Credit Risk Analysis: Retail Mortgage Loans

State-Dependent Logistic Hazard Model for 1-Month-Ahead Default Prediction

Full technical report (LaTeX PDF): Mortgage-Credit-Risk-Regression.pdf.

Antonio Melacini - December 2025

Overview

• This project builds an early-warning probability of default (PD) model that predicts whether a mortgage will default in the next month using information available in the current month. We define "default" as the event of a loan having 3+ missed payments.
• The model is trained on loan-month panel data that is comprised of loan origination characteristics, monthly loan performance, and monthly macroeconomic variables.
• The model is state-dependent in the sense that one of the predictors is the current delinquency state (number of missed payments).
• This is designed for applications in credit portfolio monitoring (e.g. flag loans with rising risk) and account management (e.g. offer deals to stable borrowers), not for modeling "ever-default" from origination.
• Note: additional summary points about the data and methodology are provided at the end of this README document.

Data

• Freddie Mac Single-Family Loan-Level Dataset (SFLLD): vintages 2013, 2016, 2020
• Train/test split (70/30):
  • Train: 2013/02 $-$ 2021/09
  • Test: 2021/10 $-$ 2025/05
• All loans are fixed-rate mortgages (FRMs) without prepayment penalties (non-PPM) in the sample.
• Total size: (before data cleaning and variable selection)
  • $\approx 18$ GB
  • 300,000 loans (cohort of 100,000 loans for each vintage)

_{Panel structure by origination vintage and time-based train/test split.}

Key Predictors

Some of the key predictors used in the model are summarized below.

The scatterplots show the covariates on the x-axis plotted against the logit transform of the empirical hazard rate on the y-axis. For categorical predictors, they are visualized with grouped Kernel Density Estimates (KDEs) of the logit transform of the empirical hazard rate.

Loan Performance (Loan- and Time-Dependent)

• deliq_num (current number of missed payments): very clear shift in distribution with each level, as expected
  • This is the current "delinquency state".
• last_vtl_est (estimated value-to-loan ratio, proxy for equity): weak positive association
  • Derived from the LTV ratio at origination and aggregate monthly growth in home prices measured with the Home Price Index (HPI).

Borrower Risk at Origination (Loan-Dependent)

• cr_spread (origination credit spread): strong positive association
  • Derived by deducting the yield on the 10-year Treasury at the time of origination from the interest rate on the loan at origination
• credit_score (FICO): strong negative association

Macroeconomic and Market-Based (Time-Dependent)

• last_vix (lagged CBOE Volatility Index): moderate-to-strong positive association
• last_unrate_chg_pos (positive part of the YoY change in the unemployment rate): strong positive association
• last_infl_yoy_low (indicator for inflation rate being at or below 2.5%): shift in distribution of risk

VIX (Volatility Index)

Max(YoY Change in Unemployment Rate, 0)

Low YoY Inflation Indicator

Controls

• Region, occupancy status, loan purpose, long-term loan indicator, and baseline hazard control using natural splines transformation of loan age with 2 degrees of freedom.

Performance Evaluation

Plots of Key Metrics on Test Set Predictions

Results (Test Set)

• AUC = 0.99 (very strong ranking performance)
• KS = 0.98 (large separation between default and non-default)
• At empirical event-rate threshold:
  • Recall (Sensitivity) = 0.98
  • Precision = 0.20
  • F1 = 0.30
• Raising the threshold to around 0.001 (a little less than double the empirical event-rate) can improve the balance:
  • F1 = 0.51 and a very small decrease in recall

Calibration (Train Set)

Repo Notes

• Report is written in R Markdown; heavy computations are done in separate code-only R scripts and saved as RDS objects and figures.
• Key generated artifacts:
  • objects/*.rds (model outputs, tables)
    • These are hidden from GitHub in the current version because some objects are very large, although all output is displayed in the full PDF report.
  • figures/* (EDA + evaluation plots)

Additional Notes on Data and Methodology

• Macroeconomic variables are lagged to prevent leakage since the data for month $t$ is published in month $t+1$.
• Due to the panel structure of the data, we use cluster-robust standard errors (clustered on loan IDs) to obtain valid inference in the presence of unobserved within-loan heterogeneity.
• There is inherent censoring at data cutoff and enforced right-truncation by treating prepayment as censoring.