Credit Risk: Default Probability, LGD, and Credit Models

Credit Risk Components

Credit risk loss depends on three variables:

Expected Loss = PD × LGD × EAD

Where:

• PD (Probability of Default) — the likelihood a borrower defaults within a given time horizon
• LGD (Loss Given Default) — the percentage of exposure lost if default occurs (1 − Recovery Rate)
• EAD (Exposure at Default) — the total amount exposed when default occurs

Expected vs. Unexpected Loss

• Expected Loss is priced into spreads and provisioned for — it is a cost of doing business
• Unexpected Loss is the volatility around expected loss — this is what requires capital

Capital = f(Unexpected Loss) = f(σ of portfolio credit losses)

Probability of Default

From Market Data — Credit Spreads

Credit spread = yield on risky bond − risk-free yield

Approximate PD (annual): PD ≈ Spread / (1 − Recovery Rate)

Example: If a bond has a 200 bp spread and expected recovery is 40%: PD ≈ 0.02 / 0.60 = 3.33%

This is the risk-neutral PD, which includes a risk premium. The physical (actual) PD is typically lower.

From Historical Data — Rating Agencies

Rating agenc

...