The lifetime behaviour of loans is notoriously difficult to model, which can compromise a bank's financial reserves against future losses, if modelled poorly. Therefore, we present a data-driven comparative study amongst three techniques in modelling a series of default risk estimates over the lifetime of each loan, i.e., its term-structure. The behaviour of loans can be described using a nonstationary and time-dependent semi-Markov model, though we model its elements using a multistate regression-based approach. As such, the transition probabilities are explicitly modelled as a function of a rich set of input variables, including macroeconomic and loan-level inputs. Our modelling techniques are deliberately chosen in ascending order of complexity: 1) a Markov chain; 2) beta regression; and 3) multinomial logistic regression. Using residential mortgage data, our results show that each successive model outperforms the previous, likely as a result of greater sophistication. This finding required devising a novel suite of simple model diagnostics, which can itself be reused in assessing sampling representativeness and the performance of other modelling techniques. These contributions surely advance the current practice within banking when conducting multistate modelling. Consequently, we believe that the estimation of loss reserves will be more timeous and accurate under IFRS 9.

翻译：贷款的全生命周期行为建模难度极高，若建模不当将损害银行对未来损失的财务储备能力。为此，我们提出一项数据驱动的比较研究，针对三种技术对每笔贷款全生命周期内违约风险估计序列（即期限结构）进行建模。贷款行为可通过非平稳时变半马尔可夫模型描述，但我们采用基于多状态回归的方法对其要素进行建模。具体而言，转移概率被明确建模为包含宏观经济变量和贷款层面输入在内的丰富输入变量集的函数。我们的建模技术按复杂度递增顺序精心选择：1）马尔可夫链；2）贝塔回归；3）多元逻辑回归。基于住房抵押贷款数据的实证结果表明，随着模型复杂度的提升，每个后续模型均优于前序模型。这一发现促使我们设计了一套新颖的简易模型诊断方法，该方法可复用于评估抽样代表性及其他建模技术的性能。这些成果无疑将推动银行业在多状态建模领域的现行实践。据此我们认为，在《国际财务报告准则第9号》框架下，损失准备金估算将更具时效性与精确性。