Claudio, Ferrarese (2006): A comparative analysis of correlation skew modeling techniques for CDO index tranches.

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Abstract
In this work we present an analysis of CDO pricing models with a focus on “correlation skew models”. These models are extensions of the classic single factor Gaussian copula and may generate a skew. We consider examples with fat tailed distributions, stochastic and local correlation which generally provide a closer fit to market quotes. We present an additional variation of the stochastic correlation framework using normal inverse Gaussian distributions. The numerical analysis is carried out using a large homogeneous portfolio approximation.
Item Type:  MPRA Paper 

Institution:  King’s College London 
Original Title:  A comparative analysis of correlation skew modeling techniques for CDO index tranches 
Language:  English 
Keywords:  default risks; CDOs; index tranches; factor model; copula; correlation skew; stochastic correlation 
Subjects:  C  Mathematical and Quantitative Methods > C6  Mathematical Methods ; Programming Models ; Mathematical and Simulation Modeling > C60  General C  Mathematical and Quantitative Methods > C0  General > C02  Mathematical Methods G  Financial Economics > G1  General Financial Markets > G12  Asset Pricing ; Trading Volume ; Bond Interest Rates 
Item ID:  1668 
Depositing User:  Claudio Ferrarese 
Date Deposited:  06. Feb 2007 
Last Modified:  11. Mar 2015 22:17 
References:  [1] E.I. Altman, A. Resti, and A. Sironi (2003) Default Recovery Rates in Credit Risk Modeling: A Review of the Literature and Empirical Evidence, Stern School of Business New York University, Bergamo University and Bocconi University, working paper, online at http://pages.stern.nyu.edu/ ealtman/Review1.pdf. [2] J. D. Amato and J. Gyntelberg (2005) CDS index tranches and the pricing of credit risk correlations Bank for International Settlements Quarterly Review, March, online at http://www.bis.org. [3] L. Andersen, J. Sidenius and S. Basu (2003) All your hedges in one basket, Risk, November, 6772. [4] L. Andersen and J. Sidenius (2005) Extension to the gaussian copula: Random recovery and random factor loadings, Journal of credit risk, 1(1), 2970. [5] O. E. BarndorNielsen (1998) Processes of normal inverse Gaussian type, Finance and Stochastics 2, 4168. [6] O. E. BarndorNielsen (1997) Normal inverse Gaussian distributions and stochastic volatility modelling, Scand. J. Statist. 24, 113. [7] Various authors (2005) Financial Stability Review, Bank of England, June, pg. 5558. [8] M. Baxter (2006) Levy Process Dynamic Modelling of SingleName Credits and CDO Tranches, Nomura Fixed Income Quant Group, working paper, online at www.nomura.com/resources/europe/pdfs/cdomodelling.pdf. [9] Various authors (2004) Credit derivatives: Valuing and Hedging Synthetic CDO Tranches Using Base Correlations, Bear Stearns. [10] T. Belsham N. Vause (2005) Credit Correlation: Interpretation and Risks, Financial Stability Review, Bank of England December. [11] F. Black and J. C. Cox (1976) Valuing corporate securities: some eects of bond indenture provisions, J. Finance 31, 351367. [12] C. Bluhm, L. Overbeck, and C. Wagner (2002) An Introduction to Credit Risk Modeling, Chapman Hall/CRC Financial Mathematics Series,Boca Raton. [13] D.C. Brody, L.P. Hughston and A. Macrina (2005) Beyond hazard rates: a new framework for creditrisk modelling, King’s College London and Imperial College London, Working paper, online at http://www.defaultrisk.com. [14] X. Burtschell, J. Gregory, and JP. Laurant (2005) A comparative analysis of cdo pricing models, ISFA Actuarial School and BNP Parisbas,working paper, online at http://www.defaultrisk.com. [15] X. Burtschell, J. Gregory, and JP. Laurant (2005) Beyond the gaussian copula: Stochastic and local correlation, ISFA Actuarial School and BNP Parisbas, working paper, online at http://www.defaultrisk.com. [16] G. Casella and R. L. Berger (2001) Statistical Inference, Duxbury Press, 2nd ed. [17] G. Chaplin (2005) Credit Derivatives: Risk Managment, Trading and Investing, Wiley. [18] U. Cherubini, E. Luciano and V. Vecchiato (2004) Copula methods in finance, Wiley Finance. [19] D. Due (1999) Credit Swap Valuation, Financial Analyst journal, 55(1), 7387. [20] B. Dupire (1994) Pricing with a smile, Risk 7, January, 1820. [21] A. Elizalde (2005) Credit Risk Models IV:Understanding and pricing CDOs, CEMFI and UPNA, working paper, online at www.cemfi.es/ elizalde. [22] C.C. Finger (2004) Issues in the pricing of synthetic CDOs, The Journal of Credit Risk, 1(1), 