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Estimating Credit Spreads from Default Probabilities and CDS Data

Article Quant Q&A · Author: Oliver Mohr Bonometti
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Summary

The document explains how to translate a rating-based default probability into an approximate credit spread. It starts with a transition matrix as a Markov chain: repeated matrix multiplication produces a cumulative probability of default over a chosen horizon. Given that probability and an assumed recovery rate, the spread can be solved from the exponential default-probability approximation, with the time horizon included in the calculation.

The response also points to estimating spread directly from the CDS default leg divided by the contract’s value of a basis point. This offers a market-based alternative to the simplified rating-derived estimate. The approximation depends on assumptions about recovery and default timing, while a rating transition matrix describes historical rating behavior rather than the institution’s current market-implied risk; the document gives no detailed calibration or validation evidence.

Key ideas

  • Repeated transition-matrix multiplication can produce a term structure of cumulative default probabilities.
  • An assumed recovery rate and the horizon are needed to convert default probability into an approximate spread.
  • The spread can be isolated by taking the negative logarithm of one minus the cumulative default probability.
  • A CDS-based estimate can be obtained from the default-leg value divided by DVO1.

Tags

Fixed incomeStatisticsDerivatives pricingRisk management
Full text
# How to calculate credit spread from rating


# How to calculate credit spread from rating












I've been trying to calculate the credit spread of a financial institution with a Fitch rate of A.

By using the transition matrix (https://www.fitchratings.com/web_content/nrsro/nav/NRSRO_Exhibit-1.pdf page 4), I obtained a default probability at `10 years` of `0.7941%` (by multiplying the matrix with itself 10 times).

After that, I tried to obtain the credit spred with a 40% of recovery rate with the following formula:

$$ PD = 1 - EXP(\frac{-spread \cdot years}{1-R}) $$

But I obtained a spread of `4,783` at 10 years which is very low to `100 bps` of credit spread obtained from a JP Morgan CDS. Results make more sense if I don't use the years in the formula, but I think they should be considered.

## Answer by Claudio Cuevas Pazos (score 1)

https://quant.stackexchange.com/a/35685

Assuming you have a transition Matrix, you can obtain a term structure for each rating (AAA,AA,BB,etc...) by a matrix multiplication, as your transition matrix is a Markov Chain. This term Structure will be a probability of default term structure. Then, applying the approximation for the probability of default you mentioned given it's credit quality as A and assuming you have a Recovery Rate for your case: $$PD_{A}^{T}=1-e^{\frac{-spread*years}{1-R}}$$,

from there, you can calculate the spread as follows:

$$spread=-\frac{1-R}{years}ln(1-PD_{A}^{T}).$$

Obviously, the best thing to do is to estimate the spread as follows:

$$ spread=\frac{CDS_{DefLeg}}{DVO1}$$

Shown in full with attribution under the source's licence. Licence: CC BY-SA 4.0 (Stack Exchange)

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