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FRM Part I · FRM Exam Part I · Measuring Credit Risk

Under the Merton model, a firm has current asset value of 150 million, a zero-coupon debt face value of 100 million due in one year, asset volatility of 25%, and a continuously compounded risk-free rate of 5%. What is the risk-neutral probability of default at maturity (N(-d2))? Use N(1.70) = 0.9554 and N(1.95) = 0.9744.

The risk-neutral default probability is about 4.5%. Computing d1 as 1.947 and d2 as 1.697 and taking N(-d2) gives roughly 1 minus 0.9554. Using N(-d1) instead would understate default risk, and N(d2) is the survival probability, not the default probability.

  1. AApproximately 4.5%Correct
  2. BApproximately 2.6%
  3. CApproximately 9.0%
  4. DApproximately 95.5%

Explanation

d1 = [ln(1.5) + (0.05 + 0.5×0.0625)]/0.25 = 0.486715/0.25 = 1.947. d2 = 1.947 - 0.25 = 1.697. Default probability = N(-1.697) ≈ 1 - 0.9554 ≈ 4.5%. Using N(-d1) gives about 2.6%, which is the wrong argument.

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