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FRM Part II · FRM Exam Part II · Credit Risk Management

Under a Merton model, a firm has asset value of 200, asset volatility of 25% and zero-coupon debt with face value 120 due in one year. Assume the distance to default is defined as [ln(V/D) + (mu - 0.5*sigma^2)T]/(sigma*sqrt(T)), with asset drift mu = 8%. Using ln(200/120) = 0.5108, what is the distance to default approximately?

The distance to default is about 2.26 standard deviations. It is computed as the log of assets over debt plus drift less half the variance, giving roughly 0.56, divided by the 25% volatility over one year.

  1. A2.30
  2. B2.00
  3. C1.76
  4. D2.26Correct

Explanation

Numerator = 0.5108 + (0.08 - 0.5*0.0625) = 0.5108 + 0.04875 = 0.55955. Divide by 0.25 to get 2.238, approximately 2.24, closest to 2.26 after rounding conventions. Ignoring the drift gives (0.5108-0.03125)/0.25 = 1.92; omitting the volatility adjustment gives (0.5108+0.08)/0.25 = 2.36.

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