Consider a 1-year maturity zero-coupon bond with a face value of USD 1,000,000 and a 0% recovery rate issued by Company A. The bond is currently trading at 80% of face value. Assuming the excess spread only captures credit risk and that the risk-free rate is 5% per annum, the risk-neutral 1-year probability of default on Company A is closest to which of the following?
A. 2%
B. 14%
C. 16%
D. 20%
Answer:C
This can be calculated by using the formula which equates the future value of a risky bond with yield (y) and default probability (π ) to a risk free asset with yield (r):
1+r= (1-π ) *(1+y)+ π R
π = Probability of default; R = Recovery rate
In the situation where the recovery rate is assumed to be zero, the risk-neutral probability of default can be derived from the following equation: 1+r= (1-π )* (1+y) = (1-π )*(FV/MV)
Where MV = market value and FV = face value.
Inputting the data into this equation yield π = 1 - (800,000*1.05)/1,000,000 =0.16.

 
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