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Abstract

Modelling portfolio credit risk is one of the crucial challenges faced by financial services industry in the last few years. We propose the valuation model of collateralized debt obligations (CDO) based on copula functions with up to three parameters, with default intensities estimated from market data and with a random loss given default that is correlated with default times. The methods presented are used to reproduce the spreads of the iTraxx Europe tranches. We apply hierarchical Archimedean copulae (HAC) whose construction allows for the fact that the risky assets of the CDO pool are chosen from six different industry sectors. The dependence among the assets from the same group is specified with the higher value of the copula parameter, otherwise the lower value of the parameter is ascribed. The copula with two and three parameters models the relation between the loss given default and the default times. Our approach describes the market prices better than the standard pricing procedure based on the Gaussian distribution.

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File URL: http://sfb649.wiwi.hu-berlin.de/papers/pdf/SFB649DP2009-038.pdf
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Bibliographic Info

Paper provided by Sonderforschungsbereich 649, Humboldt University, Berlin, Germany in its series SFB 649 Discussion Papers with number SFB649DP2009-038.

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Length: 40 pages
Date of creation: Jul 2009
Date of revision:
Handle: RePEc:hum:wpaper:sfb649dp2009-038

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Web page: http://sfb649.wiwi.hu-berlin.de
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Related research

Keywords: CDO; CDS; multivariate distributions; Copulae; correlation smile; loss given default;

Find related papers by JEL classification:

• C13 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Estimation: General
• G12 - Financial Economics - - General Financial Markets - - - Asset Pricing
• G13 - Financial Economics - - General Financial Markets - - - Contingent Pricing; Futures Pricing
• G21 - Financial Economics - - Financial Institutions and Services - - - Banks; Other Depository Institutions; Micro Finance Institutions; Mortgages

This paper has been announced in the following NEP Reports:

• NEP-ALL-2009-07-28 (All new papers)
• NEP-UPT-2009-07-28 (Utility Models & Prospect Theory)

References

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1. Prantl, Susanne & Spitz-Oener, Alexandra, 2009. "How Does Entry Regulation Influence Entry into Self-Employment and Occupational Mobility?," IZA Discussion Papers 4221, Institute for the Study of Labor (IZA).
   
   • Susanne Prantl & Alexandra Spitz-Oener, 2009. "How does entry regulation influence entry into self-employment and occupational mobility?," The Economics of Transition, The European Bank for Reconstruction and Development, vol. 17(4), pages 769-802, October.
   • Susanne Prantl & Alexandra Spitz-Oener, 2009. "How does entry regulation influence entry into self-employment and occupational mobility?," IFS Working Papers W09/14, Institute for Fiscal Studies.
   • Prantl, Susanne & Spitz-Oener, Alexandra, 2009. "How does entry regulation influence entry into selfemployment and occupational mobility?," Discussion Paper Series of SFB/TR 15 Governance and the Efficiency of Economic Systems 267, Free University of Berlin, Humboldt University of Berlin, University of Bonn, University of Mannheim, University of Munich.
2. Katja Hanewald, 2009. "Mortality modeling: Lee-Carter and the macroeconomy," SFB 649 Discussion Papers SFB649DP2009-008, Sonderforschungsbereich 649, Humboldt University, Berlin, Germany.
3. Michael C. Burda & Battista Severgnini, 2009. "TFP Growth in Old and New Europe," SFB 649 Discussion Papers SFB649DP2009-033, Sonderforschungsbereich 649, Humboldt University, Berlin, Germany.
   
   • Michael C Burda & Battista Severgnini, 2009. "TFP Growth in Old and New Europe," Comparative Economic Studies, Palgrave Macmillan, vol. 51(4), pages 447-466, December.
4. Xu, Wei & Filler, Gunther & Odening, Martin & Okhrin, Ostap, 2009. "On the Systemic Nature of Weather Risk," 2009 Annual Meeting, July 26-28, 2009, Milwaukee, Wisconsin 49131, Agricultural and Applied Economics Association.
   
