How to calculate credit spread from rating

Question

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 1

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:

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