirements, which embodies the latest international banking supervision concepts and the latest results of operational risk management. As to China's banking industry, how to raise the level of operational risk management has been an increasingly important subject. The issue of "operational risk management guidelines for the commercial banks" by the China Banking Regulatory Commission in May 2007 promotes the operational risk management greatly.
The Extreme Value Theory that was traditionally used to predict tsunamis, earthquakes, floods and other natural disasters is a branch of order statistics, but now it has been widely used in financial risk management. It focuses on the distribution of the tail and can solve the problem of how to predict and prevent financial risk events in the absence of objective samples more effectively. Therefore, more and more people come to realize the great potential of Extreme Value Theory in the management of extreme events, so they begin to try to apply it into operational risk models.
Based on the above considerations, in my dissertation firstly I introduce the status in quo of operational risk models at home and abroad, as well as the need to strengthen the operational risk management, enumerate different operational risk models and their pro and con; Secondly, I explain the basic theory of Extreme distribution in detail.And use POT theory to model operational risk, during which I present the test methods of how to estimate parameters, how to choose threshold; Finally, this theory and models in my dissertation can be a proposal to China's commercial banks.
极值理论是次序统计学的一门分支,传统上被用来预测海啸、地震、洪水等自然灾害,近年来已被广泛地应用于金融风险的管理中。它注重分布的尾部,比较有效地解决了在缺少样本的客观条件下如何预测和防范金融风险的问题,因此,越来越多的人认识到极值理论在极端事件风险管理中的巨大潜力,所以也可以应用于操作风险度量的模型中。
基于以上考虑,首先,论文分析了国内外操作风险管理的现状,进而提出了加强操作风险度量的必要性,总结了操作风险的度量模型,分析了各种模型优缺点；其次,详细的阐述了极值分布的基本理论,并利用阈顶点模型(POT)对操作风险进行了数学建模,在此过程中,给出了厚尾判断、参数估计、阈值的选取以及模型的检验方法等；最后,给出了我国商业银行选择操作风险度量模型的建议。
In recent years, with the frequent occurrence of the operational risk events in financial institutions, especially in banks, how to manage the operational risk attracts the attention of the banking industry, regulatory authorities and the academe. Compared with the theory and skills of credit and market risk management, research on operational risk management is less consummate and still in its initial stage. The "New Basel Capital Accord" in June 2004 brought operational risk into minimum capital adequacy requirements, which embodies the latest international banking supervision concepts and the latest results of operational risk management. As to China's banking industry, how to raise the level of operational risk management has been an increasingly important subject. The issue of "operational risk management guidelines for the commercial banks" by the China Banking Regulatory Commission in May 2007 promotes the operational risk management greatly.
The Extreme Value Theory that was traditionally used to predict tsunamis, earthquakes, floods and other natural disasters is a branch of order statistics, but now it has been widely used in financial risk management. It focuses on the distribution of the tail and can solve the problem of how to predict and prevent financial risk events in the absence of objective samples more effectively. Therefore, more and more people come to realize the great potential of Extreme Value Theory in the management of extreme events, so they begin to try to apply it into operational risk models.
Based on the above considerations, in my dissertation firstly I introduce the status in quo of operational risk models at home and abroad, as well as the need to strengthen the operational risk management, enumerate different operational risk models and their pro and con; Secondly, I explain the basic theory of Extreme distribution in detail.And use POT theory to model operational risk, during which I present the test methods of how to estimate parameters, how to choose threshold; Finally, this theory and models in my dissertation can be a proposal to China's commercial banks.
