VaR和CVaR在商业银行利率风险管理中的应用
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摘要
自我国加入WTO,全球金融一体化加速了我国利率市场化的进程,市场利率不再由中央银行完全主导,而是逐步由市场供求机制所决定。利率的频繁变动给银行财务状况带来了潜在的风险,从而加大了商业银行亏损或倒闭的可能性。并且越来越多的研究也表明我国商业银行存在较大的利率风险,这使得利率风险管理问题成为人们关注的焦点。为了有效的进行商业银行利率风险管理即控制和防范利率风险,首要的任务是要能够很好的度量利率风险。如何采用科学的方法度量利率风险则成为我国商业银行的核心问题。本文则是主要讨论VaR和CVaR这两种风险度量方法在我国商业银行利率风险度量中的应用。
文章重点分为四个部分:第一部分回顾了已有的商业银行利率风险度量方法并比较其优缺点;第二部分着重讨论了VaR模型的基本概念,主要的计算方法以及VaR模型在应用中的局限性;第三部分介绍CVaR模型的定义,性质、基本的计算以及相对于VaR模型的优势;第四部分则是选取2007年1月4日至2007年9月6同我国商业银行问同业拆借隔夜利率、7日利率以及中信标普国债指数收盘数据进行实证分析,结合已有的运用VaR方法度量商业银行利率风险的研究成果,将基于GARCH计算的CVaR风险度量方法引入到商业银行利率风险度量中,建立基于AR-GARCH的VaR和CVaR模型。根掘所得到的VaR和CVaR估计值定量的模拟考察我国商业银行面临的利率风险状况。
研究结果表明,AR(1)-GARCH(1,2)、AR(1)-GARCH(1,1)能够较好的模拟我国商业银行间同业拆借利率收益的波动,AR(2)-GARCH(1,1)对中信标普国债指数收益率波动的模拟也比较好,可见基于AR-GARCH的VaR和CVaR模型在度量商业银行利率风险时都有较好的适用性。并且由实证分析得到CVaR的估计值要大于VaR的估计值,而且要高出许多,说明CVaR能够度量覆盖更大范围的左尾风险。这是由于CVaR方法满足次可加性的这条性质优于VaR方法,和基于GARCH的VaR方法相比,能更好的对尾部风险进行控制。但因为我国银行间同业拆借市场和银行间债券市场并不完善,基于所选用的样本数量较小以及所使用的方法不够全面,本文所采用的模型并不能说明所有的问题,因此在文章结尾处提出了本文需进一步研究的方向。
Since China's accession to WTO, global financial integration has accelerated the process of China's liberalization of interest rates. Market interest rates have no longer completely dominated by the central bank, but gradually determined by market supply and demand mechanism. Frequent changes of interest rates brought potential risks to the financial situation of the banks, it has increased the possibility of losses or failures of the commercial banks. And a large number of research also show that the interest rate risk of Chinese commercial banks is more and more obvious, which makes people pay great attention to the interest rate risk management. In order to effectively supervise interest rate risk of commercial banks that control and prevent interest rate risk, first and foremost task is to have a good method to measure interest rate risk. How to apply scientific methods to measure interest rate risk has become the core issue of Chinese commercial banks. This article is mainly to discuss the application of VaR and CVaR these two risk measurement methods in the Chinese commercial banks interest rate risk measurement.
The paper is divided into four parts: The first section reviews the existing interest rate risk measurement methods and compare their advantages and disadvantages; The second part focuses on the basic concepts of the VaR model, the main method of calculation and the limitations of the application; The third section describes the CVaR model's definition, nature, basic computing and the advantages relative to VaR model; The fourth part selects some data such as Chinese commercial overnight inter-bank lending rate, the interest rate on the 7th and the CITIC S&P government bond index data from January 4th, 2007 to September 6th, 2007 to have empirical analysis. Combining the research results of the existing interest rate risk measurement methods of commercial banks, we introduced the model CVaR based on AR-GARCH into commercial banks to measure interest rate risk, built the model VaR and CVaR based on AR-GARCH. According to the estimates of VaR and CVaR, we may obtain quantitative simulation study of Chinese commercial banks facing interest rate risk profile.
The results show that , the model AR(1)-GARCH(1,2), AR(1)-GARCH(1,1) can be better to simulate the fluctuations in earnings of Chinese commercial inter-bank lending interest rate, AR(2)-GARCH( 1,1) that simulates the CITIC S&P government bond index data is also relatively good, We can see that the model VaR and CVaR calculated based on AR-GARCH can be well applied in the measurement of commercial bank interest rates. The estimate of CVaR obtained from the empirical analysis is bigger than the estimated value VaR, and to much higher, which illustrates CVaR can measure a wider coverage of the left tail risk than VaR. This is because CVaR possess the characteristic as subadditivity while VaR has no this nature, so compared to VaR calculated based on AR-GARCH, CVaR can be better to control the risks of the tail. Because of China's inter-bank lending market and inter-bank bond market is not perfect, the number of samples selected is relatively smaller and the method used is not comprehensive enough, the model used in this paper does not explain all the problems, therefore, this paper provides a set of suggestions for further research in the end.
