Confidence sets for asset correlations in portfolio credit risk

Asset correlations are of critical importance in quantifying portfolio credit risk and economic capital in financial institutions. Estimation of asset correlation with rating transition data has focused on the point estimation of the correlation without giving any consideration to the uncertainty around these point estimates. In this article we use Bayesian methods to estimate a dynamic factor model for default risk using rating data (McNeil et al., 2005; McNeil and Wendin, 2007). Bayesian methods allow us to formally incorporate human judgement in the estimation of asset correlation, through the prior distribution and fully characterize a confidence set for the correlations. Results indicate: i) a two factor model rather than the one factor model, as proposed by the Basel II framework, better represents the historical default data. ii) importance of unobserved factors in this type of models is reinforced and point out that the levels of the implied asset correlations critically depend on the latent state variable used to capture the dynamics of default, as well as other assumptions on the statistical model. iii) the posterior distributions of the asset correlations show that the Basel recommended bounds, for this parameter, undermine the level of systemic risk.