Latent Variable Approach to Modelling Dependence of Credit Risks: Application to French Firms and Implications for Regulatory Capital

Abstract

This paper extends the analysis in Migration Correlation: Estimation Method and Application to the French Companies Rated by the Banque de France and provides a methodology for valuing dependent defaults based on the latent variable approach. This methodology underlies all models derived from the Merton's structural model and includes in particular the Basel II proposition. The latent correlation is calibrated by developing factor models that relate changes in unobservable variable to changes in a small number of economic factors. Our model exploits the relationship between the default correlation and the latent correlation throughout the joint probability of default. Using a comprehensive rating database managed by the Banque de France, we employ this relationship to calibrate latent correlations and finally to compute credit risk charges at a portfolio level.

Keywords: Latent correlation, default correlaiton, rating, credit risk, factor models, new basel accord

JEL Classification: G21, G33, C13