9700 
5631巴塞尔委员会已经批准用期望损失（Expected Shortfall，ES）作为市场风险指标对银行业进行监管，以替代现有的在险价值指标（Value-at-Risk，VaR）。这主要是因为期望损失满足风险度量应该满足的性质，而在险价值则不满足。在这个转变过程中，金融机构面临的主要困难是没有工具可以用来评估期望损失模型，即后验分析，而本文则提出了一套简单的ES后验分析工具。具体而言，我们基于累积碰撞序列（Cumulative Violations）构造了一套ES模型的检验方法，该方法是对VaR后验分析的自然推广。我们推导出了该检验的渐进分布性质，并且通过蒙特卡洛模拟研究了它们的有限样本表现。通过将该方法应用于全球三大股票指数，我们发现，在2007年金融危机期间，VaR模型无法识别出金融危机时期与正常时期市场风险模型的差异，而ES模型则可以。
期望损失的后验分析
摘要
参考文献
2 Acerbi C, Szekely B. Backtesting expected shortfall[N]. Risk Magazine, 2014.
4 Artzner P, Delbaen F, Eber M., et al. Coherent measures of risk[J]. Mathematical Finance, 1999, 9(3):203-228. DOI:10.1111/mafi.1999.9.issue-3
5 Bai J. Testing parametric conditional distributions of dynamic models[J]. Review of Economics and Statistics, 2003, 85(3):531-549. DOI:10.1162/003465303322369704
6 Basak S, Shapiro A. Value-at-risk based risk management:Optimal policies and asset prices[J]. Review of Financial Studies, 2001, 14(2):371-405. DOI:10.1093/rfs/14.2.371
7 Basel Committee on Banking Supervision. Consultative document:Fundamental review of the trading book[R]. Basel, Switzerland, 2012.
8 Berkowitz J. Testing density forecasts with applications to risk management[J]. Journal of Business and Economic Statistics, 2001, 19(4):465-474. DOI:10.1198/07350010152596718
9 Berkowitz J, Christoffersen P, Pelletier D. Evaluating value-at-risk models with desk-level data[J]. Management Science, 2011, 57(12):2213-2227. DOI:10.1287/mnsc.1080.0964
10 Bose A. Bahadur representation of mestimates[J]. Annals of Statistics, 1998, 26(2):771-777. DOI:10.1214/aos/1028144859
11 Box G, Pierce D. Distribution of residual autocorrelations in autoregressive integrated moving average time series models[J]. Journal of American Statistical Association, 1970, 65(332):1509-1527. DOI:10.1080/01621459.1970.10481180
12 Christoffersen P. Evaluating interval forecasts[J]. International Economic Review, 1998, 39(4):841-862. DOI:10.2307/2527341
13 Christoffersen P, Goncalves P.Estimation risk in financial risk management[J]. Journal of Risk, 2005, 7(3):1-28. DOI:10.21314/JOR.2005.112
14 Christoffersen P.Value-at-risk models[M]. Handbook of Financial Time Series, 2009.
15 Colletaz G, Hurlin C, Perignon C. The risk map:A new tool for validating risk models[J]. Journal of Banking and Finance, 2013, 37(10):3843-3854. DOI:10.1016/j.jbankfin.2013.06.006
16 Du Z. Nonparametric bootstrap tests for the independence of generalized errors[R]. CAEPR Working Paper No. 023-2009, 2015.
17 Emmer S, Kratz M, Tasche D. What is the best risk measure in practice? A comparison of standard measures[R]. ESSEC Business School:Paris, France, 2014.
18 Escanciano J.Weak convergence of non-stationary multivariate marked processes with applications to martingale testing[J]. Journal of Multivariate Analysis, 2007, 98(7):1321-1336. DOI:10.1016/j.jmva.2007.03.004
19 Escanciano J, Lobato I. Testing the martingale hypothesis[M]. Palgrave Handbook of Econometrics, 2009a.
20 Escanciano J, Lobato I.An automatic portmanteau test for serial correlation[J]. Journal of Econometrics, 2009b, 151(2):140-149. DOI:10.1016/j.jeconom.2009.03.001
21 Escanciano J, Olmo J. Backtesting parametric value-at-risk with estimation risk[J]. Journal of Business and Economic Statistics, 2010, 28(1):36-51. DOI:10.1198/jbes.2009.07063
22 Escanciano J, Velasco C. Specification tests of parametric dynamic conditional quantiles[J]. Journal of Econometrics, 2010, 159(1):209-221. DOI:10.1016/j.jeconom.2010.06.003
23 Escanciano J, Pei P. Pitfalls in backtesting historical simulation models[J]. Journal of Banking and Finance, 2012, 36(8):2233-2244. DOI:10.1016/j.jbankfin.2012.04.004
24 Francq C, Zakoian J.Risk-parameter estimation in volatility models[J]. Journal of Econometrics, 2015, 184(1):158-173. DOI:10.1016/j.jeconom.2014.06.019
25 Gourieroux C, Zakoian J.Estimation-adjusted VaR[J]. Econometric Theory, 2013, 29(4):735-770. DOI:10.1017/S0266466612000680
26 Hansen B.Autoregressive conditional density estimation[J]. International Economic Review, 1994, 35(3):705-730. DOI:10.2307/2527081
27 Hong Y, Lee T. Diagnostic checking for adequacy of linear and nonlinear time series models[J]. Econometric Theory, 2003, 19(6):1065-1121.
28 Hong Y, Li H. Nonparametric specification testing for continuous-time modelswith applications to term structure of interest rates[J]. The Review of Financial Studies, 2005, 18(1):37-84. DOI:10.1093/rfs/hhh006
30 Jorion P. Value at risk:The new benchmark for managing financial risk[M]. New York:McGraw-Hill, 2006.
31 Kerkhof J, Melenberg B. Backtesting for risk-based regulatory capital[J].Journal of Banking and Finance, 2004, 28(8):1845-1865. DOI:10.1016/j.jbankfin.2003.06.007
32 Kourouma L, Dupre D, Sanfilippo G, et al. Extreme value at risk and expected shortfall during financial crisis[R]. Working Paper, 2011.
33 Kupiec P. Techniques for verifying the accuracy of risk measurement models[J]. The Journal of Derivatives, 1995, 3(2):73-84. DOI:10.3905/jod.1995.407942
35 O'Brien J, Szerszen P. An evaluation of bank VaR measures for market risk during and before the financial crisis[R]. FEDS Working Paper No. 2014-21, 2014.
36 Perignon C, Smith D. A new approach to comparing VaR estimation methods[J]. Journal of Derivatives, 2008, 16(2):54-66. DOI:10.3905/JOD.2008.16.2.054
37 Rosenblatt M. Remarks on a multivariate transformation[J]. Annals of Mathematical Statistics, 1952, 23:470-472. DOI:10.1214/aoms/1177729394
38 Shiryaev A. Probability[M]. New York:Springer, 1996.
39 van der Vaart A, Wellner J.Weak convergence and empirical processes[M]. New York:Springer, 1996.
41 Wong W.Backtesting value-at-risk based on tail losses[J]. Journal of Empirical Finance, 2010, 17(3):526-538. DOI:10.1016/j.jempfin.2009.11.004
引用本文
杜在超, JuanCarlos Escanciano. 期望损失的后验分析[J]. 财经研究, 2017, 43(12): 74–99.
导出参考文献，格式为：
上一篇：晚清捐官、政治取向与辛亥革命