文章重点分为四个部分:第一部分回顾了已有的商业银行利率风险度量方法并比较其优缺点;第二部分着重讨论了VaR模型的基本概念,主要的计算方法以及VaR模型在应用中的局限性;第三部分介绍CVaR模型的定义,性质、基本的计算以及相对于VaR模型的优势;第四部分则是选取2007年1月4日至2007年9月6同我国商业银行问同业拆借隔夜利率、7日利率以及中信标普国债指数收盘数据进行实证分析,结合已有的运用VaR方法度量商业银行利率风险的研究成果,将基于GARCH计算的CVaR风险度量方法引入到商业银行利率风险度量中,建立基于AR-GARCH的VaR和CVaR模型。根掘所得到的VaR和CVaR估计值定量的模拟考察我国商业银行面临的利率风险状况。
研究结果表明,AR(1)-GARCH(1,2)、AR(1)-GARCH(1,1)能够较好的模拟我国商业银行间同业拆借利率收益的波动,AR(2)-GARCH(1,1)对中信标普国债指数收益率波动的模拟也比较好,可见基于AR-GARCH的VaR和CVaR模型在度量商业银行利率风险时都有较好的适用性。并且由实证分析得到CVaR的估计值要大于VaR的估计值,而且要高出许多,说明CVaR能够度量覆盖更大范围的左尾风险。这是由于CVaR方法满足次可加性的这条性质优于VaR方法,和基于GARCH的VaR方法相比,能更好的对尾部风险进行控制。但因为我国银行间同业拆借市场和银行间债券市场并不完善,基于所选用的样本数量较小以及所使用的方法不够全面,本文所采用的模型并不能说明所有的问题,因此在文章结尾处提出了本文需进一步研究的方向。
Since China's accession to WTO, global financial integration has accelerated the process of China's liberalization of interest rates. Market interest rates have no longer completely dominated by the central bank, but gradually determined by market supply and demand mechanism. Frequent changes of interest rates brought potential risks to the financial situation of the banks, it has increased the possibility of losses or failures of the commercial banks. And a large number of research also show that the interest rate risk of Chinese commercial banks is more and more obvious, which makes people pay great attention to the interest rate risk management. In order to effectively supervise interest rate risk of commercial banks that control and prevent interest rate risk, first and foremost task is to have a good method to measure interest rate risk. How to apply scientific methods to measure interest rate risk has become the core issue of Chinese commercial banks. This article is mainly to discuss the application of VaR and CVaR these two risk measurement methods in the Chinese commercial banks interest rate risk measurement.
The paper is divided into four parts: The first section reviews the existing interest rate risk measurement methods and compare their advantages and disadvantages; The second part focuses on the basic concepts of the VaR model, the main method of calculation and the limitations of the application; The third section describes the CVaR model's definition, nature, basic computing and the advantages relative to VaR model; The fourth part selects some data such as Chinese commercial overnight inter-bank lending rate, the interest rate on the 7th and the CITIC S&P government bond index data from January 4th, 2007 to September 6th, 2007 to have empirical analysis. Combining the research results of the existing interest rate risk measurement methods of commercial banks, we introduced the model CVaR based on AR-GARCH into commercial banks to measure interest rate risk, built the model VaR and CVaR based on AR-GARCH. According to the estimates of VaR and CVaR, we may obtain quantitative simulation study of Chinese commercial banks facing interest rate risk profile.
The results show that , the model AR(1)-GARCH(1,2), AR(1)-GARCH(1,1) can be better to simulate the fluctuations in earnings of Chinese commercial inter-bank lending interest rate, AR(2)-GARCH( 1,1) that simulates the CITIC S&P government bond index data is also relatively good, We can see that the model VaR and CVaR calculated based on AR-GARCH can be well applied in the measurement of commercial bank interest rates. The estimate of CVaR obtained from the empirical analysis is bigger than the estimated value VaR, and to much higher, which illustrates CVaR can measure a wider coverage of the left tail risk than VaR. This is because CVaR possess the characteristic as subadditivity while VaR has no this nature, so compared to VaR calculated based on AR-GARCH, CVaR can be better to control the risks of the tail. Because of China's inter-bank lending market and inter-bank bond market is not perfect, the number of samples selected is relatively smaller and the method used is not comprehensive enough, the model used in this paper does not explain all the problems, therefore, this paper provides a set of suggestions for further research in the end.
