A new method to predict economic capital for the credit risk of a lending portfolio

We propose a method to compute the Value at Risk for a loan portfolio that involves predicting outstanding balance and repayment amounts, but not the probability of default directly. By modelling the behaviour of the borrowers in terms of repayments, balance and a default condition, we model the default occurrence more accurately than if we model the occurrence of default directly. We find that whilst including random effects increases the predictive accuracy of individual account performances, relatively simple structures give the most accurate predictions. We also find that, in terms of value at risk relative to expected loss, more complex random effects predict lower values at risk at more distant duration times whilst the omission of random effects leads to increasing values at risk over time. We compare the predicted amount of capital a bank should hold under our approach and under a standard approach and find that under certain circumstances, our approach indicates that considerably more capital should be held.