Calculating default probabilities given average hazard rates

[hiimdzun]

Hi @David Harper CFA FRM , this question is w.r.t. Hull Chapter 24: Credit Risk. Can you please help me understand why the calculation for PD between year 2 and 3 (PD2,3) uses the euler's number e whereas the calculation for PD between year 1 and 2 (PD1,2) just uses the difference between PD(0,2) - PD(0,1)? Since using the simple difference between PD(0,3) - PD(0,2) yields a different figure compared to using the euler's number e.

Have I overlooked something here?

 

[David Harper CFA FRM]

Hi @hiimdzun copy (@Clay Carter ) PD(1,2) looks correct to me as an unconditional (aka, joint) probability, but to your point PD(2,3) looks incorrect because the unconditional PD(2,3) wants to be PD(0,3) - PD(0,2) but notice that 0.995% ≈ 5.82 - 4.88% so I think it's just that "1 - exp(-0.01*1)" is a typo. Hope that's helpful,

 

[hiimdzun]

Thanks a lot!