Borrower Level Models for Stress Testing Corporate Probability of Default and the Quantification of Model Risk
Bibliographic record
Abstract
This paper addresses the building of obligor level hazard rate corporate probability-of-default (“PD”) models for stress testing, departing from the predominant practice in wholesale credit modeling of constructing segment level models for this purpose. We build models based upon varied of financial, credit rating, equity market and macroeconomic factors with an extensive history of large corporate firms sourced from Moody’s. We develop distance-to-default (“DTD”) risk factors and design hybrid structural/Merton-reduced form models as challengers to versions of the models containing only the other variables. We measure the model risk attributed to various modeling assumptions according to the principle of relative entropy and observe that the omitted variable bias with respect to the DTD risk factor, neglect of interaction effects and incorrect link function specification has the greatest, intermediate and least impacts, respectively. Our conclusion is that validation methods chosen in the stress testing context should be capable of testing model assumptions, given the sensitive regulatory uses of these models and concerns raised in the industry about the effect of model misspecification on capital and reserves. Our research is accretive to the literature by offering state of the art techniques as viable options in the arsenal of model validators, developers and supervisors seeking to manage model risk.
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How this classification was reachedexpand
Full frame machine prediction
Teacher imitationNot calibrated prevalence, not ground truth. Human validation pending. The Gemma side is a direct model label for every work in the frame, read from the title-only record. The Codex side is a classifier learned from the 10,348 direct Codex labels and calibrated to design-weighted sample rates; fields without enough sample support carry no Codex call. Candidate is the union of the two sides; consensus is their intersection. These outputs are machine_predicted_unvalidated and are not human labels.
Distilled classifier scores by category (both heads)
| Category | Codex | Gemma |
|---|---|---|
| Metaresearch | 0.007 | 0.027 |
| Meta-epidemiology (narrow) | 0.001 | 0.000 |
| Meta-epidemiology (broad) | 0.001 | 0.001 |
| Bibliometrics | 0.001 | 0.001 |
| Science and technology studies | 0.000 | 0.002 |
| Scholarly communication | 0.002 | 0.002 |
| Open science | 0.002 | 0.002 |
| Research integrity | 0.001 | 0.002 |
| Insufficient payload (model declined to judge) | 0.004 | 0.000 |
Machine scores (provisional)
The two teacher heads of the student model, read on this work. A score orders the frame for review; it never asserts a category, and the validation status ships verbatim with every row.
Baseline scores from an immature model (maturity gate not passed, 7 training rounds). Scores rank; they never assert a category.
score_only:v0-immature-baseline · verbatim from the scoring run: score_only means the number may rank works, and no category label ships from itClassification
machine, unvalidatedMachine predicted; a candidate call from one source (direct Gemma or distilled Codex), not a consensus.
How this classification was reached, model by model and score by score, is at the end of the page under "How this classification was reached".