FRM Part I · FRM Exam Part I · Corporate Bonds
A one-year zero-coupon bond with face value $100 has a risk-neutral one-year default probability of 3% and a recovery rate of 40% of face value paid at maturity. The risk-free rate is 5.00% (annual compounding). Using risk-neutral pricing, what is the bond price closest to?
Expected payoff is 0.97 x 100 + 0.03 x 40 = 98.20, discounted at 5% gives about $93.52, so the closest option is $93.43.
- A$92.57Correct
- B$95.24
- C$93.43
- D$97.14
Explanation
Expected payoff = 0.97 x 100 + 0.03 x 40 = 97 + 1.2 = 98.20. Discounting at 5%: 98.20/1.05 = 93.52. Check: the options include 92.57? Recompute: 98.20/1.05 = 93.52, so the closest listed value is 93.43 only if rounding; however the exact price 93.52 is nearest to 93.43 (diff 0.09) versus 92.57 (diff 0.95).
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