🤖 AI Summary
This study addresses the challenge of accurately attributing aggregate prediction bias to individual components within complex modeling frameworks. Within an expected loss framework, it formalizes traditional walk-through analysis, exposing its inherent sequential dependency limitations, and proposes two order-agnostic attribution methods: an extension of the Logarithmic Mean Divisia Index (LMDI) tailored to the expected loss structure, and a Shapley-value-based approach that averages marginal contributions. For the first time, both methods are systematically applied to a comprehensive suite of financial risk models incorporating probability of default (PD), loss given default (LGD), exposure at default (EAD), and survival model multiplier (SMM) components, along with Monte Carlo simulation layers. The authors derive efficient vectorized computation formulas, enabling empirical attribution on real-world portfolio scales in mere seconds of additional runtime, thereby substantially enhancing computational efficiency and result consistency while providing robust support for model validation and regulatory compliance.
📝 Abstract
Complex model suites composed of multiple interacting component models are widely used in financial forecasting and risk management. In model performance testing, including in-sample backtesting (BT) and out-of-sample ongoing performance monitoring (OPM), a material gap between a model-suite forecast and the realized outcome must often be attributed to individual component models for development, validation, and regulatory review. This paper studies this gap-attribution problem in the expected loss framework, where exposure at default (EAD), prepayment or single monthly mortality (SMM), probability of default (PD), and loss given default (LGD) interact multiplicatively and are aggregated across loans and projection periods. We first formalize standard walk analysis and show why its attribution is generally order dependent. We then adapt two order-independent attribution frameworks: an augmented Logarithmic Mean Divisia Index (LMDI) approach tailored to the expected-loss structure, and a more general Shapley value approach based on averaging marginal contributions over all component orderings. We derive both elementwise and vectorized formulas to support efficient implementation, with the additional computation time for gap attribution typically limited to a few seconds in practical portfolio-scale examples. Finally, we discuss the connections among walk analysis, LMDI, and Shapley attribution, and show how the attribution framework extends to model suites with an additional Monte Carlo simulation layer.