Powerful Backtests for Historical Simulation Expected Shortfall Models

References

• Acerbi, C., and Szekely, B. (2014), “Backtesting Expected Shortfall,” Risk, 27, 76–81.
   Google Scholar
• Acerbi, C., and Tasche, D. (2002), “On the Coherence of Expected Shortfall,” Journal of Banking & Finance, 26, 1487–1503. DOI: 10.1016/S0378-4266(02)00283-2.
   Web of Science ®Google Scholar
• Artzner, P., Delbaen, F., Eber, J.-M., and Heath, D. (1997), “Thinking Coherently,” Risk, 10, 68–71.
   Google Scholar
• ———(1999), “Coherent Measures of Risk,” Mathematical Finance, 9, 203–228.
   Web of Science ®Google Scholar
• Barone-Adesi, G., and Giannopoulos, K. (2001), “Nonparametric VaR Techniques: Myths and Realities,” Economic Notes, 30, 167–181. DOI: 10.1111/j.0391-5026.2001.00052.x.
   Google Scholar
• Barone-Adesi, G., Bourgoin, F., and Giannopoulos, K. (1998), “Don’t Look Back,” Risk, 11, 100–104.
   Google Scholar
• Barone-Adesi, G., Giannopoulos, K., and Vosper, L. (1999), “VaR Without Correlations for Portfolios of Derivative Securities,” Journal of Futures Markets, 19, 583–602. DOI: 10.1002/(SICI)1096-9934(199908)19:5<583::AID-FUT5>3.0.CO;2-S.
   Web of Science ®Google Scholar
• Basak, S., and Shapiro, A. (2001), “Value-at-Risk based Risk Management: Optimal Policies and Asset Prices,” Review of Financial Studies, 14, 371–405. DOI: 10.1093/rfs/14.2.371.
   Web of Science ®Google Scholar
• Basel Committee on Banking Supervision. (2016), “Minimum Capital Requirements for Market Risk,” Consultation paper, January.
   Google Scholar
• Bayer, S., and Dimitriadis, T. (2022), “Regression based Expected Shortfall Backtesting,” Journal of Financial Econometrics, 20, 437–471. DOI: 10.1093/jjfinec/nbaa013.
   Web of Science ®Google Scholar
• Berkowitz, J. (2001), “Testing Density Forecasts, with Applications to Risk Management,” Journal of Business & Economic Statistics, 19, 465–474. DOI: 10.1198/07350010152596718.
   Web of Science ®Google Scholar
• Carrasco, M., and Chen, X. (2002), “Mixing and Moment Properties of Various GARCH and Stochastic Volatility Models,” Econometric Theory, 18, 17–39. DOI: 10.1017/S0266466602181023.
   Web of Science ®Google Scholar
• Colletaz, G., Hurlin, C., and Perignon, C. (2013), “The Risk Map: A New Tool for Validating Risk Models,” Journal of Banking & Finance, 37, 3843–3854. DOI: 10.1016/j.jbankfin.2013.06.006.
   Web of Science ®Google Scholar
• Costanzino, N., and Curran, M. (2015), “Backtesting General Spectral Risk Measures with Application to Expected Shortfall,” Journal of Risk Model Validation, 9, 21–31. DOI: 10.21314/JRMV.2015.131.
   Web of Science ®Google Scholar
• Couperier, O., and Leymarie, J. (2020), “Backtesting Expected Shortfall via Multi-Quantile Regression,” working papers. HAL. Available at https://EconPapers.repec.org/RePEc:hal:wpaper:halshs-01909375.
   Google Scholar
• Delgado, M. A., and Escanciano, J. C. (2007), “Nonparametric Tests for Conditional Symmetry in Dynamic Models,” Journal of Econometrics, 141, 652–682. DOI: 10.1016/j.jeconom.2006.10.011.
   Web of Science ®Google Scholar
• Doukhan, P. (1994), Mixing: Properties and Examples (Vol. 85), New York: Springer-Verlag.
   Google Scholar
• Du, Z. (2016), “Nonparametric Bootstrap Tests for the Independence of Generalized Errors,” Econometrics Journal, 19, 55–83. DOI: 10.1111/ectj.12059.
