APPENDIX B
CDS Spreads and Default Probabilities
In Section 4.2.3 we claimed that
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
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, ...
Get Treasury Finance and Development Banking: A Guide to Credit, Debt, and Risk, + Website now with the O’Reilly learning platform.
O’Reilly members experience books, live events, courses curated by job role, and more from O’Reilly and nearly 200 top publishers.