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The Devil is in the Tails: Actuarial Mathematics and the Subprime Mortgage Crisis

Published online by Cambridge University Press:  09 August 2013

Catherine Donnelly  and
Paul Embrechts
Paul Embrechts
Affiliation:
RiskLab, Department of Mathematics, ETH Zurich, CH-8092 Zurich, Switzerland, E-mail: paul.embrechts@math.ethz.ch
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Abstract

In the aftermath of the 2007-2008 financial crisis, there has been criticism of mathematics and the mathematical models used by the finance industry. We answer these criticisms through a discussion of some of the actuarial models used in the pricing of credit derivatives. As an example, we focus in particular on the Gaussian copula model and its drawbacks. To put this discussion into its proper context, we give a synopsis of the financial crisis and a brief introduction to some of the common credit derivatives and highlight the difficulties in valuing some of them.

We also take a closer look at the risk management issues in part of the insurance industry that came to light during the financial crisis. As a backdrop to this, we recount the events that took place at American International Group during the financial crisis. Finally, through our paper we hope to bring to the attention of a broad actuarial readership some “lessons (to be) learned” or “events not to be forgotten”.

Information

Type
Research Article
Information
ASTIN Bulletin: The Journal of the IAA , Volume 40 , Issue 1 , May 2010 , pp. 1 - 33
Copyright
Copyright © International Actuarial Association 2010

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Footnotes

* Senior SFI Chair.

