Efficient forecasting and uncertainty quantification for large scale account level Monte Carlo models of debt recovery

TL;DR

This paper develops efficient Monte Carlo simulation methods for large-scale debt recovery forecasting, enabling precise estimates and uncertainty quantification in heterogeneous portfolios of consumer loans.

Contribution

It introduces robust variance estimators that aggregate coarse individual account estimates, improving simulation efficiency at the portfolio level.

Findings

Effective variance estimation methods demonstrated on practical models.

Improved computational efficiency in large-scale Monte Carlo simulations.

Enhanced uncertainty quantification for debt recovery forecasts.

Abstract

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.