FRM Part II · FRM Exam Part II · Credit Risk Management
A one-year zero-coupon bond has a risk-free rate of 3% and a yield of 5% (annual compounding). Assuming a recovery rate of 40% of face value and a one-period reduced-form setting, the implied risk-neutral default probability is closest to:
The implied risk-neutral default probability is about 3.3%. The 2% credit spread is divided by the loss given default of 60%, since spread is approximately probability of default times loss severity. Using the spread alone would understate default probability.
- A3.3%Correct
- B1.9%
- C2.0%
- D5.0%
Explanation
Price = 1/1.05 = 0.95238. Risk-free price with expected payoff: [(1-p) + 0.4p]/1.03 = 0.95238 gives 1 - 0.6p = 0.98095, so p = 0.0317, about 3.2%, nearest 3.3%. Spread/(1-R) = 2%/0.6 = 3.33% is the approximation. 2.0% ignores recovery.
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