How do you calculate Credit VaR for a single obligor?

Credit VaR measures the potential credit loss at a given confidence level over a specific horizon, beyond what is already expected. It captures the 'worst-case' credit loss scenario (within the confidence level) that the bank should hold capital against.

Key Concepts

• Expected Loss (EL) = PD x LGD x EAD — the average loss you anticipate and provision for.
• Unexpected Loss (UL) = The volatility of credit loss around the expected loss.
• Credit VaR = Loss at the confidence quantile − Expected Loss.

Credit VaR differs from market VaR because credit losses are heavily skewed: most of the time there's zero loss (no default), but when default occurs, the loss is large.

Single-Obligor Credit VaR Calculation

Suppose Westfield Commercial Bank has a $20 million loan to a single corporate borrower with:

• PD = 2% (1-year probability of default)
• LGD = 45% (loss given default)
• EAD = $20 million

Step 1: Expected Loss

EL = 0.02 x 0.45 x $20M = $180,000

Step 2: Loss Distribution

For a single obligor, the loss is binary:

• With probability 98%: Loss = $0
• With probability 2%: Loss = LGD x EAD = $9,000,000

Step 3: Unexpected Loss (Standard Deviation)

UL = EAD x LGD x sqrt(PD x (1 − PD))

UL = $20M x 0.45 x sqrt(0.02 x 0.98)

UL = $9M x 0.1400 = $1,260,000

Step 4: Credit VaR at 99.9% Confidence

At 99.9% confidence with PD = 2%, the borrower defaults in the worst-case scenario (since 2% > 0.1%).

Credit VaR (99.9%) = Worst-case loss − EL = $9,000,000 − $180,000 = $8,820,000

At 95% confidence (since 2% < 5%), the borrower does NOT default.

Credit VaR (95%) = $0 − $180,000 = effectively $0 (or negative, meaning EL alone covers it).

Key Insight: For a single obligor, Credit VaR is either the full default loss or zero, depending on whether PD exceeds (1 − confidence level). Portfolio Credit VaR with many obligors produces a smoother distribution where intermediate losses are possible.

Exam Tip: Don't confuse EL (provisioned from earnings) with Credit VaR (covered by capital). Capital requirements are based on unexpected loss, not expected loss.

For portfolio-level Credit VaR, check out our FRM Part II materials.