Default Correlations and Large-Portfolio Credit Analysis

A factor model with sparsely correlated residuals is used to model short-term probabilities of default and other corporate exits while permitting missing data, and serves as the basis for generating default correlations. This novel factor model can then be used to produce portfolio credit risk profiles (default-rate and portfolio-loss distributions) by complementing an existing credit portfolio aggregation method with a novel simulation–convolution algorithm. We apply the model and the portfolio aggregation method on a global sample of 40,560 exchange-listed firms and focus on three large portfolios (the U.S., Eurozone-12, and ASEAN-5). Our results reaffirm the critical importance of default correlations. With default correlations, both default-rate and portfolio-loss distributions become far more right-skewed, reflecting a much higher likelihood of defaulting together. Our results also reveal that portfolio credit risk profiles evaluated at two different time points can change drastically with moving economic conditions, suggesting the importance of modeling credit risks with a dynamic system. Our factor model coupled with the aggregation algorithm provides a useful tool for active credit portfolio management.

[1]  Cun-Hui Zhang.  Nearly unbiased variable selection under minimax concave penalty , 2010, 1002.4734.

[2]  Weidong Liu,et al.  Adaptive Thresholding for Sparse Covariance Matrix Estimation , 2011, 1102.2237.

[3]  Ke Wang,et al.  Multi-Period Corporate Default Prediction with Stochastic Covariates , 2005 .

[4]  D. Duffie,et al.  Frailty Correlated Default , 2006 .

[5]  David X. Li.  On Default Correlation: A Copula Function Approach , 1999 .

[6]  Jianqing Fan,et al.  Large covariance estimation by thresholding principal orthogonal complements , 2011, Journal of the Royal Statistical Society. Series B, Statistical methodology.

[7]  Mark H. A. Davis,et al.  Modelling default correlation in bond portfolios , 1999 .

[8]  Martin J. Wainwright,et al.  Noisy matrix decomposition via convex relaxation: Optimal rates in high dimensions , 2011, ICML.

[9]  Using distortions of copulas to price synthetic CDOs , 2008 .

[10]  P. Bickel,et al.  Regularized estimation of large covariance matrices , 2008, 0803.1909.

[11]  Inderjit S. Dhillon,et al.  Guaranteed Rank Minimization via Singular Value Projection , 2009, NIPS.

[12]  Tony Concil,et al.  A top-down approach , 2011 .

[13]  Leif B. G. Andersen,et al.  Extensions to the Gaussian Copula: Random Recovery and Random Factor Loadings , 2005 .

[14]  Oldrich A Vasicek,et al.  Probability of Loss on Loan Portfolio , 2015 .

[15]  J. Friedman,et al.  A Statistical View of Some Chemometrics Regression Tools , 1993 .

[16]  Cornell University,et al.  Cyclical correlations , credit contagion , and portfolio losses , 2003 .

[17]  Xiaowei Ding,et al.  A Top-Down Approach to Multiname Credit , 2011, Oper. Res..

[18]  Jianqing Fan,et al.  Variable Selection via Nonconcave Penalized Likelihood and its Oracle Properties , 2001 .

[19]  Jianqing Fan,et al.  High dimensional covariance matrix estimation using a factor model , 2007, math/0701124.

[20]  Jianqing Fan,et al.  High Dimensional Covariance Matrix Estimation in Approximate Factor Models , 2011, Annals of statistics.

[21]  Alan G. White,et al.  Valuation of a CDO and an n-th to Default CDS Without Monte Carlo Simulation , 2004 .

[22]  David X. Li,et al.  A Comparative Analysis of Correlation Approaches in Finance , 2013, The Journal of Derivatives.

[23]  R. Tibshirani,et al.  Regression shrinkage and selection via the lasso: a retrospective , 2011 .

[24]  Jianqing Fan,et al.  COMMENTS ON « WAVELETS IN STATISTICS : A REVIEW , 2009 .

[25]  Jin-Chuan Duan,et al.  Clustered Defaults , 2010 .

[26]  P. Schönbucher,et al.  Copula-Dependent Defaults in Intensity Models , 2001 .

[27]  J. Friedman,et al.  [A Statistical View of Some Chemometrics Regression Tools]: Response , 1993 .

[28]  R. Jarrow,et al.  Counterparty Risk and the Pricing of Defaultable Securities , 1999 .

[29]  J. Stock,et al.  Macroeconomic Forecasting Using Diffusion Indexes , 2002 .

[30]  Jianqing Fan,et al.  Comments on «Wavelets in statistics: A review» by A. Antoniadis , 1997 .

[31]  R. Tibshirani.  Regression Shrinkage and Selection via the Lasso , 1996 .

[32]  Tao Wang,et al.  Multiperiod Corporate Default Prediction - A Forward Intensity Approach , 2012 .

[33]  David X. Li.  On Default Correlation , 2000 .

[34]  Alexander J. McNeil,et al.  Modelling dependent defaults , 2001 .

[35]  Yi Ma,et al.  Robust principal component analysis? , 2009, JACM.

[36]  Karim Lounici.  High-dimensional covariance matrix estimation with missing observations , 2012, 1201.2577.

[37]  Philipp J. Schönbucher,et al.  Factor Models: Portfolio Credit Risks When Defaults are Correlated , 2001 .

[38]  Pablo A. Parrilo,et al.  Rank-Sparsity Incoherence for Matrix Decomposition , 2009, SIAM J. Optim..

[39]  D. Duffie,et al.  Common Failings: How Corporate Defaults are Correlated , 2006 .

[40]  J. Duan,et al.  Multiperiod Corporate Default Prediction with the Partially-Conditioned Forward Intensity , 2013 .

[41]  Adam J. Rothman,et al.  Generalized Thresholding of Large Covariance Matrices , 2009 .

[42]  Joost Driessen.  Is Default Event Risk Priced in Corporate Bonds , 2002 .

[43]  Ke Wang,et al.  Multi-Period Corporate Default Prediction with Stochastic Covariates , 2005 .

[44]  P. Bickel,et al.  Covariance regularization by thresholding , 2009, 0901.3079.

[45]  Correlated Defaults in Intensity-Based Models , 2005 .

[46]  G. Duffee.  Estimating the Price of Default Risk , 1996 .

[47]  K. Giesecke,et al.  Premia for Correlated Default Risk , 2008 .

[48]  Alexey Kuznetsov,et al.  Affine Markov chain model of multifirm credit migration , 2007 .

[49]  Michael B. Gordy.  Saddlepoint approximation of CreditRisk , 2002 .