# Credit Scoring Models > credit-scoring-models - Skill: `brainbytes-dev/credit-scoring-models` (Agent Skill) - Install (CLI): `npx skillmds@latest add brainbytes-dev/credit-scoring-models` - Raw SKILL.md: https://api.skillmd.com/api/skills/brainbytes-dev/credit-scoring-models/raw - Safety review: pending - Works with: Claude Code, Claude.ai, OpenAI Codex - Category: Coding & Dev Tools - Author: brainbytes-dev (https://skillmd.com/u/brainbytes-dev) - Updated: 2026-09-17 - Page: https://skillmd.com/skills/brainbytes-dev/credit-scoring-models --- # credit-scoring-models Credit scoring models — Altman Z-score, Merton, scorecards. ## When to Activate - Assessing the creditworthiness of a corporate borrower or counterparty - Building or validating a credit scorecard for lending decisions - Estimating probability of default (PD) for a portfolio - Evaluating a structural model approach to credit risk - Analyzing rating migration and transition probabilities - Calibrating internal rating systems for regulatory capital (IRB approach) - Back-testing model performance against realized defaults ## Core Concepts ### Altman Z-Score Edward Altman's discriminant analysis model predicts corporate bankruptcy using five financial ratios. Originally developed for publicly traded manufacturers (1968). **Original Z-Score (public manufacturing):** ``` Z = 1.2 * X1 + 1.4 * X2 + 3.3 * X3 + 0.6 * X4 + 1.0 * X5 X1 = Working Capital / Total Assets (liquidity) X2 = Retained Earnings / Total Assets (cumulative profitability) X3 = EBIT / Total Assets (operating efficiency) X4 = Market Value Equity / Book Value Debt (solvency) X5 = Sales / Total Assets (asset turnover) ``` - Z > 2.99 — Safe zone (low default probability) - 1.81 < Z < 2.99 — Grey zone (caution) - Z < 1.81 — Distress zone (high default probability) **Z'-Score (private firms):** Replaces market value of equity with book value. Revised coefficients and cutoffs (Z' < 1.23 = distress). **Z''-Score (non-manufacturing / emerging markets):** Drops X5 (Sales/Total Assets) to remove industry bias from asset turnover. Suitable for service firms and emerging market companies. - Apply the correct variant based on the entity type - Z-score is a point-in-time indicator — supplement with trend analysis over 3-5 years - Does not capture industry-specific risk factors or qualitative considerations ### Merton Structural Model Based on the Black-Scholes option pricing framework. Equity is modeled as a call option on the firm's assets with a strike price equal to the face value of debt. - **Asset value (V)**: Unobservable — inferred from equity market value and equity volatility using iterative methods - **Asset volatility (sigma_V)**: Also unobservable — estimated simultaneously with V - **Default point**: Firm defaults when asset value falls below the debt obligation at maturity - **Distance to Default (DD)**: Number of standard deviations the asset value is above the default point ``` DD = (ln(V/D) + (mu - 0.5 * sigma_V^2) * T) / (sigma_V * sqrt(T)) ``` - **PD from DD**: Map DD to PD using the normal distribution (theoretical) or empirical mapping (Moody's KMV / EDF approach uses historical default frequency for each DD bucket) **Strengths**: Market-based, forward-looking, continuous updating. **Weaknesses**: Requires liquid equity market, assumes single debt maturity, sensitive to equity volatility estimation. ### Credit Scorecards Statistical models (typically logistic regression) that assign points to borrower characteristics to produce a credit score. **Development process:** 1. **Data collection**: Gather historical loan-level data with default outcomes (12-month observation window typical) 2. **Variable selection**: Financial ratios, behavioral data, industry, age of firm, management quality proxies 3. **Weight of Evidence (WoE) transformation**: Bin continuous variables; calculate WoE = ln(% of goods / % of bads) for each bin 4. **Information Value (IV)**: Measures predictive power of each variable. IV > 0.3 = strong; 0.1-0.3 = medium; < 0.1 = weak 5. **Logistic regression**: Fit model using selected WoE-transformed variables 6. **Scaling**: Convert log-odds to a score. Common convention: Score = Offset + Factor * ln(odds), where Factor = PDO / ln(2), PDO = points to double the odds 7. **Scorecard format**: Each attribute level gets a partial score; total score maps to PD ### Probability of Default (PD) Estimation - **Through-the-cycle (TTC)**: Long-run average PD over a full economic cycle — used for regulatory capital - **Point-in-time (PIT)**: Current PD reflecting prevailing economic conditions — used for IFRS 9 / CECL provisioning - **PD calibration**: Ensure model-predicted PDs align with observed