引文
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[2]J.P.Morgan,Sensitive character of rate,1983.
[3]Aryan and Brueckner,Asset Values:Interest Rate Change and Duraiton,Journal of Financial and Quantitative Analysis,1986.
[4]Morgan and Smith,Interest Rate Risk Model,Chicago:GPCL,1987.
[5]F.R.Macaulay,Some theoretical problems suggested by the movements of interest rates.Bond yields and stock prices in the united states since 1856,NewYork:National Bureau of Economic Research,1938.
[6]Anwer.S,Ahmed,Amme Beatty&Carolyn Tadeda,Estimating the Value and Interest Risk of the Interest-Beating Transaction Deposits,Division if Research and Statistics,1997.
[7]William.B.English,Asset Values:Interest Rate Change and Duraiton,Journal of Financial and Quantitative Analysis,2002.
[8]马永波.西方商业银行利率风险衡量的演进及其启示[J],经济论坛,2005,(17):4-6.
[9]卢庆杰.利率市场化与商业银行利率风险管理[J],上海经济研究.2003,(4):52-57.
[10]钱水土,任健.基于我国银行业的商业银行利率风险分析[J],学习论坛,2005,21(6):53-55.
[11]王伟.利率波动与商业银行利率风险控制[J],国际金融研究,2001,(6):39-42.
[12]穆海权,余雪红,田怀姝.商业银行的利率风险管理——从敏感性缺口分析利率风险的暴露及其结果[J],现代商业银行,1999,(2):25-26.
[13]陈祖功,查奇芬.久期模型在银行利率风险测定中的应用[J],统计与决策,2008,(17):156-157.
[14]樊耘,顺敏,郑晓红.期权调整利差模型(OAS)在商业银行利率风险管理中的应用[J],科技与管理,2003,(2):72-75.
[15]王春峰,张伟.具有隐含期权的商业银行利率风险测量与管理:凸度缺口模型[J],管理科技学报,2001,4(5):22-29.
[16]戴国强.我国商业银行利率风险管理研究[M],上海财经大学出版社,2005,125-129.
[17]任晴.我国商业银行利率风险的衡量模型[J].山东经济,2003,(4):44-45.
[18]陈英顺.论利率连续下调后我国商业银行的利率风险及其防范[J],南开经济研究.1999,(6).
[19]P Morgan.Risk metrics-Technical document.4th ed.New York:Morgan Guaranty Trust Company,1996.
[20]Philippe Jorion.VAR:风险价值——金融风险管理新标准.中信出版社,1995.
[21]Chew&Lilian Risk:Measuring the risk in value at risk.Financial Analysts,1996.
[22]Artzner,Coherent Measures of Risk.Mathematical Finance,1999,(9).
[23]Gaivoronski,Pflug Georg.Properties and Computation of Value at Risk Efficient Portfolios Based on Historical Data[M],2002.
[24]王春峰.金融市场风险管理[M].天津大学出版社,2001,117-121.
[25]刘宁飞.VaR模型及其在金融监管中的应用[J].经济科学,1999,(1)39-50.
[26]田新时,刘汉中,李耀.沪深股市一般误差分布(GED)下的VaR计算[J].管理工程学报,2003,17(1):25-27.
[27]范英.VaR方法及其在股市风险分析中的应用初探[J].中国管理科学,2000,8(3):26-32.
[28]袁丽胜,朱世武.事后检验在市场风险管理中的应用[J].金融研究,2002,(10):55-59.
[29]杨晓光,马超群,文风华.VaR下厚尾分布的最优资产组合的收敛性.管理科学学报[J].2002,5(1):65-68.
[30]王春红,曹新华.VaR方法在国债利率风险管理中的应用[J],商业研究,2004,(1):147-149.
[31]李志辉,刘胜会.我国商业利率风险的度量研究——以同业拆借市场为例[J].南开经济研究,2006,(3):27-41.
[32]Rockafellar R.T.and S.Uryasev Conditional Value-at-Risk for General Loss Distributions.Journal of Banking and Finance.2002,(26).1443-1471.
[33]Pflug,G.Remarks on the value-at-risk and the conditional value-at-risk.Can be Downloaded:www.gloriamundi.org.2000
[34]A.I.Kibzun and E.A.Kuznetsov.Comparison of VaR and CVaR Criteria.Automation and Remote Control.2003,64(7):1154-1164.
[35]Nikolas Topaloglou,Hercules Vladimirou,and Stavros A.Zenios.CvaR models with selective hedgion for international asset allocation,Journal of BANKING&FINANCE26(2002).
[36]Pownall,R.A.,Koedijk,K.G.Gapturing Downside Risk in Financial Markets:The Case of The Asian Crisis.Journal of International Money and Finane.1999(18).
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