Probability of Quarterly default

FRM
#1

Company ABC was incorporated on january 1, 2004. It has expected annual default rate of 10%. Assuming a constant quarterly default rate, what is the probability that company ABC will not have defaulted by April1, 2004 ?

a) 2.4%

b) 2.5%

c) 97.4%

d) 97.5%

#2

If the quarterly default rate is d, then to survive for a year (90% chance), it has to survive all four quarters:

(1 – d)^4 = 0.9

1 – d = 0.9^(1/4) = 97.4%

d = 2.6%

The probability that it will not have defaulted by April 1 (survived one quarter) is 1 – d = 97.4%.

#3

Kudos Magician

#4

Thanks.