一份完全模拟真实商业银行 CRE PD 模型开发文档（MDD）

CRE PD Model – Model Development Document (MDD)

1. Executive Summary

1.1 Purpose of the Model

• CECL lifetime loss estimation

• Quarterly Allowance for Credit Losses (ACL)

• RWA / regulatory capital

• Portfolio monitoring

• Pricing and underwriting decision support

• SR 11-7

• Basel “Use-Test” principles

• Internal Model Governance Standards

• Data Quality Framework

1.2 Modeling Approach

• Logistic Regression using Weight of Evidence (WoE) transformed predictors

• Borrower/Loan level PD estimation

• Calibrated using CRE loan data from 2014–2024

• Includes: collateral risk, cash flow risk, borrower quality, and geographic segmentation

• Separate risk drivers for Office, Retail, Multifamily, Industrial, Mixed Use

1.3 Key Predictive Variables

1.4 Model Performance

1.5 Major Findings

2. Portfolio Description

2.1 CRE Portfolio Definition

• Income-producing properties

• Constructed and stabilized assets

• Loans secured by:
• Multifamily
• Office
• Retail
• Industrial
• Mixed Use
• Hotel (excluded in v1 model due to limited data)

2.2 Data Sources

2.3 Data Time Window

• Development dataset covers 2014–2024

• Default event window: 12-month horizon

• Out-of-time validation period: 2021–2024

2.4 Portfolio Statistics

3. Data Preparation

3.1 Data Cleaning

• Removal of duplicates (0.3%)

• Standardization of appraisal dates

• Capping of extreme values (e.g., DSCR > 5 capped)

• Consolidation of multiple properties per sponsor

• Treating negative NOI data

3.2 Default Definition

• 90+ days past due

• Classified as non-accrual

• Foreclosure initiated

• Charged-off (partial or full)

• Transferred to OREO

3.3 Outlier Handling

• Values > 150% capped

• Negative values removed

• DSCR < 0.1 winsorized

• Missing DSCR assigned to WoE “Missing” bin

• Winsorized at 5th and 95th percentiles

3.4 Missing Value Treatment

• Dedicated WoE bins

• Business confirmation (“Missing DSCR = weak financials”)

• 98%+ completeness achieved after treating missing values

4. Feature Engineering

4.1 Weight of Evidence (WoE) Transformation

1. Linearize log-odds → improve logistic regression stability

2. Guarantee monotonicity → regulator-friendly

3. Handle missing/extreme values gracefully

4. Allow business-friendly interpretation

4.2 Example WoE Table – LTV

4.3 Example WoE Table – DSCR

4.4 IV Summary Table (All Variables)

5. Feature Selection

5.1 Layer 1 – Univariate Predictive Power (IV Screening)

• Information Value (IV)

• Monotonicity of default rate

• Missing-value pattern

Summary of Univariate IV Results

5.2 Layer 2 – Multicollinearity Screening (VIF)

Multicollinearity Results

5.3 Layer 3 – Governance & Economic Rationale Screening

(1) Monotonic WoE Pattern Check

• DSCR → monotonic decreasing WoE → ✔

• LTV → monotonic increasing WoE → ✔

• Vacancy Rate → non-monotonic (W-shape) → ❌ (Dropped)

(2) Coefficient Direction Check

(3) Business Rationale Check

• Property Type risk order: Office > Retail > MF > Industrial

• Geography risk varies with micro-market cycles

• LoanAge reflects seasoning effects

5.4 Final Selected Features

6. Model Specification

6.1 Estimated Coefficients

6.2 Interpretation of Coefficients

• LTV: Strongest predictor; PD nearly doubles for highest WoE bin

• DSCR: Negative coefficient; low DSCR significantly increases PD

• Property Type: Office loans contribute positively to risk

• Geography: High-risk states (CA, NY, IL) show elevated PD

• Loan Age: PD decreases as loan seasons (first 2 years highest risk)

• Sponsor Strength: Liquidity + net worth reduce PD likelihood

6.3 Variance-Covariance Matrix

7. Model Performance

7.1 Discriminatory Power

AUC / ROC Analysis

7.2 KS Statistic

7.3 Gini Coefficient

7.4 Calibration Performance

Bin-Level Calibration (Observed vs. Expected)

8. Backtesting & Stability Testing

8.1 Backtesting Methodology

• Out-of-time tests (2021–2024)

• Vintage stability tests

• Subsegment backtests (Office, MF, Retail, Industrial)