References

Acharya, V.V., Cooley, T., Richardson, M. and Walter, I. (2010) Manufacturing tail risk: a perspective on the financial crisis of 2007-09. Foundations and Trends in Finance, 4, Forthcoming.Google Scholar
AIG (2006) 2006 Annual Report, March 1 2007.Google Scholar
AIG (2007a) Capital Markets. Investor Meeting – December 5, 2007. http://library.corporate-ir.net/library/76/761/76115/items/272197/capital.pdf.Google Scholar
AIG (2007b) Residential Mortgage Presentation (Financial figures are as at June 30, 2007) August 9, 2007 (Revised as to slide 29). http://media.corporate-ir.net/media_files/irol/76/76115/REVISED_AIG_and_the_Residential_Mortgage_Market_FINAL_08-09-07.pdf.Google Scholar
AIG (2008) 2008 Annual Report, March 27 2009.Google Scholar
AIG (2009) SEC 10-Q filing at March 31 2009.Google Scholar
Bielecki, T.R. and Rutkowski, M. (2004) Credit Risk: Modeling, Valuation and Hedging. Springer.Google Scholar
BIS (2009) Bank for International Settlements Quarterly Review, September 2009.Google Scholar
Bluhm, C. and Overbeck, L. (2007) Structured Credit Portfolio Analysis, Baskets and CDOs. Chapman and Hall/CRC.Google Scholar
Brunnermeier, M.K. (2009) Deciphering the liquidity and credit crunch 2007-2008. Journal of Economic Perspectives, 23(1), 77–100.Google Scholar
Coles, S. (2001) An Introduction to Statistical Modeling of Extreme Values. Springer.Google Scholar
Cont, R. (2006) Model uncertainty and its impact on the pricing of derivative instruments. Mathematical Finance, 16(3), 519–547.Google Scholar
Cont, R. and Kan, Y.H. (2008) Dynamic hedging of portfolio credit derivatives. SSRN: http://ssrn.com/abstract=1349847.CrossRefGoogle Scholar
Crouhy, M.C, Jarrow, R.A. and Turnbull, S.M. (2008) The subprime credit crisis of 07. Journal of Derivatives, 16(4), 81–110.Google Scholar
Danielsson, J., Embrechts, P., Goodhart, C, Keating, C, Muennich, F., Renault, O. and Shin, H. (2001) An academic response to Basel II. LSE Financial Markets Group. Special Paper Number 130.Google Scholar
Dinallo, E. (2009) American International Group: Examining what went wrong, government intervention, and implications for future regulation. Committee on Banking, Housing, and Urban Affairs. United States Senate. March 5 2009. Statement of Superintendent Eric Dinallo, New York State Insurance Department.Google Scholar
Duffie, D. (2008) Innovations in credit risk transfer: implications for financial stability. BIS Working Papers, Monetary and Economic Department, 255.Google Scholar
Embrechts, P. (2009) Copulas: a personal view. Journal of Risk and Insurance, 76(3), 639–650.Google Scholar
Embrechts, P., Kluppelberg, C. and Mikosch, T. (2008) Modelling Extremal Events for Insurance and Finance. Springer.Google Scholar
Embrechts, P., McNeil, A.J. and Straumann, D. (2002) Correlation and dependence in risk management: properties and pitfalls. In Dempster, M., editor, Risk Management: Value at Risk and Beyond, pages 176–223. Cambridge University Press. First appeared in 1998 as a RiskLab ETH Zurich report.CrossRefGoogle Scholar
Federal Reserve Board (2008a) September 16 2008, Press Release.Google Scholar
Federal Reserve Board (2008b) November 10 2008, Press Release.Google Scholar
Finger, C.C. (2005) Eating our own cooking. Risk Metrics Group, Research Monthly.Google Scholar
Finger, C.C. (2009) Testing hedges under the standard tranched credit pricing model. Risk-Metrics Journal, 9(1).Google Scholar
Föllmer, H. (2009) Alles richtig und trotzdem falsch? Anmerkungen zur Finanzkrise und zur Finanzmathematik. Preprint, Humboldt-Universität, Berlin.Google Scholar
Frey, R., McNeil, A.J. and Nyfeler, M.A. (2001) Copulas and credit models. Risk, pages 111–114.Google Scholar
Genest, C, Gendron, M. and Bourdeau-Brien, M. (2009) The advent of copulas in finance. European Journal of Finance, 15(7–8), 609–618.Google Scholar
Haldane, A.G. (2009a) Rethinking the financial network. Speech delivered at the Financial Student Association, Amsterdam. April 28 2009. http://www.bankofengland.co.uk/publications/speeches/2009/speech386.pdf. Google Scholar
Haldane, A.G. (2009b) Why banks failed the stress test. The basis for a speech given at the Marcus-Evans conference on Stress-Testing, 9-10 February 2009. February 13 2009. http://www.bankofengland.co.uk/publications/speeches/2009/speech374.pdf. Google Scholar
Hellwig, M.F. (2009) Systemic risk in the financial sector: an analysis of the subprime-mortgage financial crisis. De Economist, 157(2), 129–207.Google Scholar
IMF (2006) Global Financial Stability Report. Market developments and issues. April 2006. World Economic and Financial Surveys.Google Scholar
Jones, S. (2009) Of couples and copulas: the formula that felled Wall St. April 24 2009, Financial Times.Google Scholar
