FRM Part II · FRM Exam Part II · Fundamentals of Credit Risk
A two-year zero-coupon bond from an issuer yields 5.00% annually compounded, versus 3.00% for a risk-free two-year zero. Recovery is 0% for simplicity. Using the price ratio, what is the risk-neutral probability of default over the two years (ignoring discounting differences beyond the ratio, i.e. survival probability = corporate price / risk-free price)?
The two-year risk-neutral default probability is about 3.77%. With zero recovery, survival equals the corporate bond price divided by the risk-free price, 0.9070 divided by 0.9426, which is 0.9623, leaving a default probability of roughly 3.77%.
- A3.77%Correct
- B1.90%
- C4.00%
- D7.30%
Explanation
Corporate price = 1/1.05^2 = 0.907029. Risk-free price = 1/1.03^2 = 0.942596. Survival = 0.907029/0.942596 = 0.96227. Default probability = 3.77%. Using 2×(5%−3%)=4.00% ignores compounding; 1.90% is roughly a one-year figure.
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