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FRM Part II · FRM Exam Part II · Fundamentals of Credit Risk

A risk manager uses a Merton model with asset value V0 = 150, debt face value D = 100 due in one year, and the risk-neutral distance to default measured by d2 = 1.00 (N(d2) = 0.8413). The risk-free rate is 4% continuously compounded. Which statement is correct about the risk-neutral default probability and the debt's expected payoff under the model?

The risk-neutral default probability is 15.87%, equal to N(-d2), which is one minus 0.8413. N(d2) is the risk-neutral probability that assets finish above the debt face value, so it measures survival. N(d1) is the option delta and is not the default probability.

  1. ARisk-neutral default probability is 15.87%, equal to N(-d2)Correct
  2. BRisk-neutral default probability is 84.13%, equal to N(d2)
  3. CRisk-neutral default probability is 15.87%, equal to N(-d1)
  4. DRisk-neutral default probability is 8.00%, equal to the risk-free rate doubled

Explanation

In the Merton model, the risk-neutral probability that assets end above D is N(d2), so default probability is N(-d2) = 1 − 0.8413 = 15.87%. N(d1) is the option delta, not the exercise probability. Confusing N(d2) with default probability gives 84.13%.

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