FRM Part II · FRM Exam Part II · Introduction to Credit Risk Modeling and Assessment
In a Merton model, a firm has asset value of 120, face value of zero-coupon debt of 100 due in one year, and the risk-neutral distance to default is measured by d2 = 0.50. Using N(0.50) = 0.6915, what is the risk-neutral probability of default?
The risk-neutral default probability is N(-d2), which is 1 minus 0.6915, or 30.85%. The figure 69.15% is the survival probability, since default occurs when asset value at maturity is below the debt face value.
- A30.85%Correct
- B69.15%
- C50.00%
- D19.15%
Explanation
Risk-neutral default probability is the probability that assets finish below debt, equal to N(-d2) = 1 - N(0.50) = 1 - 0.6915 = 0.3085. The 69.15% option is the probability of survival, i.e., N(d2). The 19.15% option is N(0.5) - 0.5, a misreading of the table.
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