On the Measurement of Economic Tail Risk
Published Online:12 Sep 2016https://doi.org/10.1287/opre.2016.1539
References
- Acerbi (2002) Spectral measures of risk: A coherent representation of subjective risk aversion. J. Banking Finance 26(7):1505–1518.Crossref, Google Scholar
- (2014) Back-testing expected shortfall. Risk Magazine (November 17), 76–81.Google Scholar
- (2014) Procyclical leverage and Value-at-Risk. Rev. Financial Stud. 27(2):373–403.Crossref, Google Scholar
- (1999) Coherent measures of risk. Math. Finance 9(3):203–228.Crossref, Google Scholar
- (2008) An economic index of riskiness. J. Political Econom. 116(5):810–836.Crossref, Google Scholar
- Basel Committee on Banking Supervision (1996) Supervisory framework for the use of “backtesting” in conjunction with the internal models approach to market risk capital requirements. 1-15. Document, Bank for International Settlements, Basel, Switzerland.Google Scholar
- Basel Committee on Banking Supervision (2006) International convergence of capital measurement and capital standards: A revised framework. Document, Bank for International Settlements, Basel, Switzerland, p. 48.Google Scholar
- Basel Committee on Banking Supervision (2009) Revisions to the Basel II market risk framework. Document, Bank for International Settlements, Basel, Switzerland, p. 15.Google Scholar
- Basel Committee on Banking Supervision (2013) Fundamental review of the trading book: A revised market risk framework. Consultative Document, Bank for International Settlements, Basel, Switzerland, p. 18.Google Scholar
- (2015) On elicitable risk measures. Quant. Finance 15(5):725–733.Crossref, Google Scholar
- (2001) Testing density forecasts, applications to risk management. J. Bus. Econom. Statist. 19(4):465–474.Crossref, Google Scholar
- (2011) Evaluating value-at-risk models with desk-level data. Management Sci. 57(12):2213–2227.Link, Google Scholar
- (2009) The Fundamental Principles of Financial Regulation: 11th Geneva Report on the World Economy (Centre for Economic Policy Research, Washington, DC).Google Scholar
- (2009) Market liquidity and funding liquidity. Rev. Financial Stud. 22(6):2201–2238.Crossref, Google Scholar
- (2006) A review of backtesting and backtesting procedures. J. Risk 9(2):1–17.Crossref, Google Scholar
- (2009) New measures for performance evaluation. Rev. Financial Stud. 22(7):2571–2606.Crossref, Google Scholar
- (1998) Evaluating interval forecasts. Internat. Econom. Rev. 39(4):841–862.Crossref, Google Scholar
- (2010) Backtesting. Cont RB, ed. Encyclopedia of Quantitative Finance (John Wiley & Sons, Hoboken, NJ).Crossref, Google Scholar
- (2004) Backtesting value-at-risk: A duration-based approach. J. Financial Econometrics 2(1):84–108.Crossref, Google Scholar
- (2010) Robustness and sensitivity analysis of risk measurement procedures. Quant. Finance 10(6):593–606.Crossref, Google Scholar
- (2015) Backtesting general spectral risk measures with application to expected shortfall. Preprint, University of Toronto and Bank of Montreal.Google Scholar
- (2013) Fat tails, VaR and subadditivity. J. Econometrics 172(2): 283–291.Crossref, Google Scholar
- (2013) Consistency of risk measure estimates. Preprint, Imperial College London.Google Scholar
- (2006) Risk measures and comonotonicity: A review. Stochastic Models 22(4):573–606.Crossref, Google Scholar
- (1997) An overview of value at risk. J. Derivatives 4(3):7–49.Crossref, Google Scholar
- (2001) Analytical value-at-risk with jumps and credit risk. Finance Stochastics 5(2):115–180.Crossref, Google Scholar
- (2015) Aggregation-robustness and model uncertainty of regulatory risk measures. Finance Stochastics 19(4):763–790.Crossref, Google Scholar
- (2009) Comparing the point predictions and subjective probability distributions of professional forecasters. J. Bus. Econom. Statist. 27(1):30–41.Crossref, Google Scholar
