Conditional Value-at-Risk and Average Value-at-Risk: Estimation and Asymptotics

References

• Acerbi C. Spectral measures of risk: A coherent representation of subjective risk aversion. J. Banking and Finance (2002) 26:1505–1518Crossref, Google Scholar
• Artzner P, Delbaen F, Eber J-M, Heath D. Coherent measures of risk. Math. Finance (1999) 9:203–228Crossref, Google Scholar
• Berkowitz J, Pritsker M, Gibson M, Zhou H. How accurate are value-at-risk models at commercial banks. J. Finance (2002) 57:1093–1111Crossref, Google Scholar
• Bluhm C, Overbeck L, Wagner C. An Introduction to Credit Risk Modeling (2002) 1st ed.(Chapman & Hall/CRC)Chapman & Hall/CRC Financial Mathematics SeriesCrossref, Google Scholar
• Cai Z, Wang X. Nonparametric estimation of conditional var and expected shortfall. J. Econometrics (2008) 147(1):120–130Crossref, Google Scholar
• Chen SX, Tang CY. Nonparametric inference of value-at-risk for dependent financial returns. J. Financial Econometrics (2005) 3(2):227–255Crossref, Google Scholar
• Chernozhukov V, Umantsev L. Conditional value-at-risk: Aspects of modeling and estimation. Empirical Econom. (2001) 26(1):271–292Crossref, Google Scholar
• Detlefsen K, Scandolo G. Conditional and dynamic convex risk measures. Finance and Stochastics (2005) 9:539–561Crossref, Google Scholar
• Duffie D, Singleton KJ. Credit Risk: Pricing, Measurement, and Management (2003) (Princeton University Press, Princeton, NJ) Crossref, Google Scholar
• Engle RF, Manganelli S. CAViaR: Conditional autoregressive value at risk by regression quantiles. J. Bus. Econom. Statist. (2004) 22:367–381Crossref, Google Scholar
• Fermanian JD, Scaillet O. Sensitivity analysis of var and expected shortfall for portfolios under netting agreements. J. Banking and Finance (2005) 29:927–958Crossref, Google Scholar
• FitchRatings (2006) . Global credit derivatives survey (FitchRatings, New York)Google Scholar
• Föllmer H, Schied A. Stochastic Finance: An Introduction in Discrete Time (2011) (Walter de Gruyter & Co., Berlin) Crossref, Google Scholar
• Frey R, McNeil AJ. Var and expected shortfall in portfolios of dependent credit risks: Conceptual and practical insights. J. Banking and Finance (2002) 26(7):1317–1334Crossref, Google Scholar
• Gaglianone W, Lima L, Linton O, Smith D. Evaluating value-at-risk models via quantile regression. J. Bus. Econom. Statist. (2011) 29:150–160Crossref, Google Scholar
• Giesecke K, Weber S. Measuring the risk of large losses. J. Investment Management (2008) 6(4):1–15Google Scholar
• Gneiting T. Making and evaluating point forecasts. J. Amer. Statist. Assoc. (2011) 106(494):746–762Crossref, Google Scholar
• Huber PJ. Robust Statistics (1981) (Wiley, New York) Crossref, Google Scholar
• Jackson P, Perraudin W. Regulatory implications of credit risk modelling. J. Banking and Finance (2000) 24(1--2):1–14Crossref, Google Scholar
• Jorion P. Financial Risk Manager Handbook (2003) 2nd ed.(Wiley, New York) Google Scholar
• Koenker R. Quantile Regression (2005) (Cambridge University Press, Cambridge, UK) Crossref, Google Scholar
• Kusuoka S. On law invariant coherent risk measures. Advances in Mathematical Economics (2001) 3(Springer, Berlin) 83–95Crossref, Google Scholar
• Leorato S, Peracchi F, Tanase AV. Asymptotically efficient estimation of the conditional expected shortfall. Comput. Statist. and Data Anal. (2012) 5(4):768–784Crossref, Google Scholar
• McNeil AJ, Frey R. Estimation of tail-related risk measures for heteroscedastic financial time series: An extreme value approach. J. Empirical Finance (2000) 7:271–300Crossref, Google Scholar
• O'Kane D, Turnbull S. Valuation of credit default swaps. Quantitative Credit Research Quarterly (2003) (Lehman Brothers)Google Scholar
• Peracchi F, Tanase AV. On estimating the conditional expected shortfall. Appl. Stochastic Models Bus. Indust. (2008) 24:471–493Crossref, Google Scholar
• Pflug G, Römisch W. Modeling, Measuring, and Managing Risk (2007) (World Scientific Publishing Co., London) Google Scholar
• Pflug G, Wozabal N. Asymptotic distribution of law-invariant risk functionals. Finance and Stochastics (2010) 14:397–418Crossref, Google Scholar
• Rockafellar RT, Uryasev S. Conditional value-at-risk for general loss distributions. J. Banking and Finance (2002) 26(7):1443–1471Crossref, Google Scholar
• Rockafellar RT, Uryasev S, Zabarankin M. Risk tuning with generalized linear regression. Math. Oper. Res. (2008) 33(3):712–729Link, Google Scholar
• Scaillet O. Nonparametric estimation and sensitivity analysis of expected shortfall. Math. Finance (2004) 14(1):115–129Crossref, Google Scholar
• Scaillet O. Nonparametric estimation of conditional expected shortfall. Insurance and Risk Management J. (2005) 72:639–660Google Scholar
• Shapiro A. Asymptotic properties of statistical estimators in stochastic programming. Ann. Statist. (1989) 17:841–858Crossref, Google Scholar
• Shapiro A, Dentcheva D, Ruszczyński A. Lectures on Stochastic Programming: Modeling and Theory (2009) (SIAM, Philadelphia) Crossref, Google Scholar
• Trindade A, Uryasev S, Shapiro A, Zrazhevsky G. Financial prediction with constrained tail risk. J. Banking and Finance (2007) 31:3524–3538Crossref, Google Scholar
• Weber S. Distribution-invariant risk measures, information, and dynamic consistency. Math. Finance (2006) 16(2):419–441Crossref, Google Scholar
• Wozabal D, Wozabal N. Asymptotic consistency of risk functionals. J. Nonparametric Statist. (2009) 21(8):977–990Crossref, Google Scholar
• Zhu S, Fukushima M. Worst-case conditional value-at-risk with application to robust portfolio management. Oper. Res. (2009) 57(5):1155–1168Link, Google Scholar