   • Wei Xu & Guenther Filler & Martin Odening & Ostap Okhrin, 2010. "On the systemic nature of weather risk," Agricultural Finance Review, Emerald Group Publishing, vol. 70(2), pages 267-284, August.
   • Guenther Filler & Martin Odening & Ostap Okhrin & Wei Xu, 2009. "On the Systemic Nature of Weather Risk," SFB 649 Discussion Papers SFB649DP2009-002, Sonderforschungsbereich 649, Humboldt University, Berlin, Germany.
   • Xu, Wei & Filler, Gunther & Odening, Martin & Okhrin, Ostap, 2009. "On the Systemic Nature of Weather Risk," 2009 Conference, August 16-22, 2009, Beijing, China 51426, International Association of Agricultural Economists.
5. Denis Belomestny, 2009. "Spectral estimation of the fractional order of a Lévy process," SFB 649 Discussion Papers SFB649DP2009-021, Sonderforschungsbereich 649, Humboldt University, Berlin, Germany.
6. Ulrike Busch & Dieter Nautz, 2009. "Controllability and Persistence of Money Market Rates along the Yield Curve: Evidence from the Euro Area," SFB 649 Discussion Papers SFB649DP2009-029, Sonderforschungsbereich 649, Humboldt University, Berlin, Germany.
   
   • Ulrike Busch & Dieter Nautz, 2010. "Controllability and Persistence of Money Market Rates along the Yield Curve: Evidence from the Euro Area," German Economic Review, Verein für Socialpolitik, vol. 11, pages 367-380, 08.
   • Busch, Ulrike & Nautz, Dieter, 2009. "Controllability and persistence of money market rates along the yield curve: evidence from the euro area," Discussion Papers 2009/5, Free University Berlin, School of Business & Economics.
7. Kremer, Stephanie & Bick, Alexander & Nautz, Dieter, 2009. "Inflation and growth: new evidence from a dynamic panel threshold analysis," Discussion Papers 2009/9, Free University Berlin, School of Business & Economics.
   
   • Stephanie Kremer & Alexander Bick & Dieter Nautz, 2013. "Inflation and growth: new evidence from a dynamic panel threshold analysis," Empirical Economics, Springer, vol. 44(2), pages 861-878, April.
   • Stephanie Kremer & Alexander Bick & Dieter Nautz, 2009. "Inflation and Growth: New Evidence From a Dynamic Panel Threshold Analysis," SFB 649 Discussion Papers SFB649DP2009-036, Sonderforschungsbereich 649, Humboldt University, Berlin, Germany.
8. Alessandra Amendola & Giuseppe Storti, 2009. "Combination of multivariate volatility forecasts," SFB 649 Discussion Papers SFB649DP2009-007, Sonderforschungsbereich 649, Humboldt University, Berlin, Germany.
9. Katja Hanewald & Thomas Post & Helmut Gründl, 2009. "Stochastic Mortality, Macroeconomic Risks, and Life Insurer Solvency," SFB 649 Discussion Papers SFB649DP2009-015, Sonderforschungsbereich 649, Humboldt University, Berlin, Germany.
   