• Geography-based backtesting

8.2 Backtesting Results – Out-of-Time

8.3 Property-Type Stability

8.4 Geography Stability Test

8.5 Conclusions

• Time

• Geography

• Most property types

9. Benchmarking

1. External Benchmarking (industry loss data)

2. Internal Challenger Model (macro-driven model)

3. Legacy Model Comparison

9.1 External Benchmarking (FDIC / Trepp / Market Data)

FDIC Charge-off Rates (2014–2024)

Model PD Comparison

9.2 Internal Challenger Model

• GDP growth

• CRE Price Index

• Vacancy Rates

• Unemployment Rate

Comparison with PD Model

9.3 Legacy Model Comparison

10. Model Limitations & Assumptions

10.1 Data Limitations

1. Low Default Portfolio

• PD estimation challenges

• Wider confidence intervals

• Higher sensitivity to rare events

2. Office Market Structural Shift

• Higher PD

• Increased macro volatility

• Out-of-distribution behavior

3. Appraisal Lag

10.2 Modeling Limitations

1. Logistic Regression Functional Form

2. Missing Property-Level Tenant Data

• Tenant rollover profile

• Lease maturity schedule

• Tenant concentration

• Occupancy-by-tenant

10.3 Assumptions

10.4 Mitigants

• Monthly monitoring

• Management overlays

• Cross-validation

• Macro stress overlays for office segment

• Conservative calibration for high-risk states

11. Model Monitoring Plan

11.1 Monitoring Frequency

• Quarterly: Performance & calibration

• Semi-Annual: Data quality & drift

• Annual: Full validation by MRM

11.2 Monitoring Metrics

1. Discrimination Drift

• AUC decrease > 0.05 triggers review

• KS drop > 20% requires escalation

2. Calibration Drift

3. Data Drift

• LTV distribution

• DSCR distribution

• Property type mix

• Geographic exposure shifts

4. Stability Drift

• WoE monotonicity breaks

• Population shifts

• Increased missing rates

11.3 Triggers & Escalation Framework

11.4 Overlay Policy

• Office PD deviations > 50 bps

• Market downturn (CREPI ↓ > 10%)

• Sponsor weakness in certain regions

12. Governance & Model Use

12.1 Compliance with SR 11-7

1. Conceptual Soundness

• Justified model form

• Variable selection aligned with economics

• WoE transformations

• Diagnostic tests documented

2. Ongoing Monitoring

• Quarterly monitoring

• Annual validation

3. Outcome Analysis

• Benchmarking

• Backtesting

• Independent challenger model

12.2 Roles & Responsibilities

12.3 Model Use Policy

• CECL PD estimation

• Risk-based pricing

• Portfolio risk analytics

• Stress testing support

• Collateral valuation

• Standalone loan approval without human oversight

12.4 Change Management

• Variable set

• Data source

• Model type

• Calibration methodology

Appendices

Appendix A — Full WoE Binning Tables for 10+ CRE PD Variables

1. LTV

2. DSCR

3. Loan Age

4. Property Type

5. Geography

6. Interest Rate

7. Sponsor Strength

8. Tenant Concentration (若数据可用)

9. NOI Growth

10. Borrower Exposure / Portfolio Concentration

• Good / Bad

• Bad Rate

• Dist good / Dist bad

• WoE

• IV contribution

• 单调性检查（每个表末尾我给解释）

A.1 WoE – Loan-to-Value (LTV)

A.2 WoE – DSCR

A.3 WoE – Loan Age (Seasoning)

A.4 WoE – Property Type

A.5 WoE – Geography (State-Level PD)

A.6 WoE – Interest Rate

A.7 WoE – Sponsor Strength

A.8 WoE – Tenant Concentration

A.9 WoE – NOI Growth

A.10 WoE – Borrower Exposure

Appendix B — Performance Charts (AUC, KS, Calibration)

B.1 ROC Curve (AUC = 0.74)

B.2 KS Statistic Plot（KS = 36）

B.3 Calibration Plot（Observed vs Expected PD）

B.4 Decile Plot / Lift Chart

Appendix C — Data Dictionary

C.1 Variable List Overview

C.2 Full Data Dictionary（标准银行格式）

• Category: Collateral Risk

• Definition: Current loan balance divided by most recent appraised property value

• Formula: LTV = Loan Amount / Appraised Value

• Source System: Appraisal System + Loan Accounting

• Refresh Frequency: Quarterly

• Data Owner: Collateral Valuation Team

• Transformation: WoE monotonic bins

• Data Quality Notes:
• Values >150% capped
• Must confirm appraisal dates not post-default

• Usage: Included in model (strongest predictor)

• Category: Cash Flow Risk

• Definition: NOI divided by annual debt service

• Formula: DSCR = NOI / Debt Service

• Source System: CRE Underwriting System

• Refresh Frequency: Annual (or at renewal)

