Estimating Obligor-Level PIT PDs in Low-Default Portfolios

 Excel Example:
https://docs.google.com/spreadsheets/d/1vx3K1YsKxPD3wIc229W2QcghbUIOSe55/edit?usp=sharing&ouid=115594792889982302405&rtpof=true&sd=true

In low-default portfolios, estimating Point-in-Time (PIT) probability of default (PD) at the obligor level is particularly challenging due to data scarcity. To address this, I implemented the Basel Committee’s BCR approach and extended it with idiosyncratic adjustments for borrower-level differentiation.

Portfolio Level

• Macro Driver: GDP YoY is standardized into a Z-score.

• Systematic Link: Vasicek’s single-factor model connects portfolio Through-the-Cycle (TTC) PDs to the macroeconomic cycle.

• Calibration: Goal Seek ensures unconditional PIT PDs are consistent with observed default frequencies.

Obligor Level

• Start from TTC PDs and apply PIT adjustments consistently across obligors.

• To differentiate obligors within the same quarter, I introduced idiosyncratic shifts (e.g., Debt-to-Equity ratio).

• This framework can be extended using Principal Component Analysis (PCA) across multiple borrower-level factors (leverage, liquidity, profitability, etc.) to extract orthogonal risk drivers for richer differentiation.

• These shifts or factors adjust each obligor’s threshold in the Vasicek model, producing distinct PIT PDs.

• Finally, obligor PITs are rescaled so their average aligns with the calibrated portfolio PIT.

 This approach ensures regulatory consistency at the portfolio level while producing economically intuitive obligor-level PDs — higher leverage or weaker fundamentals result in higher PIT PDs, while PCA allows multiple dimensions of risk to be captured systematically.