Qeestion about using exponential cdf

[wrongsaidfred]

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,
Mike

 

[David Harper CFA FRM]

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

 

[wrongsaidfred]

Fantastic.

Thank you!

Mike