PIT PD Modeling Using Systematic Factor Approach

 Python Code and Data

: https://drive.google.com/drive/folders/1d7vkT9SeXlELPjRRKDU3qUezibQaUL-y?usp=sharing

Robust methodology to estimate Point-in-Time (PIT) Probability of Default (PD) for non-default obligors under IFRS9, combining obligor-level characteristics with macroeconomic indicators. The approach bridges regulatory compliance with practical portfolio forecasting.

Key Steps:

1. TTC PD Calculation:

   • We start with a Through-the-Cycle (TTC) PD model at the obligor level, capturing borrower-specific risk factors such as financial ratios, credit history, and product attributes.

   • Macro variables (Macroeconomic Exposure Variables, MEVs) are averaged over a historical period to normalize for economic cycles, ensuring stability and compliance with regulatory TTC requirements.

2. Systematic Factor Extraction (Credit Cycle Index):

   • To incorporate the impact of economic cycles on forward-looking PDs, we applied Principal Component Analysis (PCA) to a set of macroeconomic indicators.

   • The first principal component serves as a credit cycle index, representing the systematic risk factor that drives correlated changes in credit quality across obligors.

3. Forecasted Credit Cycle:

   • Using macroeconomic forecasts for upcoming quarters, we projected the credit cycle index forward, maintaining the relationship with historical MEVs.

   • This allows us to translate macroeconomic expectations into a forward-looking credit environment.

4. PIT PD Estimation via Vasicek Transformation:

   • The TTC PDs were adjusted to PIT PDs using a Vasicek-based single-factor model, incorporating a correlation coefficient (ρ) to reflect the sensitivity of obligors to the systematic credit cycle.

   • This transformation ensures that obligors’ forward-looking PDs respond dynamically to expected changes in the macroeconomic environment.

5. Portfolio-Level Forecast:

   • The final output is a matrix of PIT PDs, with each obligor in rows and forecasted quarters in columns, allowing granular IFRS9 expected credit loss calculations while remaining aligned with Basel and EBA guidance.

Benefits of this Methodology:

• Combines obligor-specific risk and macroeconomic trends for accurate PIT PD forecasting.

• Compliant with IFRS9 and regulatory expectations for forward-looking credit risk modeling.

• Avoids the need for future obligor-level forecasts, which are often unavailable.

• Easily scalable to large portfolios for quarterly IFRS9 reporting.