Inferring Credit Rating Transitions from One- and Two-Year Spreads

Summary

The document asks how to infer a one-year transition matrix for a three-state credit-rating model with two solvent ratings and a default state. It assumes zero recovery and interest rates, provides one-year and two-year credit spreads for each performing rating, and presents a proposed matrix whose default probabilities are inferred from the one-year spreads while the non-default transitions remain unknown.

The central issue is how the multi-period spread information constrains the missing transition probabilities. In a Markov model, the two-year transition probabilities follow from squaring the one-year transition matrix; survival probabilities implied by those transitions can then be related to two-year spreads under the stated assumptions. The document does not supply a solution, nor does it establish that spreads map directly to default probabilities without specifying a pricing convention. Its setup is therefore useful as an exercise in linking credit spreads, survival, and Markov transition dynamics, with conclusions limited by the simplified assumptions.

Key ideas

• A three-state credit model distinguishes two performing rating states and an absorbing default state.
• The proposed matrix uses one-year spreads to set default probabilities but leaves rating migration probabilities undetermined.
• Two-year transition behavior is obtained by composing the one-year transition matrix with itself.
• Spread-to-default-probability conversion depends on the model’s recovery, rate, and pricing assumptions.
• The document poses the calibration problem without giving a final matrix.

Tags

# Three-state Markov Chain: Credit rating question


# Three-state Markov Chain: Credit rating question












Consider a credit-rating system, with two solvency states (A & B) and a default state (D), and assuming recovery rate and interest rate are 0%.

- The one year credit spread for an A-rated company is 0.1% and for a B-rated company is 0.22%.

- The two year credit spread for an A-rated company is 0.12% and for a B-rated company is 0.2%.

What is the one-year transition probability matrix?

[My attempt: ] I used the 1 year credit spreads to obtain the respective elements of the matrix, that is the probabilities of default for both states A & B. So, my one-year transition matrix is as follows:

```
      A            B              D
A     x      0.9990005-x      0.0009995
B     y      0.9978024-y      0.0021976
D     0           0               1
```

- How do I use the two year credit spread to obtain the missing values, x & y?

- Am I on the right track?

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This summary was written by Stratmill's research agent from the original; it is not a copy of the source.