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.
翻译:我们考虑了从管理下大量不良无担保消费贷款组合中预测债务回收的问题。行业的先进经验是利用随机程序,根据若干共变办法,包括信用分数和支付历史,大致模拟个别客户的支付行为模式。蒙特卡洛模拟这些互换过程,可以预测违约债务组合的可能回报,并对不确定性进行量化。尽管个人一级模型相对简单,但在组合一级进行模拟是困难的,因为账户数量很大。账户也是多种多样的,收集差异的数值范围很广。我们的目标是解决两个主要问题:在模拟中有效分配计算资源,以尽可能准确地估计可能的收款,并对预测中的不确定性进行量化。我们表明,在某些条件下,对个别账户差异的不均匀的估算值进行总结,可以形成对人口层面差异的有力估计。建议的方法通过应用一个模型加以证明,该模型与实践中使用的关键特征分享。