how to value CDS (credit default swap) default leg with following time structure:
Suppose that default (at time ) can only occur at discrete times t1,t2,t3,..
and Qi=survival probability until time
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
Credit Default Swap spread
where is intensity and approx. equal to probability of default in first year.