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FRM Part II · FRM Exam Part II · Credit Risk

Under the Merton model, a firm has asset value of 120, zero-coupon debt with face value of 100 due in one year, and the risk-neutral probability that assets end below 100 is 15%. Which statement about the firm's equity and the risk-neutral default probability is correct?

Equity is a call option on the firm's assets with a strike equal to the debt face value of 100, since shareholders receive the residual above debt. Default happens when assets finish below 100, so the risk-neutral default probability is the stated 15%.

  1. AEquity is a put option on assets, and the default probability is 85%
  2. BEquity is a call option on assets with strike 100, and the risk-neutral default probability is 15%Correct
  3. CEquity is a call option on assets with strike 120, and the default probability is 15%
  4. DEquity is a put option on assets with strike 100, and the default probability is 15%

Explanation

Shareholders receive max(A-D,0), which is a call on assets with strike equal to debt face value of 100. Default occurs when assets end below 100, which is given as 15% under the risk-neutral measure, i.e., N(-d2). The strike is not current asset value, and equity is not a put.

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