Keys, B.J., Mukherjee, T., Seru, A. and Vig, V. (2008) Financial regulation and securitization. Evidence from subprime loans. Journal of Monetary Economics, 56(5), 700–720.CrossRefGoogle Scholar
Kherraz, A. (2006) The May 2005 correlation crisis: did the models really fail? Portuguese Finance Network, 4th Finance Conference, July 6-8 2006, Porto, Portugal, http://www.fep.up.pt/conferencias/pfn2006/ConferencePapers/592.pdf.Google Scholar
Kohn, D.L. (2009) American International Group: Examining what went wrong, government intervention, and implications for future regulation. Committee on Banking, Housing, and Urban Affairs. United States Senate. March 5 2009. Statement of Donald L. Kohn, Vice Chairman, Board of Governors of the Federal Reserve System.Google Scholar
Li, D. (2000) On default correlation: a copula function approach. Journal of Fixed Income, 9(4), 43–54.CrossRefGoogle Scholar
Liedtke, P.M. (Ed.) (2010) Anatomy of the credit crisis. The Geneva Reports, Risk and Insurance Research, 3.Google Scholar
Lohr, S. (2009) Wall Street's math wizards forgot a few variables. September 12 2009, New York Times.Google Scholar
Markopolos, H. (2005) The world's largest hedge fund is a fraud. November 7 2005. Submission to the SEC.Google Scholar
McNeil, A.J., Frey, R. and Embrechts, P. (2005) Quantitative Risk Management. Concepts, Techniques, Tools. 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(2), 449–470.Google Scholar
Mollenkamp, C., Ng, S., Pleven, L. and Smith, R. (2008) Behind AIG's fall, risk models failed to pass real-world test. October 31 2008, Wall Street Journal.Google Scholar
Morgenson, G. (2008) Behind insurer's crisis: blind eye to a web of risk. September 28 2008, New York Times.Google Scholar
Nelsen, R.B. (2006) An Introduction to Copulas. Springer, second edition.Google Scholar
O'kane, D. (2008) Modelling Single-Name and Multi-Name Credit Derivatives. Wiley.Google Scholar
Polakoff, S.M. (2009) American International Group: Examining what went wrong, government intervention, and implications for future regulation. Committee on Banking, Housing, and Urban Affairs. United States Senate. March 5 2009. Statement of Scott M. Polakoff, Acting Director, Office of Thrift Supervision.Google Scholar
Resnick, S. (2007) Extreme Values, Regular Variation, and Point Processes. Springer.Google Scholar
Rogers, L.C.G. (2009) Financial mathematics and the credit crisis. Document in response to questions posed by Lord Drayson, UK Science and Innovation Minister.Google Scholar
Rogge, E. and Schönbucher, P.J. (2003) Modelling dynamic portfolio credit risk. Working paper.Google Scholar
Rutledge, W.L. (2008) Observations on risk management practices during the recent market turbulence. March 6 2008. Senior Supervisors Group, http://www.newyorkfed.org/newsevents/news/banking/2008/SSG_Risk_Mgt_doc_final.pdf. Google Scholar
Salmon, F. (2009) Recipe for disaster: the formula that killed Wall Street. February 23 2009, Wired Magazine.Google Scholar
Schönbucher, P.J. (2003) Credit Derivatives Pricing Models: Models, Pricing and Implementation. Wiley.Google Scholar
Schweizer, B. and Sklar, A. (1983) Probabilistic Metric Spaces. Elsevier Science Publishing Co.Google Scholar
SEC (2008) Summary report of issues identified in the commission staff's examinations of select credit rating agencies. July 8 2008, United States Securities and Exchange Commission, http://www.sec.gov/news/studies/2008/craexamination070808.pdf. Google Scholar
Sibuya, M. (1960) Bivariate extreme statistics. Annals of the Institute of Statistical Mathematics, 11, 195–210.Google Scholar
Sjostrom, W.K. Jr., (2009) The AIG bailout. Washington and Lee Law Review, 66, 943–991.Google Scholar
St Denis, J.W. (2008) Letter to Chairman Henry A. Waxman and Ranking Member Thomas M. Davis III from Joseph W. St Denis. Letter provided by Joseph W. St Denis to the Committee on Oversight and Government Reform, House of Representatives, USA, dated October 4 2008.Google Scholar
Stiglitz, J.E. (2008) It doesn't take Nostradamus. The Economists' Voice, 5(8). Article no. 1.Google Scholar
The Economist (2008). Confessions of a risk manager. August 7 2008.Google Scholar
Turner, J.A. (2009) The Turner Review. March 2009. Financial Services Authority, UK. http://www.fsa.gov.uk/pubs/other/turner_review.pdf. Google ScholarPubMed
Wallace, D. (2009) The Turner Review. Letter to Lord Turner, Financial Services Authority, UK. June 5 2009.Google Scholar
Whitehouse, M. (2005) Slices of risk: how a formula ignited market that burned some big investors. September 12 2005, Wall Street Journal.Google Scholar
Wolf, M. (2008) Regulators should intervene in bankers' pay. January 15 2008, Financial Times.Google Scholar