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 by taking the expected payoff under the risk-neutral measure and discounting it back at the risk-free rate. The expected payoff is $(1 - 0.1) * $1 + 0.1 * $0.40 = $0.94. Discounting this at the 5% risk-free rate gives $0.94 / (1 + 0.05) = $0.895.

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