- (2004) CAViaR: Conditional autoregressive value at risk by regression quantiles. J. Bus. Econom. Statist. 22(4):367–381.Crossref, Google Scholar
- (1972) The Theory of Finance (Dryden Press, Hinsdale, IL).Google Scholar
- (2016) Higher order elicitability and Osband’s principle. Ann. Statist. 44(4):1680–1707.Crossref, Google Scholar
- (2015) Expected shortfall is jointly elicitable with value at risk—Implications for backtesting. Risk Magazine (December).Google Scholar
- (2002) Convex measures of risk and trading constraints. Finance Stochastics 6(4):429–447.Crossref, Google Scholar
- (2009) An operational measure of riskiness. J. Political Econom. 117(5):785–814.Crossref, Google Scholar
- (2013) A wealth-requirement axiomatization of riskiness. Theoret. Econom. 8(2):591–620.Crossref, Google Scholar
- (2002) Putting order in risk measures. J. Banking Finance 26(7):1473–1486.Crossref, Google Scholar
- (2005) Law invariant convex risk measures. Adv. Math. Econom. 7:33–46.Crossref, Google Scholar
- (2011) Evaluating value-at-risk models via quantile regression. J. Bus. Econom. Statist. 29(1): 150–160.Crossref, Google Scholar
- (2007) Proper conditioning for coherent VaR in portfolio management. Management Sci. 53(3):483–494.Link, Google Scholar
- (1989) Maxmin expected utility with non-unique prior. J. Math. Econom. 18(2):141–153.Crossref, Google Scholar
- (2013) Design of risk weights. Oper. Res. 62(6): 1204–1220.Link, Google Scholar
- (2014) Robust risk measurement and model risk. Quant. Finance 14(1):29–58.Crossref, Google Scholar
- (2011) Making and evaluating point forecasts. J. Amer. Statist. Assoc. 106(494):746–762.Crossref, Google Scholar
- (2003) A risk-factor model foundation for ratings-based bank capital rules. J. Financial Intermediation 12(3):199–232.Crossref, Google Scholar
- (2006) Procyclicality in Basel II: Can we treat the disease without killing the patient? J. Financial Intermediation 15(3):395–417.Crossref, Google Scholar
- (2005) Improved duration-based backtesting of value-at-risk. J. Risk 8:17–38.Crossref, Google Scholar
- (2013) Challenges in identifying and measuring systemic risk. Brunnermeier M, Krishnamurthy A, eds. Risk Topography: Systemic Risk and Macro Modeling (University of Chicago Press, Chicago), 15–30.Google Scholar
- (2001) Robust control and model uncertainty. Amer. Econom. Rev. 91(2):60–66.Crossref, Google Scholar
- (2007) Robustness (Princeton University Press, Princeton, NJ).Crossref, Google Scholar
- (2011) Comparing risks by acceptance and rejection. J. Political Econom. 119(4):617–638.Crossref, Google Scholar
- (2014) The role of the information set for forecasting–with applications to risk management. Ann. Appl. Statist. 8(1):595–621.Crossref, Google Scholar
- (1981) Robust Statistics (John Wiley & Sons, New York).Crossref, Google Scholar
- (2009) Robust Statistics, 2nd ed. (John Wiley & Sons, Hoboken, NJ).Crossref, Google Scholar
- (2009) Portfolio diversification and value at risk under thick-tailedness. Quant. Finance 9(5):565–580.Crossref, Google Scholar
- (2007) The limits of diversification when losses may be large. J. Banking Finance 31(8):2551–2569.Crossref, Google Scholar
- (2007) Value at Risk: The New Benchmark for Managing Financial Risk, 3rd ed. (McGraw-Hill, Boston).Google Scholar
- (2010) Unintended consequences of the market risk requirement in banking regulation. J. Econom. Dynam. Control 34(10):2192–2214.Crossref, Google Scholar
- (2004) Backtesting for risk-based regulatory capital. J. Banking Finance 28:1845–1865.Crossref, Google Scholar
- (2014) On the measurement of economic tail risk. Preprint, version February 2014, Arxiv: http://arxiv.org/abs/1401.4787v2.Google Scholar
- (2006) What is a good risk measure: Bridging the gaps between data, coherent risk measures, and insurance risk measures. Preprint, Columbia University, New York.Google Scholar
- (2013) External risk measures and Basel Accords. Math. Oper. Res. 38(3):393–417.Link, Google Scholar
