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 42%.The risk free interest rate for one year is 5%.If the credit spread on the bond is 2.5%,what is the risk-neutral probability of default of the bond? Assume all yields are stated in simple terms with annual compounding.
A)0.01
B)0.02
C)0.03
D)0.04

Question

Quizplus · Accepted Answer

The risk-neutral probability of default can be calculated using the formula for the price of a risky bond, which is the expected payoff discounted at the risk-free rate. The expected payoff is (1 - PD) * 1 + PD * Recovery, where PD is the probability of default and Recovery is the recovery rate. The price of the bond can also be expressed as the present value of its payoff, discounted at the risk-free rate plus the credit spread. Setting these two expressions equal and solving for PD gives us the risk-neutral probability of default. Given a risk-free rate of 5%, a credit spread of 2.5%, and a recovery rate of 42%, we find that the probability of default that matches the given conditions is 4%.

Suppose We Have a Zero Coupon Bond That Pays $1