Implicit default prob (#2)

[nanchary]

The market trades a 1-year bond at 50bp credit spread, and a 3-year bond at 60bp. In the USD market conditions as of fall 2001 and with a recovery rate of 50 percent, what is the implicit probability of default before year 3?

a) 1%.
b) 2%.
c) 3%.
d) 4%.

What are the treasury rates for 1yr and 3yr?

Thanks,
Narender

 

[David Harper CFA FRM]

Narender,

I can't solve this. There are two unknown forward rates: f(1,2) and f(2,3) and, as far as i can tell, only one equation.

If you could solve for these two forward rates (or if the problem simply replaced a 2-year bond with a 3-year bond, you'd have only one unknown, the f[1,1]), you could solve for the implied prob of repayment (p = 1 - PD) given the spreads (and you don't actually need the treasuries b/c you have the recovery).

Then you'd have a series of three one year PDs so then answer would simply be = 1 - [(p1)(p2)(p3)].

But like the last question you gave me from your secret source (who's questions are these?) it is imprecise, they probably meant to ask "what is the implied cumulative default probability before year 3?"

David