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 today's fair price for this bond?
A)$0.875
B)$0.895
C)$0.915
D)$0.935

Question

Quizplus · Accepted Answer

The fair price of the bond can be calculated using the expected payoff under the risk-neutral measure, discounted at the risk-free rate. The expected payoff is $(1 - 0.10) * $1 + 0.10 * $0.40 = $0.94$. Discounting this at the risk-free rate of 5% gives $0.94 / (1 + 0.05) = $0.895.

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