   Web of Science ®Google Scholar
• Du, Z., and Escanciano, J. C. (2017), “Backtesting Expected Shortfall: Accounting for Tail Risk,” Management Science, 63, 940–958. DOI: 10.1287/mnsc.2015.2342.
   Web of Science ®Google Scholar
• Emmer, S., Tasche, D., and Kratz, M. (2015), “What is the Best Risk Measure in Practice? A Comparison of Standard Measures,” Journal of Risk, 18, 31–60. DOI: 10.21314/JOR.2015.318.
   Web of Science ®Google Scholar
• Escanciano, J. C., and Lobato, I. N. (2009), “An Automatic Portmanteau Test for Serial Correlation,” Journal of Econometrics, 151, 140–149. DOI: 10.1016/j.jeconom.2009.03.001.
   Web of Science ®Google Scholar
• Escanciano, J. C., and Olmo, J. (2010), “Backtesting Parametric Value-at-Risk with Estimation Risk,” Journal of Business & Economic Statistics, 28, 36–51. DOI: 10.1198/jbes.2009.07063.
   Web of Science ®Google Scholar
• Escanciano, J. C., and Pei, P. (2012), “Pitfalls in Backtesting Historical Simulation VaR Models,” Journal of Banking & Finance, 36, 2233–2244. DOI: 10.1016/j.jbankfin.2012.04.004.
   Web of Science ®Google Scholar
• Fissler, T., and Ziegel, J. F. (2016), “Higher Order Elicitability and Osband’s Principle,” The Annals of Statistics, 44, 1680–1707. DOI: 10.1214/16-AOS1439.
   Web of Science ®Google Scholar
• Francq, C., and Zakoïan, J.-M. (2004), “Maximum Likelihood Estimation of Pure GARCH and ARMA-GARCH Processes,” Bernoulli, 10, 605–637. DOI: 10.3150/bj/1093265632.
   Web of Science ®Google Scholar
• ———(2006), “Mixing Properties of a General Class of GARCH(1,1) Models Without Moment Assumptions on the Observed Process,” Econometric Theory, 22, 815–834.
   Web of Science ®Google Scholar
• Gao, F., and Song, F. (2008), “Estimation Risk in GARCH VaR and ES Estimates,” Econometric Theory, 24, 1404–1424. DOI: 10.1017/S0266466608080559.
   Web of Science ®Google Scholar
• Gneiting, T. (2011), “Making and Evaluating Point Forecasts,” Journal of the American Statistical Association, 106, 746–762. DOI: 10.1198/jasa.2011.r10138.
   Web of Science ®Google Scholar
• Hansen, B. E. (1994), “Autoregressive Conditional Density Estimation,” International Economic Review, 35, 705–730. DOI: 10.2307/2527081.
   Web of Science ®Google Scholar
• Hurlin, C., and Tokpavi, S. (2006), “Backtesting Value-at-Risk Accuracy: A Simple New Test,” Journal of Risk, 9, 19–37. DOI: 10.21314/JOR.2007.148.
   Google Scholar
• Inglot, T., and Ledwina,T. (2006a), “Towards Data Driven Selection of a Penalty Function for Data Driven Neyman Tests,” Linear Algebra and its Applications, 417, 124–133. DOI: 10.1016/j.laa.2005.10.023.
   Web of Science ®Google Scholar
• ———(2006b), “Data Driven Score Tests of Fit for Semiparametric Homoscedastic Linear Regression Model,” Preprint 665, Institute of Mathematics Polish Academy of Sciences.
   Google Scholar
• Kerkhof, J., and Melenberg, B. (2004), “Backtesting for Risk-based Regulatory Capital,” Journal of Banking and Finance, 28, 1845–1865. DOI: 10.1016/j.jbankfin.2003.06.007.
   Web of Science ®Google Scholar
• Kratz, M., Lok, Y. H., and McNeil, A. J. (2018), “Multinomial VaR Backtests: A Simple Implicit Approach to Backtesting Expected Shortfall,” Journal of Banking & Finance, 88, 393–407. DOI: 10.1016/j.jbankfin.2018.01.002.
   Web of Science ®Google Scholar
• Lambert, N. S., Pennock, D. M., and Shoham, Y. (2008), Eliciting Properties of Probability Distributions, pp. 129–138, New York, NY: Association for Computing Machinery. DOI: 10.1145/1386790.1386813.
