## Wednesday, 9 November 2011

### Probability-5 (FRM)

A company has a constant 7% per year probability of default. What is the probability the company will be in default after three years?
(a)19.6%          (b) 22.5%        (c) 21%              (d) 7%
Solution follows here:
Solution:
Probability of default (per year) = 7% = 0.07
It is asked for the probability of getting default after three years => it is not sure whether getting default in 4th year or 5th year or  etc..,
A company getting default is a one time job. If a company defaults this year, there is no need to check for the status on the next year. So we need to proceed with the reverse logic here. We need to go for iterations by considering “The probability of not getting default” but not “The probability of getting default”.
Probability of not getting default for the first year = (0.93)
Probability of not getting default for the first two years = (0.93) *(0.93) = (0.93)2
Probability of not getting default for the first three years = (0.93)3
Probability of getting default after three years
= 1- (Probability of not getting default for the first three years)
= 1-(0.93)3 = 1-(0.804) = 0.1956 = 19.56%