- (1995) Techniques for verifying the accuracy of risk management models. J. Derivatives 3(2):73–84.Crossref, Google Scholar
- (2011) Evaluating probability forecasts. Ann. Statist. 39(5):2356–2382.Crossref, Google Scholar
- (2008) Eliciting properties of probability distributions. Proc. 9th ACM Conf. Electronic Commerce, EC ’08 (ACM, New York), 129–138.Crossref, Google Scholar
- (2013) Estimation of and inference about the expected shortfall for time series with infinite variance. Econometric Theory 29(4):771–807.Crossref, Google Scholar
- (1999a) Methods for evaluating value-at-risk estimates. Federal Reserve Bank of San Francisco Econom. Rev. 2(2):3–17.Google Scholar
- (1998) Regulatory evaluation of value-at-risk models. J. Risk 1(2):37–64.Crossref, Google Scholar
- (2006) Ambiguity aversion, robustness, and the variational representation of preferences. Econometrica 74(6):1447–1498.Crossref, Google Scholar
- (2000) Estimation of tail-related risk measures for heteroskedastic financial time series: An extreme value approach. J. Empirical Finance 7:271–300.Crossref, Google Scholar
- (2005) Quantitative Risk Management: Concepts, Techiniques, Tools (Princeton University Press, Princeton, NJ).Google Scholar
- (2004) The modelling of operational risk: Experience with the analysis of the data collected by the basel committee. Preprint 517, Banca d’Italia.Google Scholar
- (1985) Providing Incentives for Better Cost Forecasting. PhD thesis, University of California at Berkeley.Google Scholar
- (2013) Asset allocation under the Basel Accord risk measures. Preprint, Peking University.Google Scholar
- (2002) Conditional value-at-risk for general loss distributions. J. Banking Finance 26(7):1443–1471.Crossref, Google Scholar
- (1971) Elicitation of personal probabilities and expectations. J. Amer. Statist. Assoc. 66(336):783–810.Crossref, Google Scholar
- (1986) Integral representation without additivity. Proc. Amer. Math. Soc. 97(2):255–261.Crossref, Google Scholar
- (1989) Subjective probability and expected utility without additivity. Econometrica 57(3):571–587.Crossref, Google Scholar
- (2012) Short-horizon regulation for long-term investors. J. Banking Finance 36(12):3227–3238.Crossref, Google Scholar
- (2012) Estimation of multiple period expected shortfall and median shortfall for risk management. Quant. Finance 12(5):739–754.Crossref, Google Scholar
- (2006) The representation of two types of functionals on ℒ∞ (Ω, ℱ) and ℒ∞ (Ω, ℱ, ℙ). Sci. China Ser. A: Math. 49(10):1376–1382.Crossref, Google Scholar
- (2009) Risk measures with comonotonic subadditivity or convexity and respecting stochastic orders. Insurance: Math. Econom. 45(3):459–465.Crossref, Google Scholar
- (2002) Expected shortfall and beyond. J. Banking Finance 26(7):1519–1533.Crossref, Google Scholar
- (1979) Eliciting production possibilities from a well-informed manager. J. Econom. Theory 20(3):360–380.Crossref, Google Scholar
- (2005) Mean, median, and skew: Correcting a textbook rule. J. Statist. Ed. 13(2).Google Scholar
- (2015) Elicitable distortion risk measures: A concise proof. Statist. Probab. Lett. 100(May):172–175.Crossref, Google Scholar
- (1997) Axiomatic characterization of insurance prices. Insurance: Math. Econom. 21(2):173–183.Crossref, Google Scholar
- (2006) Distribution-invariant risk measures, information, and dynamic consistency. Math. Finance 16(2):419–442.Crossref, Google Scholar
- (2011) Scoring rules. Cochran J, ed. Wiley Encyclopedia of Operations Research and Management Science, Vol 7 (John Wiley & Sons, New York), 4733–4744.Crossref, Google Scholar
- (2014) A gradual non-convexification method for minimizing VaR. J. Risk 16(3):23–47.Google Scholar
- (2013) Comonotonic convex preferences. Preprint, Academy of Mathematics and Systems Science, Chinese Academy of Sciences.Google Scholar
- (2014) Coherence and elicitability. Math. Finance, ePub ahead of print September 3, http://dx.doi.org/10.1111/mafi.12080.Crossref, Google Scholar

