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 3% and the risk-neutral probability that the firm defaults is 5%. What is today's fair price for this bond?
A) $87.55
B) $89.23
C) $92.59
D) $94.66

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 the probability of no default times the payoff in that case plus the probability of default times the recovery value. Mathematically, this is (1 - 0.05) * $100 + 0.05 * ($100 * 0.5) = $95 + $2.5 = $97.5. Discounting this at the risk-free rate of 3% gives $97.5 / (1 + 0.03) = $94.66.

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