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On Implied probability of default (FRM Exam 2002, question 87)

Liming

New Member
Dear David,
I’ve have struggling with the following question from FRM practice and past exams. Appreciate your kind help on this!

4) On Implied probability of default (FRM Exam 2002, question 87)
A 1-year government bond yields 10% per annum while a 1-year corporate bond yields 12%. Assuming a recovery rate of 50%m what is the best estimate of the implied default probability of the corporate bond?
Answer provided: default rate of 4% as they use the shortcut to compute the default probability: p x LGD = credit spread
 p = (12% - 10%)/50% = 4%

My question: I used the slower approach for computing the default probability and get a quite different value for p:
p x LGD + (1-p) x (1+risky yield) = (1+riskless yield)
 p x 50% + (1-p)x(1+12%) = 1+10%
 p = 3.226%

Is my approach correct?
If correct, why GARP didn’t use that approach but went for the shortcut?

Thank you for your enlightenment and correction!
Cheers
Liming
10/11/09
 
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