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

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 collections from portfolios of defaulted debt.
Even though 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 heterogeneous accounts, 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, under the constraint that all the accounts must be simulated to enable valuation at the account level. 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.