   Google Scholar
• McNeil, A. J., and Frey, R. (2000), “Estimation of Tail-Related Risk Measures for Heteroscedastic Financial Time Series: An Extreme Value Approach,” Journal of Empirical Finance, 7, 271–300. DOI: 10.1016/S0927-5398(00)00012-8.
   Google Scholar
• McNeil, A. J., Frey, R., and Embrechts, P. (2015), Quantitative Risk Management: Concepts, Techniques and Tools (Revised ed.), Princeton: Princeton University Press.
   Google Scholar
• Mincer, J., and Zarnowitz, V. (1969), “The Evaluation of Economic Forecasts,” in Economic Forecasts and Expectations: Analysis of Forecasting Behavior and Performance, pp. 3–46, Cambridge, MA: National Bureau of Economic Research, Inc.
   Google Scholar
• Nolde, N., and Ziegel, J. F. (2017), “Elicitability and Backtesting: Perspectives for Banking Regulation,” The Annals of Applied Statistics, 11, 1833–1874. DOI: 10.1214/17-AOAS1041.
   Web of Science ®Google Scholar
• Novales, A., and Garcia-Jorcano, L. (2019), “Backtesting Extreme Value Theory Models of Expected Shortfall,” Quantitative Finance 19, 799–825. DOI: 10.1080/14697688.2018.1535182.
   Web of Science ®Google Scholar
• Osband, K. H. (1985), “Providing Incentives for Better Cost Forecasting,” Ph.D. thesis. University California, Berkeley.
   Google Scholar
• Patton, A. J., Ziegel, J. F., and Chen, R. (2019), “Dynamic Semiparametric Models for Expected Shortfall (and Value-at-Risk),” Journal of Econometrics, 211, 388–413. DOI: 10.1016/j.jeconom.2018.10.008.
   Web of Science ®Google Scholar
• Pérignon, C., and Smith, D. R. (2008), “A New Approach to Comparing VaR Estimation Methods,” Journal of Derivatives, 16, 54–66. DOI: 10.3905/JOD.2008.16.2.054.
   Web of Science ®Google Scholar
• ———(2010), “The Level and Quality of Value-at-Risk Disclosure by Commercial Banks,” Journal of Banking & Finance, 34, 362–377.
   Web of Science ®Google Scholar
• Roccioletti, S. (2015), Backtesting Value at Risk and Expected Shortfall, Wiesbaden: Springer Fachmedien Wiesbaden.
   Google Scholar
• Su, Q., Qin, Z., Peng, L., and Qin, G. (2021), “Efficiently Backtesting Conditional Value-at-Risk and Conditional Expected Shortfall,” Journal of the American Statistical Association, 116, 2041–2052. DOI: 10.1080/01621459.2020.1763804.
   Web of Science ®Google Scholar
• Sun, S. X. (2006), “The Bahadur Representation for Sample Quantiles Under Weak Dependence,” Statistics & Probability Letters, 76, 1238–1244. DOI: 10.1016/j.spl.2005.12.021.
   Web of Science ®Google Scholar
• Van der Vaart, A. W. (1998), Asymptotic Statistics, New York: Cambridge University Press.
   Google Scholar
• Weber, S. (2006), “Distribution-Invariant Risk Measures, Information, and Dynamic Consistency,” Mathematical Finance, 16, 419–441. DOI: 10.1111/j.1467-9965.2006.00277.x.
   Web of Science ®Google Scholar
• Wong, W. K. (2008), “Backtesting Trading Risk of Commercial Banks Using Expected Shortfall,” Journal of Banking & Finance, 32, 1404–1415. DOI: 10.1016/j.jbankfin.2007.11.012.
   Web of Science ®Google Scholar
• ———(2010), “Backtesting Value-at-Risk based on Tail Losses,” Journal of Empirical Finance, 17, 526–538.
   Web of Science ®Google Scholar
• Yoshihara, K.-i. (1995), “The Bahadur Representation of Sample Quantiles for Sequences of Strongly Mixing Random Variables,” Statistics & Probability Letters, 24, 299–304. DOI: 10.1016/0167-7152(94)00187-D.
   Web of Science ®Google Scholar