default rates. Central tendency adjustment to match long-run average - **Low-default portfolios**: Where defaults are rare (e.g., investment-grade corporates, sovereigns), use external data, expert judgment, or Bayesian techniques to estimate PD ### Rating Migration Matrices Transition matrices show the probability of moving from one rating grade to another over a defined horizon (typically one year). ``` From \ To AAA AA A BBB BB B CCC/D AAA 90.0 8.5 1.0 0.3 0.1 0.0 0.1 AA 1.0 88.0 8.5 1.5 0.5 0.3 0.2 A 0.1 2.0 87.0 7.5 2.0 0.8 0.6 BBB 0.0 0.3 4.0 84.0 7.0 3.0 1.7 BB 0.0 0.1 0.5 5.0 78.0 10.0 6.4 ``` - **Upgrade/downgrade ratios**: Track the health of a portfolio over time - **Absorbing state**: Default is absorbing — once an entity defaults, it cannot migrate back - **Multi-year PDs**: Derived by raising the one-year transition matrix to the power of n ### Model Validation - **Discriminatory power**: AUROC (area under ROC curve), Gini coefficient (= 2 * AUROC - 1), Kolmogorov-Smirnov statistic - **Calibration accuracy**: Binomial test, Hosmer-Lemeshow test, traffic light approach (compare predicted PD to observed default rate by grade) - **Stability**: Population Stability Index (PSI) measures drift in score distributions over time. PSI > 0.25 signals significant shift - **Backtesting**: Compare predicted defaults to actual defaults; analyze by segment, time period, and rating grade ## Methodology 1. **Define scope**: Identify the portfolio segment, default definition (e.g., 90 days past due, bankruptcy), and observation period 2. **Data preparation**: Collect financial statements, market data, behavioral data. Clean and validate. Apply exclusions (e.g., newly formed entities, data errors) 3. **Model development**: Choose model type (scorecard, structural, hybrid). Develop candidate variables, test statistical significance, build the model 4. **Calibration**: Map model output to PD. Validate central tendency against long-run default rates. Adjust for economic cycle if TTC PD required 5. **Validation**: Test discriminatory power, calibration accuracy, and stability. Compare against benchmark models 6. **Implementation**: Integrate into credit approval workflow, pricing, and portfolio monitoring. Define override policy 7. **Ongoing monitoring**: Track model performance quarterly. Re-estimate or recalibrate when PSI exceeds thresholds or discriminatory power degrades ## Templates ### Altman Z-Score Calculation ``` Company: [Name] Year: [Year] Value Ratio Working Capital $12.5M Total Assets $85.0M X1 = 0.147 Retained Earnings $28.0M X2 = 0.329 EBIT $10.2M X3 = 0.120 Market Value of Equity $45.0M Book Value of Total Debt $35.0M X4 = 1.286 Sales $92.0M X5 = 1.082 Z-Score = 1.2(0.147) + 1.4(0.329) + 3.3(0.120) + 0.6(1.286) + 1.0(1.082) = 0.176 + 0.461 + 0.396 + 0.772 + 1.082 = 2.887 Assessment: Grey zone — monitor closely. Declining from 3.15 prior year. Key concern: Working capital deterioration (X1 dropped from 0.210 to 0.147) ``` ### Scorecard Output Summary ``` Borrower: [Name] Application Date: [Date] Attribute Value WoE Bin Points Debt/EBITDA 3.2x 2.5-4.0x +35 Interest Coverage 4.5x 3.0-5.0x +28 Current Ratio 1.4x 1.2-1.6x +22 Revenue Growth (3yr) 8% 5-10% +18 Years in Business 12 10-20 +15 Industry Risk Medium B +10 Management Quality Strong A +20 Total Score: 148 + Base Score (200) = 348 Mapped PD: 0.85% Internal Rating: BB+ ``` ### Model Validation Dashboard ``` Metric Current Period Prior Period Threshold Status AUROC 0.82 0.84 > 0.70 Pass Gini Coefficient 0.64 0.68 > 0.40 Pass KS Statistic 0.52 0.55 > 0.30 Pass PSI (score distribution) 0.12 0.08 < 0.25 Pass Hosmer-Lemeshow (p-value) 0.35 0.42 > 0.05 Pass Predicted vs Actual DR 1.2% vs 1.4% 1.1% vs 1.0% Within 20% Pass ``` ## Quality Gate - [ ] Correct Z-score variant applied for the entity type (public, private, non-manufacturing, emerging market) - [ ] Merton model inputs validated: equity value, equity volatility, debt structure, risk-free rate - [ ] Scorecard developed on representative data with adequate default observations - [ ] Variable selection justified statistically (IV, p-values) and economically (business logic) - [ ] PD calibration aligned with chosen philosophy (TTC or PIT) and long-run default rates - [ ] Model validation completed: AUROC, Gini, KS, calibration tests all within thresholds - [ ] Population Stability Index monitored; recalibration triggered if PSI > 0.25 - [ ] Rating migration matrix computed and compared to external benchmarks - [ ] Model documentation meets regulatory standards (IRB, IFRS 9, CECL) - [ ] Override rate tracked and within policy limits (typically < 10-15% of decisions) - [ ] Independent model validation function has signed off