Moody's Correlated Binomial Default Distributions for Inhomogeneous Portfolios

This paper generalizes Moody's correlated binomial default distribution for homogeneous (exchangeable) credit portfolio, which is introduced by Witt, to the case of inhomogeneous portfolios. As inhomogeneous portfolios, we consider two cases. In the first case, we treat a portfolio whose assets have uniform default correlation and non-uniform default probabilities. We obtain the default probability distribution and study the effect of the inhomogeneity on it. The second case corresponds to a portfolio with inhomogeneous default correlation. Assets are categorized in several different sectors and the inter-sector and intra-sector correlations are not the same. We construct the joint default probabilities and obtain the default probability distribution. We show that as the number of assets in each sector decreases, inter-sector correlation becomes more important than intra-sector correlation. We study the maximum values of the inter-sector default correlation. Our generalization method can be applied to any correlated binomial default distribution model which has explicit relations to the conditional default probabilities or conditional default correlations, e.g. Credit Risk${}^{+}$, implied default distributions. We also compare some popular CDO pricing models from the viewpoint of the range of the implied tranche correlation.Comment: 29 pages, 17 figures and 1 tabl

Default Estimation for Low-Default Portfolios

The problem in default probability estimation for low-default portfolios is that there is little relevant historical data information. No amount of data processing can fix this problem. More information is required. Incorporating expert opinion formally is an attractive option.

To Default or Not to Default?

Finanzmarktkrise; Wirtschaftskrise; Europäische Wirtschafts- und Währungsunion

Forecasting Credit Portfolio Risk

The main challenge of forecasting credit default risk in loan portfolios is forecasting the default probabilities and the default correlations. We derive a Merton-style threshold-value model for the default probability which treats the asset value of a firm as unknown and uses a factor model instead. In addition, we demonstrate how default correlations can be easily modeled. The empirical analysis is based on a large data set of German firms provided by Deutsche Bundesbank. We find that the inclusion of variables which are correlated with the business cycle improves the forecasts of default probabilities. Asset and default correlations depend on the factors used to model default probabilities. The better the point-in-time calibration of the estimated default probabilities, the smaller the estimated correlations. Thus, correlations and default probabilities should always be estimated simultaneously. --asset correlation,bank regulation,Basel II,credit risk,default correlation,default probability,logit model,probit model

Delayed Default Dependency and Default Contagion

Delayed, hence non-simultaneous, dependent defaults are discussed in a reduced form model. The model is a generalization of a multi-factor model based on simultaneous defaults to incorporate delayed defaults. It provides a natural smoothening of discontinuities in the joint probability densities in models with simultaneous defaults. It is a dynamic model that exhibits default contagion in a multi-factor setting. It admits an efficient Monte Carlo simulation algorithm that can handle heterogeneous collections of credit names. It can be calibrated to provide exact fits to CDX.NA.IG and iTraxx Europe CDOs just as its version with simultaneous defaults.Default Risk; Default Correlation; Default Contagion; Delayed Default; CDO; Monte Carlo