Albanese, Claudio and Vidler, Alicia (2008): Dynamic Conditioning and Credit Correlation Baskets. Forthcoming in: The Complete Guide to CDOs - Market, Application, Valuation, and Hedging No. Book (1. July 2008)
Download (1MB) | Preview
Dynamic conditioning is a technique that allows one to formulate correlation models for large baskets without incurring in the curse of dimensionality. The individual price processes for each reference name can be described by a lattice model specified semi-parametrically or even nonparametrically and which can realistically have about 1000 sites. The time discretization step is chosen so small to satisfy the Courant stability condition and is typically of about a few hours. This constraint ensures needed smoothness for the single name probability kernels which can thus be directly manipulated. A flexible multi-factor correlation model can be obtained by means of conditioning trees corresponding to binomial processes with jumps. There is one conditioning tree associated to each reference names, one associated to each industry sector and a global one to the basket itself. Since the conditioning trees are correlated, the underlying processes are also mutually correlated.
In this paper, we discuss a modeling framework for CDOs based on dynamic conditioning in greater detail than previously done in our other papers. We also show that the model calibrates well to index tranches throughout in the period from 2005 to the Spring of 2008 and yields instructive insights.
|Item Type:||MPRA Paper|
|Original Title:||Dynamic Conditioning and Credit Correlation Baskets|
|Keywords:||CDO, pricing, dynamic conditioning, correlation modeling, semi-parametric, operator methods|
|Subjects:||E - Macroeconomics and Monetary Economics > E5 - Monetary Policy, Central Banking, and the Supply of Money and Credit > E50 - General
G - Financial Economics > G1 - General Financial Markets > G13 - Contingent Pricing ; Futures Pricing
|Depositing User:||Claudio Albanese|
|Date Deposited:||21. Apr 2008 14:06|
|Last Modified:||21. Feb 2013 13:54|
Albanese, C. (2006). Operator Methods, Abelian Path dependents and Dynamic Conditioning. preprint.
Albanese, C. (2007). Kernel Convergence Estimates for Diffusions with Continuous Coefficients. arXiv:0711.0132v1 [math.NA].
Albanese, C. and A. Osseiran (2007). Moment Methods for Exotic Volatility Derivatives. preprint.
Albanese, C. and A. Vidler (2006). A Structural Model for Credit-Equity Derivatives and Bespoke CDOs. Willmott Magazine.
Albanese, C. and O. Chen (2004). Implied migration rates from credit barrier model. The Journal of Banking and Finance, to appear.
Albanese, C. and O. Chen (2005a). Credit barrier models in a discrete framework. Contemporary Mathematics 351, Mathematical Finance pp. 1–11.
Albanese, C. and O. Chen (2005b). Discrete credit barrier models. Quantitative Finance 5, 247–256.
Albanese, C., J. Campolieti, O. Chen and A. Zavidonov (2003). Credit barrier models. Risk 16(6), 109–113.
Albanese, C., O. Chen, A. Dalessandro and A. Vidler (2005-2006). Dynamic Credit Correlation Modelling. preprint.
Andersen, Leif and Jakob Sidenius (2004). Extensions to the gaussian copula: random recovery and random factor loadings. Journal of Credit Risk 1, 1:29.
di Graziano, G. and C. Rogers (2006). A Dynamic Approach to the Modelling of Correlation Credit Derivatives Using Markov Chains. preprint, Cambridge University.
Duffie, D., J. Pan and K. Singleton (2000). Transform analysis and asset pricing for affine jumpd-iffusions. Econometrica.
Duffie, Darrell, Andreas Eckner, Guillaume Horel and Leandro Saita (2006). Frailty Correlated Default. preprint, Stanford University.
Giesecke, Kay and Lisa Goldberg (2005). A top down approach to multi-name credit. Working paper, Cornell University.
Hull, John and Alan White (2003). Valuation of a cdo and an n-th to-default cds without monte carlo simulation. Working paper, University of Toronto.
Joshi, Mark S. and Alan Stacey (2005). Intensity gamma: a new approach to pricing portfolio credit derivatives. Working paper, Royal Bank of Scotland.
Li, David. X. (2000). On default correlation: A copula function approach. working paper 99-07, Risk Metrics Group.
Lucas, A., P. Klaassen, P. Spreij and S. Staetmans (2001). An analytic approach to credit risk of large corporate bond and loan portfolios. Journal of Banking and Finance 9, 1635–1664.
O’Kane, D. and M. Livesey (2004). Base correlation explained. QCR Quarterly Q3/4, Lehman Brothers Fixed Income Quantitative Research.
Schonbucher, P. (2006). Portfolio losses and the term structure of loss transition rates: a new methodology for the pricing of portfolio credit derivatives. Working paper, ETHZ.