引文
1.张燕.巴塞尔新资本协议框架下我国银行业操作风险度量研究[D],长沙：湖南大学,2005
2.巴塞尔监管委员会.新巴塞尔协议(征求意见稿)[R].2001,2003
3.张吉光.商业银行操作风险识别与管理[M],北京：中国人民大学出版社,2005,10-18
4.Sheedy, Elizabeth. Applying an Agency Framework to Operational Risk Management.http://www.gloriamundi.org/picsresources/es.pdf,1999-8
5.Basle Committee on Banking Supervision. The New Basel Capital Accord. http://www.bis.org,2001-1
6.Frachot, Antoine, Georges, P.,Roncalli, Thierry. Loss Distribution Approach for Operational Risk.http://gro.creditlyonnais.fr/content/wp/lda.pdf,2001-3
7.Cruz, Marcelo G.Modeling, Measuring and Hedging Operational Risk. http://www.gloriamundi.org/detailpopup.asp?ID=453054814,2002-2
8.Embrechts, Paul, Resnick, Sidney, Samorodnitsky, Gennady. Extreme Value Theory as a Risk Management Tool http://www.gloriamundi.org/picsresources/pesrgs.pdf
9.Elena Medova. Extreme Values and The Measurement of Operational Risk. http://www.gloriamundi.org/picsresources/emorm.pdf,2002-7
10.Carol Alexander. Bayesian methods for measuring operational risk. ISMA Centre,2000
11.Reimer Kiihn, Peter Neu. Functional Correlation Approach to Operational Risk in Banking Organizations[J],Physica A,2003,322:650-666
12.Muermann, A.Oktem,u. The Near-Miss Management of Operational Risk[J], The Journal of Risk Finance,2002,4(1):35-51
13.田玲,蔡秋杰.中国商业银行操作风险度量模型的选择和应用[J],中国软科学,2003,8：38-42
14.樊欣,杨晓光.操作风险管理的方法与现状[J],证券市场导报,2003,6：64-69
15.张静,马黎.商业银行操作风险的度量与管理[J],管理现代化,2003,5：49-53
16.王旭东.新巴塞尔资本协议与商业银行操作风险量化管理[J],金融论坛,2004,2：57-61
17.高丽君.我国商业银行操作风险度量与资本金分配研究[D],北京：中国科学院研究生院,2006
18.Dodd. E. L. The Greatest and Least Variate under General Laws of Error. Trans.Amer[J],Math. Soc.,1923,25:525-539
19. Frechet M. Sur La Loi de Probalilite de Ecart Maximum. Ann. Soc.Polonaise[J], Math. Cracow,1927,6:93
20. Fisher R A, Tippett L H C.Limiting Forms of the Frequency Distributions of theLargest of Smallest Member of a Sample[J],Proceedings of Cambridge Philosophical Society.,1928,24:180-190
21.Gnedenko B..Sur la distribution limit du terme maximum d'une serie aleatoire[J].Annals of Mathematics,1943,44:423-453
22.Weibull W. A Statistical Theory of Strength of Materials.Proc.Ing. Vetenskapsakad,1939,151
23.Weibull W. A Statistical Distribution of Wide Applicability. J. Appl.Mechanics, 1951,18:293-297
24. Gumbel E J.Statistics of Extremes. New York:Columbia University Press,1958
25.Jenkinson, A.F. The frequency distribution of the annual maximum (or minimum) values of meteorological elements[J],Quarterly Journal of the Royal Meteorological Society,1955,81:145-158
26. Pickands, J. Statistical inference using extreme order statistics[J].Ann.Statist, 1975.3:119-131
27.田宏伟,詹原瑞,邱军.极端值理沦(EVT)方法用于风险价值(VaR)计算的实证比较与分析[J],系统工程理论与实践,2000,10：27-57
28.王旭,史道济.极值统计理论在金融风险中的应用[J],数量经济技术经济研究,2001,8：109-111
29.刘元庆,杨旭.银行操作风险模型研究评述[J],经济管理,2006,10：87-91
30.Brandts, S.,2004,Operational Risk and Insurance:Quantitative and qualitative aspects, EFMA 2004 Basel Meetings Paper, April
31.潘建国,王惠.我国商业银行操作风险度量模型的选择[J],金融论坛,2006,4：43-48
32.樊欣,杨晓光.操作风险管理的方法与现状[J],证券市场导报,2003,6：64-69
33.Basel Committee on Banking Supervision.The Quantitative Impact Study for Operational Risk(1-3).http://www.bis.org,2004-7-12
34.Toshihiko Mori &Eiji Harada.Internal Measurement Approach to Operational Risk Capital Charge (discuss paper).http://www.bis.org
35.Carol Alexander,This translation of Operational Risk:Regulation, Analysis and Management [M].Pearson Education Limited,2003
