TITLE:
The Quantification of Model Risk According to the Principle of Relative Entropy with Case Studies
AUTHORS:
Michael Jacobs Jr.
KEYWORDS:
Cryptocurrencies, Model Risk, Asset Price Bubbles, Value-at-Risk, Relative Entropy, Constant Elasticity of Variance, Credit Risk, Probability of Default, Stress Testing
JOURNAL NAME:
Journal of Financial Risk Management,
Vol.14 No.2,
April
15,
2025
ABSTRACT: Risk measurement relies on modeling assumptions, the errors in which expose such models to model risk. In this study, we introduce and apply a tool for quantifying model risk and making risk measurement robust to modeling errors. As simplifying assumptions are inherent to all modeling frameworks, the prime directive of model risk management is to assess vulnerabilities to and consequences of model errors. In this study, consistent with this objective in model risk measurement, we focus on calculating bounds on measures of loss that can result over a range of model errors within a certain distance of a nominal model, for a range of alternative models. To this end, we quantify such bounds according to the principle of relative entropy. We illustrate the application of this principle through three case studies where the measure of loss varies according to the application: models for corporate probability-of-default (PD) considering alternative use cases (Aikakie Information Criterion), corporate obligor level PD stress testing (forecasted stressed PD estimates) and models for detecting asset price bubbles in cryptocurrency markets (normalized Value-at-Risk—VaR). Our principal finding is that model risk bounds differ in how they are measured significantly according to model methodology and use; and further that more complex parameterizations may not always be justified depending upon the modeling context. We contribute to the literature and practice in model risk management and measurement through proposing novel and practical tools that may be deployed across a range of modeling contexts by academics and practitioners.