Tsui, L. K. (2010): Multi-Factor Bottom-Up Model for Pricing Credit Derivatives.
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In this note we continue the study of the stress event model, a simple and intuitive dynamic model for credit risky portfolios, proposed by Duffie and Singleton (1999). The model is a bottom-up version of the multi-factor portfolio credit model proposed by Longstaff and Rajan (2008). By a novel identification of independence conditions, we are able to decompose the loss distribution into a series expansion which not only provides a clear picture of the characteristics of the loss distribution but also suggests a fast and accurate approximation for it. Our approach has three important features: (i) it is able to match the standard CDS index tranche prices and the underlying CDS spreads, (ii) the computational speed of the loss distribution is very fast, comparable to that of the Gaussian copula, (iii) the computational cost for additional factors is mild, allowing for more ﬂexibility for calibrations and opening the possibility of studying multi-factor default dependence of a portfolio via a bottom-up approach. We demonstrate the tractability and efficiency of our approach by calibrating it to investment grade CDS index tranches.
|Item Type:||MPRA Paper|
|Original Title:||Multi-Factor Bottom-Up Model for Pricing Credit Derivatives|
|Keywords:||credit derivatives, CDO, bottom-up approach, multi-name, intensity-based, risk and portfolio.|
|Subjects:||C - Mathematical and Quantitative Methods > C0 - General > C02 - Mathematical Methods|
|Depositing User:||Lung Kwan Tsui|
|Date Deposited:||06. Jun 2010 02:41|
|Last Modified:||24. Feb 2013 20:05|
Andersen, L., J. Sidenius, and S. Basu, 2003: All your hedges in one basket. Risk, November.
Arnsdorf, M. and I. Halperin, 2008: Bslp: Markovian bivariate spread-loss model for portfolio credit derivatives. Journal of Computational Finance, 12, 77–100.
Bayraktar, E. and B. Yang, 2009: Multi-scale time-changed birth processes for pricing multi-name credit derivatives. Applied Mathematical Finance, 16(5), 429–449.
Brigo, D., A. Pallavicini, and R. Torresetti, 2007: CDO calibration with the dynamical generalized Poisson loss model. Risk Magazine, June.
Cont, R. and A. Minca, 2008: Extracting portfolio default rates from cdo spreads. Working paper, Columbia University.
Duffie, D. and N. Gˆrleanu, 2001: Risk and valuation of collateralized debt obligations. Financial Analysts Journal, 57, 41–59.
Duffie, D., J. Pan, and J. Singleton, 2000: Transform analysis and asset pricing for affine jump diffusions. Econometrica, 68, No. 6 (November).
Duﬃe, D. and K. Singleton, 1999: Simulating correlated defaults, graduate School of Business, Stanford University.
Eckner, A., 2009: Computational techniques for basic aﬃne models of portfolio credit risk. Journal of Computational Finance, 13.
Errais, E., K. Giesecke, and L. Goldberg, 2006: Pricing credit from top down with affine point processes. Working paper, Stanford University.
Giesecke, K., L. Goldberg, and X. Ding, 2010: A top-down approach to multi-name credit. Operations Research, forthcoming.
Hamilton, D., P. Varma, S. Ou, and R. Cantor, 2004: Default and recovery rates of corporate bond issuers. Moody’s Investors Service, New York, January.
Joshi, M. and A. Stacey, 2006: Intensity gamma: A new approach to pricing portfolio credit derivatives. RISK, 19, July 78–83.
Longstaff, F. and A. Rajan, 2008: An empirical analysis of the pricing of collateralized debt obligations. Journal of Finance, 63, 529–563.
Mortensen, A., 2006: Semi-analytical valuation of basket credit derivatives in intensity-based models. Journal of Derivatives, 13, No. 4, 8–26.
O’Kane, D., 2008: Modelling Single-name and Multi-name Credit Derivatives. The Wiley Finance Series.
Papageorgiou, E. and R. Sircar, 2007: Multiscale intensity models and name grouping for valuation of multi-name credit derivatives. Applied Mathematical Finance, 15(1), 73–105.
Peng, X. and S. S. G. Kou, 2008: Default clustering and valuation of collateralized debt obligations. Working paper, Columbia University.
Schonbucher, P., 2003: Credit Derivatives Pricing Models. John Wiley & Son Ltd.
Shelton, D., 2004: Back to normal, proxy integration: A fast accurate method for cdo and cdo-squared pricing. Citigroup Structured Credit Research, August.
Tsui, L. K., 2010: Exact numerical algorithm for n-th order derivative of a single variable function. Working paper, University of Pittsburgh.