63491687-Goldman-Sachs-State-of-the-Market-Cds-101

Building a Survival Probability Curve using observed CDS spreads 

NPV of an at-market CDS is zero: N

N

i1

i1

NPV   (1  R)  (pi1  pi )  di   s  pi1  di  0 

For a single period:

NPV  (1  R)  (1  p1 )  d1  s  d1  0  (1  R)  (1  p1)  s  (1  p1 )  s /(1  R)  q1  s /(1  R) 

<= The conditional default probability is spread / loss, a convenient rule of thumb!

What is the one-year survival probability and default probability rate for a 50 bp credit when recovery R = 50%?

 

q1 = 0.005 / (1-0.5) = 0.01 or 100 bp / year p1 = 1 - q1 = 1 - 0.01= 99%

37