• Data Owner: CRE Underwriting

• Transformation: WoE

• Missing Values: Put into "Missing" WoE bin

• Usage: Included in model (2nd most predictive)

• Category: Structural Risk

• Possible Values: Multifamily, Office, Retail, Industrial, Mixed Use

• Source System: Collateral / CRE Underwriting

• Business Relevance: CRE segment risk varies significantly (Office = highest PD)

• Transformation: WoE categorical encoding

• Usage: Included in model

• Category: Regional Economic Risk

• Definition: Loan's primary collateral state grouped by risk clusters

• Source System: Loan Origination System

• Transformation: WoE (state → region risk bins)

• Usage: Included in model

• Category: Behavioral / Vintage

• Definition: Months since loan origination

• Source System: Loan Accounting

• Transformation: WoE monotonic seasoning pattern

• Usage: Included in model

• Category: Borrower Quality

• Definition: Bank’s internal rating of sponsor’s liquidity + net worth

• Source: Borrower Financials

• Scale: 1 = Weak, 5 = Strong

• Transformation: WoE

• Usage: Included in model

• Category: Pricing

• Definition: Current contractual rate

• Source: Loan System

• Transformation: WoE (kept monotonic)

• Usage: Not included in final model (low IV)

• Category: Cash Flow

• Definition: NOI / Loan Balance

• Source: CRE Underwriting

• Notes: Highly correlated with DSCR → removed

• Usage: Not included due to VIF > 5

• Category: Property Performance

• Source: External CRE data provider

• Notes: WoE non-monotonic → removed

• Category: Property Performance

• Definition: Year-over-year growth of property NOI

• Source: Financial Reporting

• Usage: Removed (weak IV)

Appendix D — Model Code Snippets

D.1 数据导入与初始准备

import pandas as pd
import numpy as np
from sklearn.linear_model import LogisticRegression
from sklearn.metrics import roc_auc_score, roc_curve

df = pd.read_csv("cre_loan_data.csv")

TARGET = "default_flag"

D.2 自动分箱（Supervised Monotonic Binning）

def monotonic_binning(x, y, max_bins=5):
    df_temp = pd.DataFrame({'x': x, 'y': y})
    df_temp = df_temp.sort_values('x')

    bins = pd.qcut(df_temp['x'], max_bins, duplicates='drop')
    df_temp['bin'] = bins

    grouped = df_temp.groupby('bin')['y'].mean()

    # enforce monotonicity
    while not (grouped.is_monotonic_increasing or grouped.is_monotonic_decreasing):
        max_bins -= 1
        bins = pd.qcut(df_temp['x'], max_bins, duplicates='drop')
        df_temp['bin'] = bins
        grouped = df_temp.groupby('bin')['y'].mean()

    return df_temp['bin']

D.3 WoE 计算函数

def compute_woe_iv(df, feature, target):
    df_woe = df.groupby(feature).agg({target: ['sum', 'count']})
    df_woe.columns = ['bad', 'total']

    df_woe['good'] = df_woe['total'] - df_woe['bad']
    df_woe['dist_good'] = df_woe['good'] / df_woe['good'].sum()
    df_woe['dist_bad'] = df_woe['bad'] / df_woe['bad'].sum()

    df_woe['woe'] = np.log(df_woe['dist_good'] / df_woe['dist_bad'])
    df_woe['iv'] = (df_woe['dist_good'] - df_woe['dist_bad']) * df_woe['woe']

    return df_woe[['woe', 'iv']]

D.4 对所有变量生成 WoE 编码

features = ["LTV", "DSCR", "Loan_Age", "Property_Type",
            "Geography", "Sponsor_Strength"]

woe_maps = {}

for var in features:
    df[var + "_bin"] = monotonic_binning(df[var], df[TARGET])
    woe_table = compute_woe_iv(df, var + "_bin", TARGET)
    woe_maps[var] = woe_table['woe'].to_dict()
    df[var + "_WOE"] = df[var + "_bin"].map(woe_maps[var])

D.5 Logistic Regression 训练

X = df[[f"{v}_WOE" for v in features]]
y = df[TARGET]

model = LogisticRegression(max_iter=200)
model.fit(X, y)

pd.Series(model.coef_[0], index=X.columns)

D.6 评分函数（生产可用）

def score_new_loan(record):
    z = model.intercept_[0]
    for v in features:
        bin_value = pd.Interval(left=record[v+"_bin"].left, right=record[v+"_bin"].right)
        woe = woe_maps[v][bin_value]
        z += model.coef_[0][features.index(v)] * woe
    pd_value = 1 / (1 + np.exp(-z))
    return pd_value

• CECL monthly batch

• PD score generation

• Stress testing scenario PD