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FRM Part II · FRM Exam Part II · Introduction to Credit Risk Modeling and Assessment

In the Merton structural model, a firm has a single zero-coupon debt issue maturing at time T. From the perspective of shareholders, which option position best describes their claim on the firm's assets at maturity?

Equity is a long European call option on the firm's assets with strike equal to the face value of debt, because shareholders receive the residual max(A minus D, 0) at maturity. Debt holders instead hold risk-free debt minus a put.

  1. AA long put option on firm assets with strike equal to the face value of debt
  2. BA short call option on firm assets with strike equal to the face value of debt
  3. CA long call option on firm assets with strike equal to the face value of debtCorrect
  4. DA short put option on firm assets with strike equal to the equity value

Explanation

At maturity equity holders receive max(A_T - D, 0), which is the payoff of a European call on assets struck at the debt face value. The short put is the position associated with debt holders' risky exposure (risk-free debt minus a put), not equity.

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