Modelling Credit Risk: the loss distribution of a loan portfolio

Abstract

The aim of this work is to present a methodology that allows in a simple way to compute the regulatory capital for credit risk. The Vasicek model is a popular one-factor model that derives the limiting form of the portfolio loss. This model will allow calculating different risk measures such as, for example, the expected loss (EL), the value at risk (VaR) and the Expected Shortfall (ES). Due to the difficulty of obtaining real data, simulated data were used. For this study, three different portfolios were proposed: the first was a homogeneous portfolio that had the same weighting among all loans, then a portfolio with unequal weights was considered and finally a mixed portfolio with different weights and different probabilities of default was used. Monte Carlo simulation with 100.000 scenarios served as our benchmark. It was observed that the Vasicek model correctly estimates the results of the homogeneous portfolio. On the other hand, when the portfolio is not homogeneous (portfolio unequal weights and mixed) the Vasicek model correctly estimates the mean (Expected Losses) but underestimates the Value at Risk and the Expected Shortfall. This is because the approximation of the Vasicek model is good on average but not at the extremes.