Ebook Modelling LGD for unsecured personal loans: Decision tree approach
The New Basel Accord allows a bank to calculate credit risk capital requirements according to either of two approaches: a standardized approach which uses agency ratings for risk-weighting assets and internal ratings based (IRB) approach which allows a bank to use internal estimates of components of credit risk to calculate credit risk capital. Institutions using IRB need to develop methods to estimate the following components for each segment of their loan portfolio:
- – PD (probability of default in the next 12 months);
– LGD (loss given default);
– EAD (expected exposure at default).
Modelling PD, the probability of default has been the objective of credit scoring systems for fifty years but modelling LGD is not something that had really been addressed in consumer credit until the advent of the Basel regulations. What LGD modelling had been done was mainly in the corporate lending market where LGD (or its opposite Recovery Rate RR, where RR=1-LGD), was needed as part of the more sophisticated bond pricing formulae. Even there, until fifteen years ago LGD was assumed to be a deterministic value obtained from a historical analysis of bond losses or from bank work out experience (Altman et al 1977). Only when it was recognised that LGD was needed for the pricing formula for non-defaulted risky bonds and hence one can use their values to estimate LGD were models of LGD developed. If defaults are rare in a particular bond class then it is likely the LGD got from the bond price is essentially a subjective judgment by the market.
The market also trades and hence prices defaulted bonds and so one can get directly market values of the bonds after reorganisation or restructuring of the finances of the defaulting firm (Altman and Eberhart 1994). These market values or implied market values of Loss Given Default were then used to build regression models that related LGD to relevant factors, such as the seniority of the debt, country of issue, size of issue and size of firm, industrial sector of firm but most of all to economic conditions which determined where the economy was in relation to the business cycle. The need for such models was identified by Altman and Kishore ( Altman and Kishore 1996) and reviews of some of the models are given in several recent books (Altman, Resti, Sironi 2005, de Servigny and Oliver 2004, Engelmann and Rauhmeier 2006). Such modelling is not appropriate for consumer credit LGD models since there is no continuous pricing of the debt as is the case on the bond market.
The Basel Accord (BCBS 2004 paragraph 465) suggests using implied historic LGD as one approach in determining LGD for retail portfolios. This involves identifying the realised losses (RL) per unit amount loaned in a segment of the portfolio and then if one is able to estimate the default probability PD for that segment, one can calculate LGD since RL=LGD.PD. One difficulty with this approach is that it is accounting losses that are often recorded and not the actual economic losses, which should include the collection costs and any repayments after a write-off. Also since LGD must be estimated at the segment level of the portfolio, if not at the individual loan level there is often insufficient data in some segments to make robust estimated.
The alternative method suggested in the Basel Accord is to model the collections or work out process. Such data was used by Dermine and Neto de Carvalho ( Dermine and Neto de Carvalho 2006) for bank loans to small and medium sized firms in Portugal, but they used a regression approach, al beit a log-log form of the regression to estimate the data. The purpose of this paper is to investigate how to model the collections process in order to get a handle on LGD estimates in unsecured consumer lending.
The idea of using the collection process to model LGD was suggested for mortgages by Lucas (2006). The collection process was split into whether the property was repossessed and the loss if there was repossession. So a scorecard was built to estimate the probability of repossession and then a model used to estimate the “haircut” the percentage of the estimated sale value of the house that is actually realised at sale time.
In this paper we introduce a decision tree model of a collections process for unsecured consumer loans. When we look at the repayment sub-models within this overall approach we will describe them by using a case study involving data from an in house collections process for personal loans. This consisted of collections data on 50K personal loans over the period from 1989 to 2004. In section two we describe the general decision tree model and why it is important to separate out the decisions of the lender from the uncertainty about the debtor’s behaviour. In section three we explain why one needs to distinguish classes of defaulters in the repayment sub model, while in section four we investigate how to distinguish these classes of defaulters using logistic regression on the personal loan data. In section five we suggest how a regression approach may be appropriate for estimating LGD within a class, while in section 6 we summarise the results obtained.
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