Probability

[sucheta_isi]

David,
If someone says " A company will/over be in default after 3 years"
then what do you conclude?
Does it mean that it can be in default after 1/2 3 years?
so 3 mutually exclusive cases?

 

[David Harper CFA FRM]

Hi sray,

I think your question illustrates why we want to rely on specific definitions, at least in the FRM; as Hull shows in credit risk (chapter 22) we can have three different definitions.
But our primary FRM focus is on conditional vs. cumulative; e.g., conditional PD =1% (aka hazard rate or default intensity) means the prob of default in a year conditional on survival up until then.
Such that 3-year cumulative PD = 1 - (conditional survival)^3 = 1 - (1-1%)^3 = 1 - 99%^3 = ~97+% ... the probability of a default in either years 1, 2, or 3 is the probability of not surviving all three years.
... re: "A company will/over be in default after 3 years," that appears to refer to an application of the exponential distribution (see Rachev) where we are asking the complement to "what is the prob that we will experience an event [e.g.,] default within the next three years?" ... we can similarly ask, per exponential, what is the probability the next default occurs at three years or later.

David