A Question on Default Probability

FRM
#1

Dear All,

I have some problem with the following question and could someone please explain to me?

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

The answer is 97.4%.

Does anyone have any idea? Thanks.

#2

Annulaized probability not defaulting = 1 - annualized probability of defaulting = 1- 0.10 = 0.9

Probability of not defaulting in 3 months = 0.9^(3/12) = 0.974

#3

It is a bloody idiotic problem if you ask me.

How on earth can somebody assume a linear spread of Default Probability.

Very crude.