Treasury Finance and Development Banking: A Guide to Credit, Debt, and Risk, + Website

APPENDIX B

CDS Spreads and Default Probabilities

In Section 4.2.3 we claimed that

(2.1)

That is, the probability of default is roughly equal to the CDS rate divided by one minus recovery. Here is how to get this result. From the definition of CDS we have

We only want to show that our claim is reasonable for a short-dated T (which is quite normal since when we calculate default probabilities we are gauging something fairly imminent). Equation B.1 is equivalent to showing that

One can assume the special case in which, particularly for a short-dated CDS, all the premium is paid up front, reducing the above to

(2.2)

From the short-dated assumption it should follow that and also , in practice approximating the integral to a one-step calculation, which is Equation B.2 itself.

Incidentally since we have (from Equation 3.13) that

using a simple binomial expansion we obtain

from which it follows, ...