Hi
@pint0 I think it's a good question because I've definitely struggled with the non-mathematical interpretation of the
unconditional PD. Despite not being currently assigned to the topic, I actual favor Hull's interpretation (emphasize mine): "We will refer to this as the unconditional default probability. It is the probability of default during the third year
as seen today."
That's only three words ("as seen today") but I find them helpful. Why? Well, first we must acknowledge the key assumption of a
constant hazard rate. Our assumption here is that the conditional default probability is constant; e.g., as the instantaneous PD, λ = 2.0% implies conditional PD is
constant at 1 - exp(-2%) = 1.98%. This may not be realist but if we assume it then ...
The unconditional PD during a future Year X declines because it is
from the perspective of today ("as we see it today, time zero") and, as a joint probability of (cumulatively) surviving to the beginning of year X and then (conditionally) defaulting during Year X, is must decline because the cumulative probability of survival declines as we extend the horizon forward. The conditional PD each year does not change, but we are pushing forward a declining survival rate. I literally visualize standing on a seashore and looking out to the horizon: if we were to imagine the constant conditional PD as a fixed-length piece of lumber that is constant length, as it drifts out to the horizon, it shrinks in appearance to us. The length of the lumber is unchanged (aka, conditional PD is unchanged) but the distance between us and the lumber is increasing (aka, the cumulative default probability is increasing such that cumulative survival is decreasing). By way of analogy, for me, the key here is that unconditional PD is from the perspective of today. I hope that's helpful,
Stay connected