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FRM Part II · FRM Exam Part II · Estimating Default Probabilities

In the Merton structural model, a firm has issued a single zero-coupon bond maturing at time T. How is the firm's equity value at time T best described?

Equity is a European call option on the firm's assets with strike equal to the face value of debt, because shareholders receive the maximum of asset value minus debt, or zero, at maturity. The put option relates to the creditors' loss exposure.

  1. AA European put option on the firm's assets with strike equal to the debt face value
  2. BA European call option on the firm's assets with strike equal to the debt face valueCorrect
  3. CAn American call option on the firm's assets with strike equal to the market value of debt
  4. DA risk-free bond plus a short position in the firm's assets

Explanation

At maturity shareholders receive max(V - D, 0), where V is asset value and D is the face value of debt. This is the payoff of a European call on assets struck at D. The put description corresponds to the value of the creditors' default guarantee, not to equity.

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