   • Katja Hanewald & Thomas Post & Helmut Gr�ndl, 2011. "Stochastic Mortality, Macroeconomic Risks and Life Insurer Solvency," The Geneva Papers on Risk and Insurance - Issues and Practice, Palgrave Macmillan, vol. 36(3), pages 458-475, July.
   • Hanewald, Katja & Post, Thomas & Gründl, Helmut, 2011. "Stochastic mortality, macroeconomic risks, and life insurer solvency," ICIR Working Paper Series 01/11, International Center for Insurance Regulation (ICIR), Goethe University Frankfurt.
10. Edward I. Altman & Brooks Brady & Andrea Resti & Andrea Sironi, 2005. "The Link between Default and Recovery Rates: Theory, Empirical Evidence, and Implications," The Journal of Business, University of Chicago Press, vol. 78(6), pages 2203-2228, November.
11. Wolfgang Härdle & Alena Mysickova, 2009. "Stochastic Population Forecast for Germany and its Consequence for the German Pension System," SFB 649 Discussion Papers SFB649DP2009-009, Sonderforschungsbereich 649, Humboldt University, Berlin, Germany.
12. Ostap Okhrin & Yarema Okhrin & Wolfgang Schmid, 2009. "Properties of Hierarchical Archimedean Copulas," SFB 649 Discussion Papers SFB649DP2009-014, Sonderforschungsbereich 649, Humboldt University, Berlin, Germany.
13. Wolfgang Härdle & Ostap Okhrin, 2009. "De copulis non est disputandum - Copulae: An Overview," SFB 649 Discussion Papers SFB649DP2009-031, Sonderforschungsbereich 649, Humboldt University, Berlin, Germany.
14. Barbara Meller & Dieter Nautz, 2009. "The Impact of the European Monetary Union on Inflation Persistence in the Euro Area," SFB 649 Discussion Papers SFB649DP2009-037, Sonderforschungsbereich 649, Humboldt University, Berlin, Germany.
    
    • Meller, Barbara & Nautz, Dieter, 2009. "The impact of the European Monetary Union on inflation persistence in the euro area," Discussion Papers 2009/8, Free University Berlin, School of Business & Economics.
15. Roland Strausz, 2009. "Regulatory Risk under Optimal Incentive Regulation," SFB 649 Discussion Papers SFB649DP2009-006, Sonderforschungsbereich 649, Humboldt University, Berlin, Germany.
    
    • Roland Strausz, 2009. "Regulatory Risk under Optimal Incentive Regulation," CESifo Working Paper Series 2638, CESifo Group Munich.
16. Tijmen Daniëls & Henk Jager & Franc Klaassen, 2009. "Defending Against Speculative Attacks," SFB 649 Discussion Papers SFB649DP2009-011, Sonderforschungsbereich 649, Humboldt University, Berlin, Germany.
17. Ji Cao & Wolfgang Härdle & Julius Mungo, 2009. "A Joint Analysis of the KOSPI 200 Option and ODAX Option Markets Dynamics," SFB 649 Discussion Papers SFB649DP2009-019, Sonderforschungsbereich 649, Humboldt University, Berlin, Germany.
18. Bernd Droge & Deniz Dilan Karaman Örsal, 2009. "Panel Cointegration Testing in the Presence of a Time Trend," SFB 649 Discussion Papers SFB649DP2009-005, Sonderforschungsbereich 649, Humboldt University, Berlin, Germany.

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Citations

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Cited by:

1. Roland Strausz, 2010. "The Political Economy of Regulatory Risk," CESifo Working Paper Series 2953, CESifo Group Munich.
   
   • Roland Strausz, 2009. "The Political Economy of Regulatory Risk," SFB 649 Discussion Papers SFB649DP2009-040, Sonderforschungsbereich 649, Humboldt University, Berlin, Germany.
2. Michal Grajek & Lars-Hendrik Röller, 2009. "Regulation and Investment in Network Industries: Evidence from European Telecoms," ESMT Research Working Papers ESMT-09-004, ESMT European School of Management and Technology.
   
   • Michał Grajek & Lars-Hendrik R�ller, 2012. "Regulation and Investment in Network Industries: Evidence from European Telecoms," Journal of Law and Economics, University of Chicago Press, vol. 55(1), pages 189 - 216.
   • Michał Grajek & Lars-Hendrik Röller, 2009. "Regulation and Investment in Network Industries: Evidence from European Telecoms," SFB 649 Discussion Papers SFB649DP2009-039, Sonderforschungsbereich 649, Humboldt University, Berlin, Germany.
3. Maria Grith & Wolfgang Härdle & Juhyun Park, 2009. "Shape invariant modelling pricing kernels and risk aversion," SFB 649 Discussion Papers SFB649DP2009-041, Sonderforschungsbereich 649, Humboldt University, Berlin, Germany.

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