M.C. So

Using a transactor/revolver scorecard to make credit and pricing decisions

In consumer lending the traditional approach is to develop a credit scorecard which ranks borrowers according to their risk of defaulting. Bads have a high risk of default and Goods have a low risk. To maximise the profitability of credit card customers, a second classification between revolvers and transactors becomes important. Building a transactor/revolver scorecard together with a Good/Bad scorecard over the revolvers, gives rise to a risk decision system whose ranking of risk is comparable with the standard approach. The paper develops a profitability model of card users including the transactor/revolver score leads. This gives more accurate profitability estimates than models which ignore the transactor/revolver split.

Modelling repayment patterns in the collections process for unsecured consumer debt: a case study

One approach to modelling Loss Given Default (LGD), the percentage of the defaulted amount of a loan that a lender will eventually lose is to model the collections process. This is particularly relevant for unsecured consumer loans where LGD depends both on a defaulters ability and willingness to repay and the lenders collection strategy. When repaying such defaulted loans, defaulters tend to oscillate between repayment sequences where the borrower is repaying every period and non-repayment sequences where the borrower is not repaying in any period. This paper develops two models – one a Markov chain approach and the other a hazard rate approach to model such payment patterns of debtors. It also looks at simplifications of the models where one assumes that after a few repayment and non-repayment sequences the parameters of the model are fixed for the remaining payment and non-payment sequences. One advantage of these approaches is that they show the impact of different write-off strategies. The models are applied to a real case study and the LGD for that portfolio is calculated under different write-off strategies and compared with the actual LGD results.

When to Rebuild or When to Adjust Scorecards

Data-based scorecards, such as those used in credit scoring, age with time and need to be rebuilt or readjusted. Unlike the huge literature on modelling the replacement and maintenance of equipment there have been hardly any models that deal with this problem for scorecards. This paper identifies an effective way of describing the predictive ability of the scorecard and from this describes a simple model for how its predictive ability will develop. Using a dynamic programming approach one is then able to find when it is optimal to rebuild and when to readjust a scorecard. Failing to readjust or rebuild a scorecard when they aged was one of the defects in credit scoring identified in the investigations into the sub-prime mortgage crisis.

A simheuristic approach to the vehicle ferry revenue management problem

We propose a Simheuristic approach to the vehicle ferry revenue management problem, where the aim is to maximize the revenue by varying the prices charged to different vehicle types, each occupying a different amount of deck space. Customers arrive and purchase tickets according to their vehicle type and their willingness-to-pay, which varies over time. The optimization problem can be solved using dynamic programming but the possible states in the selling season are the set of all feasible vehicle mixes that fit onto the ferry. This makes the problem intractable as the number of vehicle types increases. We propose a state space reduction, which uses a vehicle ferry loading simulator to map each vehicle mix to a remaining-space state. This reduces the state space of the dynamic program, enabling it to be solved rapidly. We present simulations of the selling season using this reduced state space to validate the method.

Lending decisions with limits on capital available: the polygamous marriage problem

In order to stimulate or subdue the economy, banking regulators have sought to impose caps or floors on individual banks lending to certain types of borrowers. This paper shows that the resultant decision problem for a bank of which potential borrower to accept is a variant of the marriage/secretary problem where one can accept several applicants. The paper solves the decision problem using dynamic programming. We give results on the form of the optimal lending problem and counter examples to further “reasonable” conjectures which do not hold in the general case. By solving numerical examples we show the potential loss of profit and the inconsistency in the lending decision that are caused by introducing floors and caps on lending. The paper also describes some other situations where the same decision occurs.

Stress testing credit card portfolios: an application in South Africa

Motivated by a real problem, this study aims to develop models to conduct stress testing on credit card portfolios. Two modelling approaches were extended to include the impact of lenders’ actions within the model. The first approach was a regression model of the aggregate losses based on economic variables with autocorrelations of the errors. The second approach was a set of vintage-level models that highlighted the months-on-book effect on credit losses. A case study using the models was described using South African credit card data. In this case, the models were used to stress test the credit card portfolio under several economic scenarios.