36. Prescott, P. and Walden, A.T. Maximum-likelihood estimation of the parameters of the three-parameter generalized extreme-value distribution from censored samples[J],J. Statist. Comput. Simulation,1983,16:241-250
37. Hosking, J. R. M. Maximum-likelihood estimation of the parameters of the generalized extreme-value distribution[J],Applied Statistics,1985,34:301-310
38.Smith, R. L. Maximum-likelihood estimation in a class of non-regular cases[J], Biometrika,1985,72:67-90
39.Hosking, J. R. M.,Wallis, J.R. and Wood, E.F.estimation of the generalized extreme-value distribution by the method of probability-weighted moments[J], Technometrics,1985,2:251-261
40.欧阳资生著.极值理论在金融保险中的应用[M],北京：中国经济出版社,2006,35-37
41.Hill, B.M. A simple general approach to inference about the of a distribution[J], Ann. Statist,1975,3(5):1163-1174
42.Dekkers, A. and de Haan, L.,A moment estimator for the index of an extreme-value distribution[J],Ann.Statist,1989,17(4):1833-1855
43.CsorgS, S.,Deheuvels, P. and Mason, D.M. kernel estimator on the tail index of a distribution[J],Ann. Statist.,1985,13:1050-1077
44.Beirlant, J.,Dierckx,G,Goegebeur, Y. and Matthys, G.Tail index estimation and an exponential regression model J],Extremes,1999,22:177-200
45. Groeneboom, P.,Lopuha/I, H.P. Kernel-type estimators for the extreme value index[J],Ann. Statist,2003,31:1956-1995
46.Davison, A. C.and Hinkley, D.V.(1997).Bootstrap methods and their application, Cambridge University Pre
47.Philippe Jorion著,陈跃等译.风险价值VAR[M],北京：中信出版社,2005
48.Choulakian, V.and Stephens, M. A. Goodness-of-fit tests for the generalized parato distribution[J],Technometrics,2001,43(4):478-484
49.李志辉,范洪波.商业银行操作风险损失数据分析[J],2005,12：55-58
2.巴塞尔监管委员会.新巴塞尔协议(征求意见稿)[R].2001,2003
3.张吉光.商业银行操作风险识别与管理[M],北京：中国人民大学出版社,2005,10-18
4.Sheedy, Elizabeth. Applying an Agency Framework to Operational Risk Management.http://www.gloriamundi.org/picsresources/es.pdf,1999-8
5.Basle Committee on Banking Supervision. The New Basel Capital Accord. http://www.bis.org,2001-1
6.Frachot, Antoine, Georges, P.,Roncalli, Thierry. Loss Distribution Approach for Operational Risk.http://gro.creditlyonnais.fr/content/wp/lda.pdf,2001-3
7.Cruz, Marcelo G.Modeling, Measuring and Hedging Operational Risk. http://www.gloriamundi.org/detailpopup.asp?ID=453054814,2002-2
8.Embrechts, Paul, Resnick, Sidney, Samorodnitsky, Gennady. Extreme Value Theory as a Risk Management Tool http://www.gloriamundi.org/picsresources/pesrgs.pdf
9.Elena Medova. Extreme Values and The Measurement of Operational Risk. http://www.gloriamundi.org/picsresources/emorm.pdf,2002-7
10.Carol Alexander. Bayesian methods for measuring operational risk. ISMA Centre,2000
11.Reimer Kiihn, Peter Neu. Functional Correlation Approach to Operational Risk in Banking Organizations[J],Physica A,2003,322:650-666
12.Muermann, A.Oktem,u. The Near-Miss Management of Operational Risk[J], The Journal of Risk Finance,2002,4(1):35-51
13.田玲,蔡秋杰.中国商业银行操作风险度量模型的选择和应用[J],中国软科学,2003,8：38-42
14.樊欣,杨晓光.操作风险管理的方法与现状[J],证券市场导报,2003,6：64-69
15.张静,马黎.商业银行操作风险的度量与管理[J],管理现代化,2003,5：49-53
16.王旭东.新巴塞尔资本协议与商业银行操作风险量化管理[J],金融论坛,2004,2：57-61
17.高丽君.我国商业银行操作风险度量与资本金分配研究[D],北京：中国科学院研究生院,2006
18.Dodd. E. L. The Greatest and Least Variate under General Laws of Error. Trans.Amer[J],Math. Soc.,1923,25:525-539
19. Frechet M. Sur La Loi de Probalilite de Ecart Maximum. Ann. Soc.Polonaise[J], Math. Cracow,1927,6:93
