Asymptotic Analysis of the Loss Given Default in the Presence of Multivariate Regular Variation

REFERENCES

• Acharya , V. V. , Bharath , S. T. and Srinivasan , A. 2003 . Understanding the Recovery Rates on Defaulted Securities , London : London Business School . Working Paper
   Google Scholar
• Artzner , P. , Delbaen , F. , Eber , J. M. and Heath , D. 1999 . Coherent Measures of Risk . Mathematical Finance , 9 : 203 – 228 .
   Web of Science ®Google Scholar
• Asimit , A. V. , Furman , E. , Tang , Q. and Vernic , R. 2011 . Asymptotics for Risk Capital Allocations Based on Conditional Tail Expectation . Insurance: Mathematics and Economics , 49 : 310 – 324 .
   Web of Science ®Google Scholar
• Basrak , B. , Davis , R. A. and Mikosch , T. 2002 . Regular Variation of GARCH Processes . Stochastic Processes and Their Applications , 99 : 95 – 115 .
   Web of Science ®Google Scholar
• Bassamboo , A. , Juneja , S. and Zeevi , A. 2008 . Portfolio Credit Risk with Extremal Dependence: Asymptotic Analysis and Efficient Simulation . Operations Research , 56 ( 2008 ) : 593 – 606 .
   Google Scholar
• Bingham , N. H. , Goldie , C. M. and Teugels , J. L. 1987 . Regular Variation. , Cambridge : Cambridge University Press .
   Google Scholar
• Bücker , K. and Klüppelberg , C. 2010 . Multivariate Models for Operational Risk . Quantitative Finance , 10 : 855 – 869 .
   Web of Science ®Google Scholar
• Brazauskas , V. , Jones , B. L. , Puri , M. L. and Zitikis , R. 2008 . Estimating Conditional Tail Expectation with Actuarial Applications in View . Journal of Statistical Planning and Inference , 138 : 3590 – 3604 .
   Web of Science ®Google Scholar
• Brereton , T. J. , Chan , J. C. and Kroese , D. P. 2013 . “ Monte Carlo Methods for Portfolio Credit Risk ” . In Credit Portfolio Securitizations and Derivatives , Edited by: Scheule , H. and Rosch , D. 128 – 151 . New York : John Wiley & Sons .
   Google Scholar
• Charpentier , A. and Segers , J. 2009 . Tails of Multivariate Archimedean Copulas . Journal of Multivariate Analysis , 100 : 1521 – 1537 .
   Web of Science ®Google Scholar
• Chava , S. , Stefanescu , C. and Turnbull , S. 2011 . Modeling the Loss Distribution . Management Science , 57 : 1267 – 1287 .
   Web of Science ®Google Scholar
• Chavez-Demoulin , V. and Embrechts , P. 2011 . “ An EVT Primer for Credit Risk ” . In The Oxford Handbook of Credit Derivatives , Edited by: Lipton , A. and Rennie , A. 500 – 532 . Oxford : Oxford University Press .
   Google Scholar
• Dhaene , J. , Vanduffel , S. , Goovaerts , M. J. , Kaas , R. , Tang , Q. and Vyncke , D. 2006 . Risk Measures and Comonotonicity: A Review . Stochastic Models , 22 : 573 – 606 .
   Web of Science ®Google Scholar
• Duffie , D. and Pan , J. 1997 . An Overview of Value at Risk . Journal of Derivative , 4 : 7 – 49 .
   Google Scholar
• Embrechts , P. , Lambrigger , D. D. and Wüthrich , M. V. 2009 . Multivariate Extremes and the Aggregation of Dependent Risks: Examples and Counter-examples . Extremes , 12 : 107 – 127 .
   Web of Science ®Google Scholar
• Embrechts , P. , Resnick , S. I. and Samorodnitsky , G. 1998 . Living on the Edge . Risk , 11 : 96 – 100 .
   Google Scholar
• Embrechts , P. , Resnick , S. I. and Samorodnitsky , G. 1999 . Extreme Value Theory as a Risk Management Tool . North American Actuarial Journal , 3 : 30 – 41 .
   Google Scholar
• Farinelli , S. and Shkolnikov , M. 2012 . Two Models of Stochastic Loss Given Default . Journal of Credit Risk , 8 : 3 – 20 .
   Web of Science ®Google Scholar
• Fougeres , A. and Mercadier , C. 2012 . Risk Measures and Multivariate Extensions of Breiman's Theorem . Journal of Applied Probability , 49 : 364 – 384 .
   Web of Science ®Google Scholar
• Frees , E. W. and Valdez , E. A. 1998 . Understanding Relationships Using Copulas. North American Actuarial Journal , 2 : 1 – 25 .
   Google Scholar
• Frey , R. and McNeil , A. J. 2003 . Dependent Defaults in Models of Portfolio Credit Risk . Journal of Risk , 6 : 59 – 92 .
   Google Scholar
• Frey , R. , McNeil , A. J. and Nyfeler , M. A. 2001 . Copulas and Credit Risk Models . Risk , 14 : 111 – 114 .
   Google Scholar
• Gupton , G. M. , Finger , C. C. and Bhatia , M. 1997 . CreditMetrics^TM—Technical Document. Technical Report , New York : J. P. Morgan & Co. .
   Google Scholar
• Gupton , G. M. and Stein , R. M. 2002 . Losscalc^TM: Moody's Model for Predicting Loss Given Default (LGD) , New York : Moody's Investor Services, Global Credit Research . Working Paper
   Google Scholar
• Hardy , M. R. 2003 . Investment Guarantees: The New Science of Modeling and Risk Management for Equity-Linked Life Insurance. , New York : John Wiley & Sons .
