Quantification of model risk that is caused by model misspecification.

Area of Science:

• Financial Risk Management
• Statistical Modeling
• Credit Risk Analysis

Background:

• Model risk, particularly misspecification, is a critical concern in financial risk management.
• Probability of default (PD) models are essential for credit risk assessment but can be prone to misspecification.
• Quantifying model misspecification is crucial for ensuring the reliability of financial risk predictions.

Purpose of the Study:

• To develop and present a technique for quantifying model misspecification in binary response regression.
• To compare the performance of binary logistic regression and complementary log-log models in the context of probability of default modeling.
• To assess the impact of simulation iterations on model goodness-of-fit and performance measures.

Main Methods:

• Utilized maximum likelihood estimation for parameter estimation in both models.
• Assessed statistical inference through goodness-of-fit and model performance measurements.
• Employed simulation datasets and the Taiwan credit card default dataset for empirical analysis.

Main Results:

• Initially, both binary logistic regression and complementary log-log models showed similar goodness-of-fit with limited simulation iterations.
• Performance measures differed significantly between the two techniques even with small sample sizes and few iterations.
• With increased iterations, binary logistic regression demonstrated superior goodness-of-fit and performance metrics compared to complementary log-log, particularly on balanced datasets.

Conclusions:

• Binary logistic regression offers more robust performance and goodness-of-fit than complementary log-log for probability of default modeling, especially with sufficient data and iterations.
• Model misspecification can lead to divergent performance outcomes, highlighting the importance of careful model selection and validation in financial risk.
• The choice of statistical technique and the number of simulation iterations significantly influence the assessment of model reliability in credit risk analysis.