Suppose we have a zero-coupon bond that pays $100 after one year if the issuing firm is not in default.If the firm is in default the recovery rate is 50%.The simple risk-free interest rate for one year is 5% and the risk-neutral probability that the firm defaults is 10%.What is todayÕs fair credit spread for this bond?
A)5.5%
B)6.5%
C)7.5%
D)8.5%

Question

Quizplus · Accepted Answer

The fair credit spread is the difference between the yield to maturity of the risky bond and the risk-free rate. The yield to maturity of the risky bond is the rate that equates the present value of the bond's cash flows to its current price. The present value of the bond's cash flows is:PV = $100 / (1 + r)where r is the yield to maturity.The current price of the bond is:Price = $100 * (1 - 0.1) / (1 + r)where 0.1 is the risk-neutral probability of default.Equating the present value of the bond's cash flows to its current price, we get:$100 / (1 + r) = $100 * (1 - 0.1) / (1 + r)Solving for r, we get:r = 0.055The fair credit spread is:Fair credit spread = r - 0.05 = 0.055 - 0.05 = 0.005 = 0.5%

Suppose We Have a Zero-Coupon Bond That Pays $100 After