Merton structural model and IRB compliance

Abstract

This paper discusses the 1974 Merton's model in light of the minimum regulatory requirements of the Internal Ratings-Based (IRB) Approach provided in the Directive 2006/48/EC of the European Parliament and of the Council for the calculation of capital requirement for credit risk. The basic purpose is to illustrate potential deficiencies of the model in assigning obligors ratings and/or estimating probability of default to which supervisors should be attentive when validating this model in bank's IRB approach. The procedures of three estimation methods of Merton's model are described (calibration, Moody's KMV, maximum likelihood estimation), based on which deficiencies of this model can be identified. The Merton's model per se does not ensure compliance with the minimum requirements of the IRB approach for the estimation of probability of default, as its theoretical assumptions often do not reflect reality. It is therefore necessary to calibrate the fundamental parameters estimated by the model using empirical data on defaults, which must be defined in accordance with the regulatory minimum requirements, and must be representative of the population for which the model is valid. Results on the simulated data also show that calibration method provides different estimates of probability of default for the same obligors compared to other two methods. Differences are mainly influenced by the volatility of equity and leverage in the time series, which calibration method does not sufficiently account for. Some regulatory minimum requirements can be relaxed when obligors are being assigned ratings on the basis of the Merton's model estimation methods. However, the results of the analysis on simulated and empirical data show that different estimation methods generate different obligor credit rating assignments.