What's new

Qeestion about using exponential cdf

Thread starter #1
Hi David,

I have a quick question about default intensity. This may be a silly question, but does past history (not including defaults) have anything to do with default intensity for the Poisson or exponential distributions? I think the answer is no but I am not sure. In other words, if a firm is in business today and the lambda is 0.2, this means that at this very instant there is a 20% chance of it defaulting. It also means that if I want to find the probability that it will default in the next 3 years I just use the exponential cdf. If I do the same “test” in one year, the parameters are the same because of the distribution we are using, and the info I get will tell me the exact same thing.

Perform “test” in 2009: 45.12% chance of failing in three years (by 2012)
Perform “test” in 2010(conditional that it still has not defaulteded): 45.12% chance of failing in three years (by 2013)

Thank you,

David Harper CFA FRM

David Harper CFA FRM
Staff member
Hi Mike,

In my opinion, what you say is exactly correct. Hazard rate (aka, default intensity) is an instantaneous, conditional probability of default. The exponential function uses the hazard rate as a parameter, such that the exponential CDF returns the cumulative PD. (And it has no built-in way to vary that parameter over time).

The exponential function is indeed "memoryless" (Markovian: http://en.wikipedia.org/wiki/Markov_property ) and does not depend on the time (today, tomorrow, next week). The Rachev chapter notes this as a feature, in contrast to using the Weibull distribution which can vary the hazard rate as a function of time. In the FRM, with respect to credit risk, we are generally always making (and it terms of calculations, we are only dealing with) a "markovian assumption;" e.g., in L2, if we compound a one-year ratings matrix over three years, we implicitly assume rating transition probabilities are independent from year-to-year. Hope that helps, David