PROBABILITY OF DEFAULT (PD)

Definition

Probability of Default (PD) is the likelihood that a borrower will fail to meet their debt obligations (interest or principal payments) within a specified time horizon, usually 12 months or over the life of the exposure.

It is a central metric in credit risk analysis, banking regulation (Basel Accords), and credit ratings, used to estimate potential credit losses and determine required capital reserves.

Origins

• "Probability" derives from the Latin probabilis (“likely”).

• "Default" originates from the Old French defaute (“failure, lack”).

• PD became formalized as a regulatory concept under Basel II (2004) and further refined under Basel III/IV, which require banks to estimate PD as part of their Internal Ratings-Based (IRB) approach.

Usage

• Banking & Lending – Estimating borrower creditworthiness.

• Bond Markets – Assessing issuer default risk and spreads.

• Derivatives – Calculating counterparty credit exposure.

• Insurance & Trade Finance – Evaluating client solvency risk.

• Sovereign Debt – Measuring risk of government defaults.

How PD Works

1. Assessment – Analyze borrower financials, credit history, and market data.

2. Modeling – Use statistical or structural models to estimate default likelihood.

3. Regulatory Use – Feed PD into capital adequacy and risk-weighted asset (RWA) calculations.

4. Portfolio Level – Aggregate PDs to assess systemic credit risk.
   
   

Types of Probability of Default

1. Point-in-Time (PIT) PD – Reflects current economic conditions.

2. Through-the-Cycle (TTC) PD – Smoothed over business cycles, less volatile.

3. One-Year PD – Probability of default within 12 months.

4. Lifetime PD – Used in IFRS 9 / CECL accounting standards for credit impairment.
   
   

Key Takeaway

• A higher PD signals a greater chance of borrower default.

• Used alongside LGD and EAD to estimate credit losses.

• Integral to Basel regulatory frameworks for bank capital requirements.

• Rating agencies (Moody’s, S&P, Fitch) provide PD estimates tied to credit ratings.

Context in Financial Modeling

• Credit Risk Models – Merton model, logistic regression, and machine learning approaches.

• Bond Pricing – Credit spreads reflect implied PD.

• Stress Testing – PDs increase under adverse economic scenarios.

• Valuation – Discounting cash flows with credit-adjusted rates.
  
  

Nuances & Complexities

• Data limitations – Low default portfolios make PD estimation difficult.

• Model risk – Different modeling techniques yield different PDs.

• Cyclicality – PIT PDs can fluctuate significantly in downturns.

• Wrong-way risk – PD may rise as exposure to the counterparty increases.

Mathematical Formulas

PD is a probability and thus takes a value between 0 and 1.

$$EL = PD \times LGD \times EAD$$

Where:

• $EL$ = Expected Loss

• $PD$ = Probability of Default

• $LGD$ = Loss Given Default (portion not recovered)

• $EAD$ = Exposure at Default (outstanding loan value)

Related Terms

• Credit Risk

• Loss Given Default (LGD)

• Exposure at Default (EAD)

• Expected Loss (EL)

• Basel Accords

• Credit Rating

Real-World Applications

Corporate Borrower: A BB-rated corporate bond has an estimated PD of ~3% over 1 year, implying a 3 in 100 chance of default.

Mortgage Loan: A bank assigns a PD of 0.5% annually to a prime mortgage borrower based on credit score and history.

Sovereign Debt: Credit markets implied a high PD for Greece (2011–2012) as spreads on government bonds spiked.

References & Sources

• Moody's: Features of a lifetime PD model