EFFICIENT RISK MEASURES CALCULATIONS FOR GENERALIZED CREDITRISK+ MODELS
Bibliographic record
Abstract
Numerical calculations of risk measures and risk contributions in credit risk models amount to the evaluation of various forms of quantiles, tail probabilities and tail expectations of the portfolio loss distribution. Though the moment generating function of the loss distribution in the [Formula: see text] model is available in analytic closed form, efficient, accurate and reliable computation of risk measures (Value-at-Risk and Expected Shortfall) and risk contributions for the [Formula: see text] model poses technical challenges. We propose various numerical algorithms for risk measures and risk contributions calculations of the enhanced [Formula: see text] model under the common background vector framework using the Johnson curve fitting method, saddlepoint approximation method, importance sampling in Monte Carlo simulation and check function formulation. Our numerical studies on stylized credit portfolios and benchmark industrial credit portfolios reveal that the Johnson curve fitting approach works very well for credit portfolios with a large number of obligors, demonstrating high level of numerical reliability and computational efficiency. Once we implement the systematic procedure of finding the saddlepoint within an approximate domain, the saddlepoint approximation schemes provide efficient calculation and accurate numerical results. The importance sampling in Monte Carlo simulation methods are easy to implement, but they compete less favorably in accuracy and efficiency with other numerical algorithms. The less commonly used check function formulation is limited to risk measures calculations. It competes favorably in accuracy and reliability, but an extra optimization algorithm is required.
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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 | 0.002 | 0.005 |
| 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 | 0.001 |
| Scholarly communication | 0.001 | 0.002 |
| Open science | 0.001 | 0.001 |
| Research integrity | 0.001 | 0.001 |
| Insufficient payload (model declined to judge) | 0.005 | 0.001 |
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".