20. Fisher R A, Tippett L H C.Limiting Forms of the Frequency Distributions of theLargest of Smallest Member of a Sample[J],Proceedings of Cambridge Philosophical Society.,1928,24:180-190
21.Gnedenko B..Sur la distribution limit du terme maximum d'une serie aleatoire[J].Annals of Mathematics,1943,44:423-453
22.Weibull W. A Statistical Theory of Strength of Materials.Proc.Ing. Vetenskapsakad,1939,151
23.Weibull W. A Statistical Distribution of Wide Applicability. J. Appl.Mechanics, 1951,18:293-297
24. Gumbel E J.Statistics of Extremes. New York:Columbia University Press,1958
25.Jenkinson, A.F. The frequency distribution of the annual maximum (or minimum) values of meteorological elements[J],Quarterly Journal of the Royal Meteorological Society,1955,81:145-158
26. Pickands, J. Statistical inference using extreme order statistics[J].Ann.Statist, 1975.3:119-131
27.田宏伟,詹原瑞,邱军.极端值理沦(EVT)方法用于风险价值(VaR)计算的实证比较与分析[J],系统工程理论与实践,2000,10：27-57
28.王旭,史道济.极值统计理论在金融风险中的应用[J],数量经济技术经济研究,2001,8：109-111
29.刘元庆,杨旭.银行操作风险模型研究评述[J],经济管理,2006,10：87-91
30.Brandts, S.,2004,Operational Risk and Insurance:Quantitative and qualitative aspects, EFMA 2004 Basel Meetings Paper, April
31.潘建国,王惠.我国商业银行操作风险度量模型的选择[J],金融论坛,2006,4：43-48
32.樊欣,杨晓光.操作风险管理的方法与现状[J],证券市场导报,2003,6：64-69
33.Basel Committee on Banking Supervision.The Quantitative Impact Study for Operational Risk(1-3).http://www.bis.org,2004-7-12
34.Toshihiko Mori &Eiji Harada.Internal Measurement Approach to Operational Risk Capital Charge (discuss paper).http://www.bis.org
35.Carol Alexander,This translation of Operational Risk:Regulation, Analysis and Management [M].Pearson Education Limited,2003
36. Prescott, P. and Walden, A.T. Maximum-likelihood estimation of the parameters of the three-parameter generalized extreme-value distribution from censored samples[J],J. Statist. Comput. Simulation,1983,16:241-250
37. Hosking, J. R. M. Maximum-likelihood estimation of the parameters of the generalized extreme-value distribution[J],Applied Statistics,1985,34:301-310
38.Smith, R. L. Maximum-likelihood estimation in a class of non-regular cases[J], Biometrika,1985,72:67-90
39.Hosking, J. R. M.,Wallis, J.R. and Wood, E.F.estimation of the generalized extreme-value distribution by the method of probability-weighted moments[J], Technometrics,1985,2:251-261
40.欧阳资生著.极值理论在金融保险中的应用[M],北京：中国经济出版社,2006,35-37
41.Hill, B.M. A simple general approach to inference about the of a distribution[J], Ann. Statist,1975,3(5):1163-1174
42.Dekkers, A. and de Haan, L.,A moment estimator for the index of an extreme-value distribution[J],Ann.Statist,1989,17(4):1833-1855
43.CsorgS, S.,Deheuvels, P. and Mason, D.M. kernel estimator on the tail index of a distribution[J],Ann. Statist.,1985,13:1050-1077
44.Beirlant, J.,Dierckx,G,Goegebeur, Y. and Matthys, G.Tail index estimation and an exponential regression model J],Extremes,1999,22:177-200
45. Groeneboom, P.,Lopuha/I, H.P. Kernel-type estimators for the extreme value index[J],Ann. Statist,2003,31:1956-1995
46.Davison, A. C.and Hinkley, D.V.(1997).Bootstrap methods and their application, Cambridge University Pre
47.Philippe Jorion著,陈跃等译.风险价值VAR[M],北京：中信出版社,2005
48.Choulakian, V.and Stephens, M. A. Goodness-of-fit tests for the generalized parato distribution[J],Technometrics,2001,43(4):478-484
49.李志辉,范洪波.商业银行操作风险损失数据分析[J],2005,12：55-58