Question

Given the following information:

1-year zero-coupon Corporate yield: 3.8%
1-year zero-coupon Treasury bonds yield: 2.8%
Recovery rate of Corporate Bond: 0.44 with probability 0.34 and 0.57 with probability 0.66

Calculate the probability of default of the Corporate Bond.

NOTE: Round all calculations to 4 decimal places. If you get 0.1234 then write 12.34

Answer 1

Given that,

1-year zero-coupon Corporate yield Rb = 3.8%
1-year zero-coupon Treasury bonds yield Rf = 2.8%
Recovery rate of Corporate Bond: 0.44 with probability 0.34 and 0.57 with probability 0.66

So, total recovery rate RR = 0.44*0.34 + 0.57*0.66 = 0.5258 or 52.58%

Probability of default PD of corporate bond can be calculatedd using following formula

(1 + Rf) = (1 + Rb)*(1-PD) + (1+Rb)*PD*RR

So, 1.028 = 1.038*(1-PD) + 1.038*PD*0.5258

=> 1.038PD - 0.54578PD = 0.01

=> PD = 20.32%

So, probability of default of the Corporate Bond is 20.32%