Suppose we have a zero-coupon bond that pays $1 after one year if the issuing firm is not in default. If the firm is in default the recovery rate is 40%. The one-year risk free interest rate in simple terms is 5% and the risk-neutral probability that the firm defaults is 10%. What is the fair credit spread on the bond (again, in simple terms)?
A) 5.0%
B) 6.7%
C) 10.5%
D) 11.7%

Question

Quizplus · Accepted Answer

To calculate the fair credit spread on the bond, we need to first calculate the expected loss in case of default:
Expected loss = Probability of default * (Face value - Recovery value)
= 0.1 * (1 - 0.4)
= 0.06

Next, we need to calculate the risk-neutral present value of the bond:
PV = Face value / (1 + risk-free rate)
= 1 / (1 + 0.05)
= 0.9524

Finally, the fair credit spread is:
Credit spread = Expected loss / PV
= 0.06 / 0.9524
= 0.063 or 6.3%

Therefore, the closest option is B) 6.7%.

Suppose We Have a Zero-Coupon Bond That Pays $1 After