   Google Scholar
• Hardy , M. R. and Wirch , J. L. 2004 . The Iterated CTE: A Dynamic Risk Measure . North American Actuarial Journal , 8 : 62 – 75 .
   Google Scholar
• Hua , L. 2012 . Multivariate Extremal Dependence and Risk Measures , University of British Columbia . Doctoral thesis
   Google Scholar
• Huang , W. , Weng , C. and Zhang , Y. 2013 . Multivariate Risk Models under Heavy-Tailed Risks . Applied Stochastic Models in Business and Industry ,
   Web of Science ®Google Scholar
• Joe , H. and Li , H. 2011 . Tail Risk of Multivariate Regular Variation . Methodology and Computing in Applied Probability , 13 : 671 – 693 .
   Web of Science ®Google Scholar
• Li , H. and Wu , P. 2013 . Extremal Dependence of Copulas: A Tail Density Approach . Journal of Multivariate Analysis , 114 : 99 – 111 .
   Web of Science ®Google Scholar
• Li , H. and Sun , Y. 2009 . Tail Dependence for Heavy-Tailed Scale Mixtures of Multivariate Distributions . Journal of Applied Probability , 46 : 925 – 937 .
   Web of Science ®Google Scholar
• Manistre , B. J. and Hancock , G. H. 2005 . Variance of the CTE Estimator . North American Actuarial Journal , 9 : 129 – 156 .
   Google Scholar
• Mashal , R. , Naldi , M. and Zeevi , A. 2003 . “ Extreme Events and Multi-name Credit Derivatives ” . In Credit Derivatives: The Definitive Guide , Edited by: Gregory , J. 313 – 338 . London : Risk Waters Group .
   Google Scholar
• McNeil , A. J. , Frey , R. and Embrechts , P. 2005 . Quantitative Risk Management: Concepts, Techniques and Tools , Princeton : Princeton University Press .
   Google Scholar
• Merton , R. C. 1974 . On the Pricing of Corporate Debt: The Risk Structure of Interest Rates . Journal of Finance , 29 : 449 – 470 .
   Web of Science ®Google Scholar
• Mikosch , T. 2003 . “ Modeling Dependence and Tails of Financial Time Series ” . In Extreme Values in Finance, Telecommunications, and the Environment , Edited by: Finkenstaedt , B. and Rootzén , H. 185 – 286 . New York : Chapman & Hall/CRC. .
   Google Scholar
• Nelsen , R. B. 2006 . An Introduction to Copulas. 2nd ed. Springer Series in Statistics. , New York : Springer .
   Google Scholar
• Pykhtin , M. 2003 . Unexpected Recovery Risk . Risk , 16 : 74 – 78 .
   Google Scholar
• Resnick , S. I. 1987 . Extreme Values, Regular Variation, and Point Processes. , New York : Springer .
   Google Scholar
• Resnick , S. I. 2004 . The Extremal Dependence Measure and Asymptotic Independence . Stochastic Models , 20 : 205 – 227 .
   Web of Science ®Google Scholar
• Resnick , S. I. 2007 . Heavy-Tail Phenomena. Probabilistic and Statistical Modeling. , New York : Springer .
   Google Scholar
• Salmon , F. 2012 . The Formula That Killed Wall Street . Significance , 9 : 16 – 20 .
   Google Scholar
• Schloegl , L. and O’Kane , D. 2005 . A Note on the Large Homogeneous Portfolio Approximation with the Student-t Copula . Finance and Stochastics , 9 : 577 – 584 .
   Web of Science ®Google Scholar
• Schuermann , T. 2004 . “ What Do We Know about Loss Given Default? ” . In Credit Risk: Models and Management, , 2nd ed. , Edited by: Shimko , D. 249 – 274 . London : Risk Books .
   Google Scholar
• St´ric´ , C. 1999 . Multivariate Extremes for Models with Constant Conditional Correlations . Journal of Empirical Finance , 6 : 515 – 553 .
   Google Scholar
• Taleb , N. N. 2007 . The Black Swan , New York : Random House .
   Google Scholar
• Tang , Q. and Yuan , Z. 2012 . A Hybrid Estimate for the Finite-Time Ruin Probability in a Bivariate Autoregressive Risk Model with Application to Portfolio Optimization . North American Actuarial Journal , 16 : 378 – 397 .
   Google Scholar
• Tasche , D. 2003 . The Single Risk Factor Approach to Capital Charges in Case of Correlated Loss Given Default Rates , Bundesbank . Working Paper
   Google Scholar
• van Damme , G . 2011 . A Generic Framework for Stochastic Loss-Given-Default . Journal of Computational and Applied Mathematics , 235 : 2523 – 2550 .
   Web of Science ®Google Scholar
• van der Vaart , A. W. 1998 . Asymptotic Statistics. , Cambridge : Cambridge University Press .
   Google Scholar
• Wüthrich , M. V. 2003 . Asymptotic Value-at-Risk Estimates for Sums of Dependent Random Variables . ASTIN Bulletin , 33 : 75 – 92 .
   Google Scholar
• Yan , J. 2007 . Enjoy the Joy of Copulas: With a Package Copula . Journal of Statistical Software , 21 : 1 – 21 .
   Web of Science ®Google Scholar
• Zhu , L. and Li , H. 2012 . Asymptotic Analysis of Multivariate Tail Conditional Expectations . North American Actuarial Journal , 16 : 350 – 363 .
   Google Scholar