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：贷款的存续期行为建模极为困难，若建模不当，可能损害银行抵御未来损失的财务储备。因此，我们开展了一项数据驱动的比较研究，评估了三种技术对每笔贷款存续期内一系列违约风险估计值（即其期限结构）的建模效果。贷款行为可使用非平稳且时间依赖的半马尔可夫模型描述，但我们采用基于多重状态回归的方法对其各要素进行建模。据此，转移概率被显式建模为一组丰富输入变量（包括宏观经济变量和贷款层面变量）的函数。我们特意按复杂度递增顺序选择了三种建模技术：1）马尔可夫链；2）贝塔回归；3）多项逻辑回归。利用住房抵押贷款数据的实证结果表明，每个后续模型均优于前序模型，这很可能源于其更高的复杂程度。这一发现需要设计一套新颖的简易模型诊断工具，该工具本身可复用于评估抽样代表性及其他建模技术的性能。这些贡献无疑推进了银行业当前在进行多重状态建模时的实践。因此，我们相信在IFRS 9准则下，损失储备的估算将更为及时和准确。