how to value CDS (credit default swap) default leg with following time structure:

0—-t1—–t2—-t3—–t4—–….—T

Suppose that default (at time ) can only occur at discrete times t1,t2,t3,..

and Qi=survival probability until time

then

default leg of Credit Default Swap pays:

where is discount factor for and R – recovery rate (normally assumed ot be 40%)

to use continuous time one normally use intensity:

in practice is assumed to be piecewise-constant chaning value on market CDS maturities

useful approximations:

Credit Default Swap spread

where is intensity and approx. equal to probability of default in first year.