How does CreditMetrics calculate portfolio credit VaR?

Question

AcadiFi · Accepted Answer

CreditMetrics, developed at JPMorgan in 1997, values a credit portfolio by simulating future obligor credit ratings and revaluing each position under those ratings. The workflow has five steps:

(1) Build rating transition matrix: Moody's or S&P publishes one-year probabilities that, say, a BBB issuer becomes AAA, AA, A, BBB, BB, B, CCC, or defaults. For a BBB name: 0.02%, 0.33%, 5.95%, 86.93%, 5.30%, 1.17%, 0.12%, 0.18%.

(2) Define rating thresholds: map transition probabilities to standard normal thresholds via inverse CDF. BBB-to-default threshold z_D = Phi^-1(0.0018) = -2.91.

(3) Simulate correlated normal variables: for a two-obligor portfolio with asset correlation 0.25, draw (X1, X2) from a bivariate normal. Compare to thresholds to determine each obligor's simulated rating.

(4) Revalue positions: discount each bond's cash flows at the credit spread curve corresponding to the simulated rating. A BBB bond that migrates to BB might lose 8% of its value due to spread widening.

(5) Aggregate and take quantile: after 100,000 Monte Carlo paths, compute portfolio P&L distribution and extract the 99% VaR as the negative of the 1st percentile.

```mermaid
flowchart TD
  A[Transition Matrix] --> B[Rating Thresholds]
  B --> C[Correlated Draws]
  C --> D[Simulated Ratings]
  D --> E[Revalue Bonds]
  E --> F[Portfolio P&L]
  F --> G[99% VaR]
```

Key insight: VaR captures not only defaults but also credit migration, which often dominates losses for investment-grade portfolios.

How does CreditMetrics calculate portfolio credit VaR?

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