The state-of-the-art in forecasting debt recovery from portfolios of non-performing unsecured consumer loans is to use stochastic models of payment behaviour of individual customers. Monte Carlo simulation of these models can enable forecasting of collections, where computational complexity arises from the very large number of heterogeneous accounts. We aim to solve 2 problems: efficient allocation of computational resources and quantification of uncertainty. We show that robust estimators of population-level variance can be constructed using unbiased estimators of the variance of individual accounts. The proposed methods are demonstrated through application to a model similar to those used in practice.
We consider the problem of forecasting debt recovery from large portfolios of non-performing unsecured consumer loans under management. The state of the art in industry is to use stochastic processes to approximately model payment behaviour of individual customers based on several covariates, including credit scores and payment history. Monte Carlo simulation of these stochastic processes can enable forecasting of the possible returns from portfolios of defaulted debt, and the quantification of uncertainty. Despite the fact that the individual-level models are relatively simple, it is challenging to carry out simulations at the portfolio level because of the very large number of accounts. The accounts are also heterogeneous, with a broad range of values for the collection variances. We aim to solve two main problems: efficient allocation of computational resources in the simulations to estimate the likely collections as precisely as possible, and quantification of the uncertainty in the forecasts. We show that under certain conditions, robust estimators of population-level variance can be constructed by summing over coarse unbiased estimators of the variance of individual accounts. The proposed methods are demonstrated through application to a model which shares key features with those that are used in practice.
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