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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 100, a zero-coupon debt with face value 80 due in one year, a risk-free rate of 5% (continuous), and asset volatility of 25%. Using N(-d2) as the risk-neutral default probability, which is closest to the probability of default?

The risk-neutral default probability is about 16.7%. Here d2 is roughly 0.968, and the default probability equals N(-d2). The 11.2% figure wrongly uses d1, and 83.3% is the probability of repayment rather than default.

  1. A16.7%Correct
  2. B11.2%
  3. C83.3%
  4. D33.4%

Explanation

d2 = [ln(100/80) + (0.05 - 0.5*0.25^2)*1]/0.25 = (0.2231 + 0.01875)/0.25 = 0.9676. N(-0.9676) is about 0.1666, or 16.7%. Using d1 = 1.2176 gives N(-d1) = 11.2%, which is the wrong quantity. N(d2) = 83.3% is the probability of no default.

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