Conditional default probability (hazard rate)

Study note: Hazard rate (default intensity) is a conditional PD but it connotes an instantaneous rate of failure. As such, it can be used with elegance in the exponential distribution to compute the cumulative probability of default (cumulative PD). The conditional PD is the probability of default conditional on survival so far; e.g., 3-year conditional PD = probability of default in year 3 assuming the bond survives the prior two years.