eqlx-credit

Open tools for credit-risk model work: discriminatory power with confidence intervals, PD back-testing that allows for correlated defaults, cohort default rates, calibration, master scales, low-default portfolio methods and the Basel IRB risk-weight functions.

Built by eqlx from public regulation and published research. Part of eqlx.org.

Status: alpha (0.2). Every function is tested against a closed form, a published table or worked example, a brute-force calculation, or a simulation. The API may still change.

Install

pip install git+https://github.com/eqlx-ai/eqlx-credit

Python 3.10+, depends only on NumPy and SciPy.

What is inside

Conventions: grades run from lowest to highest risk; by default a higher score means higher risk (higher_is_riskier=False for scorecards where a high score is safe); 1 in a default flag means default; a PD of 1 maps to the master scale's defaulted grade, never to a performing grade.

Agent skill: annual PD validation

skills/annual-pd-validation is an Agent Skill that lets an AI agent prepare the evidence for an annual PD validation: it runs every test through eqlx-credit, reads the results, and drafts the report in the user's language. The agent never computes a number itself and never gives the validation opinion; the conclusion and signature stay with the validator. On the bundled synthetic portfolio it finds the planted problems: a significant AUC decline since initial validation and one grade with far more defaults than its PD implies.

An annual validation pass

examples/validation_report.py, on a synthetic grade table:

import numpy as np
import eqlx_credit as ec

n = np.array([820, 1450, 1910, 1320, 640, 210])  # obligors per grade at the start of the year
d = np.array([1, 4, 11, 19, 21, 17])  # defaults during the year
pd = np.array([0.0012, 0.0035, 0.0070, 0.0140, 0.0300, 0.0700])

cur = ec.auc_ci_from_counts(n, d)  # AUC with DeLong confidence interval
ec.auc_decline_test(0.80, cur)  # vs the AUC at initial validation
ec.jeffreys_test(n, d, pd).rows()  # one dict per grade, ready for a report table
ec.traffic_light(n, d, pd, rho=0.12).colours  # allowing for correlated defaults
ec.risk_weight(pd, 0.45)  # Basel IRB, corporate, LGD 45%, M 2.5

AUC 0.785 (95% CI 0.734-0.836), Gini 0.570
Decline vs initial 0.800: S = 0.57, p = 0.285
grade 1:   1 defaults vs   1.0 expected, Jeffreys p = 0.421, traffic light green
grade 2:   4 defaults vs   5.1 expected, Jeffreys p = 0.662, traffic light green
grade 3:  11 defaults vs  13.4 expected, Jeffreys p = 0.734, traffic light green
grade 4:  19 defaults vs  18.5 expected, Jeffreys p = 0.437, traffic light green
grade 5:  21 defaults vs  19.2 expected, Jeffreys p = 0.327, traffic light green
grade 6:  17 defaults vs  14.7 expected, Jeffreys p = 0.259, traffic light green
Normal test over 5 years: z = 0.89
Risk weights: 33.0% 58.8% 80.5% 103.4% 128.4% 168.9%

A low-default portfolio

examples/quickstart.py:

n_obligors = np.array([120, 340, 510, 430, 260, 90])
n_defaults = np.array([0, 0, 1, 2, 3, 2])

ec.pluto_tasche(n_obligors, n_defaults, confidence=0.9, rho=0.12)
ec.fit_ct_ar(n_obligors, central_tendency=0.015, accuracy_ratio=0.65).pd
ec.van_der_burgt(n_obligors, central_tendency=0.015, accuracy_ratio=0.65).pd

Pluto-Tasche (90%, rho=0.12): [ 2.511  2.652  3.172  4.263  6.336 10.761] %
CT/AR curve:                  [ 0.037  0.135  0.421  1.205  3.383 10.692] %
van der Burgt:                [0.044 0.093 0.366 1.525 4.246 7.134] %
Master scale grades:          [ 2  5  8 11 14 17]

How it is tested

• Basel IRB: all eight columns of Basel II Annex 5 ("Illustrative IRB Risk Weights") reproduced to the published two decimals.
• Pluto–Tasche: the paper's worked example (0.29%, 0.33%, 0.76%).
• DeLong: against an explicit obligor-by-obligor placement calculation, and by simulation: the standard error matches the spread of simulated AUCs and the 95% interval covers the true AUC about 95% of the time.
• Correlated binomial: against a Monte Carlo simulation of the one-factor model.
• Spiegelhalter: a hand calculation, and standard normal under correct PDs by simulation.
• Cohorts: hand-built panels, including the horizon boundary and 29 February.

Notes on the methods

• Use the obligor-average PD at the start of the period per grade as the grade PD in back-tests.
• binomial_test with rho=0 assumes independent defaults and rejects too often when defaults are correlated; pass an asset correlation, or read it next to traffic_light(..., rho=).
• Thresholds (test levels, traffic-light quantiles, PSI readings) are policy choices; set your own.
• hosmer_lemeshow uses K degrees of freedom for K grades (out-of-sample use).
• pluto_tasche is the single-period version; in practice the bounds are often rescaled to the central tendency afterwards.
• fit_ct_ar uses Tasche's robust-logit grade positions by default but matches the accuracy ratio exactly on the grade distribution rather than through his moment approximation; placement="even" gives the v0.1 behaviour.
• van_der_burgt returns each grade's PD as the average slope of the CAP curve over that grade, so the weighted mean equals the central tendency exactly; grading makes the grade-level AR a little lower.
• risk_weight defaults to no 1.06 scaling factor (Basel III final); pass scaling=1.06 for Basel II / CRR. PD floors differ by framework and are the caller's choice.

References

• Basel Committee on Banking Supervision (2006). International Convergence of Capital Measurement and Capital Standards, ¶272–330 and Annex 5.
• Basel Committee on Banking Supervision (2005). An Explanatory Note on the Basel II IRB Risk Weight Functions.
• Basel Committee on Banking Supervision (2005). Studies on the validation of internal rating systems. Working Paper No. 14.
• European Central Bank (2019). Instructions for reporting the validation results of internal models: IRB Pillar I models for credit risk.
• European Banking Authority (2017). Guidelines on PD estimation, LGD estimation and the treatment of defaulted exposures (EBA/GL/2017/16).
• DeLong, E. R., DeLong, D. M. and Clarke-Pearson, D. L. (1988). Comparing the areas under two or more correlated receiver operating characteristic curves. Biometrics 44(3).
• Spiegelhalter, D. J. (1986). Probabilistic prediction in patient management and clinical trials. Statistics in Medicine 5(5).
• Tasche, D. (2003). A traffic lights approach to PD validation. arXiv:cond-mat/0305038.
• Tasche, D. (2013). The art of probability-of-default curve calibration. Journal of Credit Risk 9(4). arXiv:1212.3716.
• Pluto, K. and Tasche, D. (2005). Thinking positively. Risk, August 2005. Longer version: arXiv:cond-mat/0411699.
• van der Burgt, M. (2008). Calibrating low-default portfolios, using the cumulative accuracy profile. Journal of Risk Model Validation 1(4).
• Vasicek, O. (2002). The distribution of loan portfolio value. Risk, December 2002.
• Siddiqi, N. (2006). Credit Risk Scorecards. Wiley.

Development

uv sync
uv run pytest
uv run ruff check . && uv run ruff format --check . && uv run mypy src

Contributing

Issues and pull requests are welcome. See CONTRIBUTING.md.

License

Apache-2.0. See LICENSE and NOTICE.