113124. [23] A. Friend and E. Rogge (2005) Correlation at first sight, Economic Notes 34, No. 2, 155183. [24] S.S. Galiani (2003) Copula functions and their application in pricing and risk managing multiname credit derivative products, Master Thesis Kings College London, working paper, online at http://www.defaultrisk.com. [25] S.S. Galiani, M. Shchetkovskiy and A. Kakodkar (2004). Factor Models for Synthetic CDO Valuation, Merrill Lynch Credit Derivatives. [26] L.P. Hughston and S. Turnbull (2000) Credit derivatives made simple. Risk 13, 3643. [27] J. Hull (2003) Options Futures and Other Derivatives Fifth edition, Prentice Hall. [28] J. Hull and A. White (2004) Valuation of a CDO and an nth default CDS without Monte Carlo Simulation. Journals of Derivatives 122, 823. [29] J. Hull and A. White (2005) The perfect copula, working paper, online at http://www.defaultrisk.com. [30] R.A. Jarrow and S.M. Turnbull (1995) Pricing derivatives on Fnancial securities subject to credit risk, J. Finance 50, 5385. [31] A. Kalemanova, B. Schmidt and R. Werner (2005) The normal inverse gaussian distribution for synthetic cdo pricing, working paper, online at http://www.defaultrisk.com. [32] D. Lando (1998) On Cox processes and credit risky securities, Department of Operational Research, University of Copenhagen, working paper. [33] JP. Laurant and J. Gregory (2005) I Will Survive, Risk, June, 103107. [34] JP. Laurant and J. Gregory (2003) Basket Default Swaps, CDOs and Factor Copulas, ISFA Actuarial School and BNP Parisbas, working paper, online at http://www.defaultrisk.com. [35] H. E. Leland and K. B. Toft (1996) Optimal capital structure, endogenous bankruptcy and the term structure of credit spreads, J. Finance 50, 789819. [36] D. Li. (2000) On default correlation: A copula function approach, Journal of Fixed Income 9,March, 4354. [37] D. Li. (1998) Constructing a credit curve, Credit Risk, a Risk Special report, November, 4044. [38] A. L¨uscher (2005) The normal Synthetic CDO pricing using the double inverse Gaussian copula with stochastic factor loadings, Diploma Thesis ETH Zurich, working paper, online at www.msfinance.ch/pdfs/AnnelisLuescher.pdf. [39] R. Mashal and A. Zeevi (2002) Beyond Correlation: Extreme Comovements Between Financial Assets, Columbia University, working paper. [40] L. McGinty, E. Beinstein, R. Ahluwalia, and M. Watts (2004) Introducing base correlations, Credit Derivatives Strategy JP Morgan. [41] R.C. Merton (1974) On the Pricing of Corporate Debt: The Risk Structure of Interest Rates, Journal of Finance, 29, MIT, 449470. [42] J. P. Nolan (1997) Numerical calculation of stable densities and distribution functions, Commun. Statist. Stochastic Models 13, 759774. [43] J. P. Nolan (2006) Stable Distributions  Models for Heavy Tailed Data, Boston: Birkh¨auser, In progress, Chapter 1 online at academic2. american.edu/ jpnolan. [44] D. Prange and W. Scherer(2006) Correlation Smile Matching with AlphaStable Distributions and Fitted Archimedan Copula Models, Risk Methodology Trading, Model Validation Credit Derivatives, Dresdner Kleinwort Wasserstein, online at http://www.defaultrisk.com. [45] L. Schloegl (2006) Stochastic Recovery Rates and NoArbitrage in the Tranche Markets, Fixed Income Quantitative Research Lehman Brothers, presentation at King’s College London Financial Mathematics seminars. [46] P.J. Sch¨onbucher (2000) Factor Models for Portfolio Credit Risk, Department of Statistics Bonn University, working paper. [47] P.J. Sch¨onbucher and E. Rogge. (2003) Modeling dynamic portfolio credit risk, working paper, online at www.finasto.unibonn.de/ schonbuc/papers/schonbucher rogge dynamiccreditrisk.pdf. [48] P.J. Sch¨onbucher (2003) Computational Aspects of Portfolio Credit Risk Managment, Risk Lab Workshop Computational Finance Z¨urich, September, working paper. [49] P.J. Sch¨onbucher (2003) Credit derivatives pricing models, Wiley. [50] P.A.C. Tavares Nguyen, T.U. Chapovsky and A. Vaysburd (2004). Composite basket model, Merrill Lynch Credit Derivatives. [51] J. Turc, P. Very and D. Benhamou (2005) Pricing CDOs with a smile,SG Credit Research. [52] O. Vasicek (1987) Probability of Loss on Loan Portfolio, KMV Corporation, technical report.. [53] O. Vasicek (1991) Limiting Loan Loss Probability Distribution, KMV Corporation, technical report. [54] M. van der Voort (2005) Factor copulas: Totally external defaults, ABN AMRO Bank and Erasmus University Rotterdam, working paper. [55] M. van der Voort (2006) An Implied Loss Model, ABN AMRO Bank and Erasmus University Rotterdam, working paper. 
URI:  https://mpra.ub.unimuenchen.de/id/eprint/1668 