信用行为的函数表示用于违约概率建模
A Functional Representation of Credit Behavior for Probability of Default Modeling
- Nykredit
- Aalborg University（奥尔堡大学）
- Advisense
机构由 AI 辅助整理，请以论文原文为准。
AI总结：
本文提出基于函数数据分析的违约概率建模框架，将信用变量表示为连续过程，并开发相对时间框架对齐周期性事件，在保持线性模型可解释性的同时达到与XGBoost相当的预测性能。
AI中文摘要：
本文提出了一个通过函数数据分析对违约概率进行建模的框架。通过将一系列信用变量表示为函数，我们研究了线性模型中月内信息是否能提高违约预测能力。我们进一步展示了多种广泛使用的变量，包括可用资金、利用率和透支，都可以从随时间观测的三个量中推导出来，即：1）每个账户的类型，2）账户余额，以及3）账户的信用额度大小。将这些量保留为连续时间过程，而不是将其简化为月度汇总值，可以产生对借款人的连续忠实表示。在分析这三个过程时，我们发现与银行工作日中的序数位置相关的重复事件产生了强烈的周期性模式。因此，我们开发了一个相对时间框架，将不同借款人之间的重复事件对齐，确保借款人具有相同的周期性模式，而无论实际时间如何。我们使用函数逻辑回归评估该框架。这种方法适应连续表示，同时与信用风险实践中常用的逻辑回归模型保持紧密相关，这得益于严格的监管约束。我们表明，当配备有效的交易轨迹函数表示时，所提出的模型达到了与XGBoost相当的预测性能，同时始终优于逻辑回归。重要的是，该模型在机器学习模型的预测性能与线性违约模型的可解释性之间取得了平衡，可能使金融机构即使在严格监管下也能使用该模型。
英文摘要：
This paper proposes a framework for modeling probability of default via functional data analysis. By representing a series of credit variables as functions, we investigate whether intra-monthly information improves default predictability in linear models. We further show how a range of widely used variables, among them available funds, utilization rate, and overdraft, can all be derived from three quantities observed over time. Namely, 1) the type of each account, 2) the balance of the account, and 3) the size of the credit limit on the account. Retaining these quantities as continuous-time processes, rather than reducing them to monthly aggregated values, yields a continuous faithful representation of the borrower. When analyzing these three processes, we discovered that recurring events associated with the ordinal position among banking days created strong cyclical patterns. We therefore develop a relative time framework that aligns the recurring events across borrowers, ensuring that borrowers possess the same cyclical pattern, regardless of real time. We assess the framework using functional logistic regression. This approach accommodates the continuous representation while remaining closely related to a logistic regression model commonly used in credit risk practice, due to strict regulatory constraints. We show that, when equipped with an effective functional representation of transactional trajectories, the proposed model attains predictive performance on par with XGBoost while consistently outperforming logistic regression. Importantly, the model balances predictive performance of a machine learning model with the interpretability of linear default models, potentially enabling financial institutions to use the model, even under strict regulation.
