BCR Approach for Regulatory Reporting (PD in Low-Default Portfolios)

Attached: Excel workbook with full BCR implementation (macro-driven, quarterly defaults, confidence intervals, and model diagnostics)
https://docs.google.com/spreadsheets/d/1ltVYX4vhGeTllOQkEWKrED2DV33eb55M/edit?usp=sharing&ouid=115594792889982302405&rtpof=true&sd=true

Excel Implementation Details (see link above)

• Historical GDP YoY data as a macro factor

• Z-score standardization of macro series

• Conditional PD computed using Vasicek model

• Expected defaults calculated for each period

• Goal Seek used to backsolve for portfolio PD

• Bayesian posterior estimate and 95% confidence bound from Beta distribution

  
  
  

 BCR Approach for Regulatory Reporting (PD in Low-Default Portfolios)

To calculate PD for low-default portfolios like sovereigns, large corporates, or prime mortgages, the Benjamin, Cathcart, and Ryan (BCR) methodology (2006) is a robust statistical approach used in both regulatory modeling and internal risk management:

It leverages:

- Vasicek (asymptotic single risk factor) model

-Observed macroeconomic conditions (e.g., GDP YoY growth)

-Asset correlation

-Observed default count over a given period

Excel Implementation Steps (Included in Attached File)

Inputs:

• #Obligors (e.g., 54,000)

• Observed defaults (e.g., 150)

• Correlation (e.g., 0.20)

• Historical GDP YoY (%) path as macro risk driver