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

In the Merton structural model, a firm has a single zero-coupon debt issue maturing at time T, and the firm's equity is valued as a financial claim on the firm's assets. Which description of the equity payoff at T is correct?

Equity in the Merton model is a European call option on the firm's assets with strike equal to the face value of debt, because shareholders receive the residual max(V minus D, 0) at maturity and walk away if assets fall short.

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

Explanation

At maturity shareholders receive max(V_T - D, 0), which is a European call on assets with strike D. Debt holders hold the risk-free debt minus a put on assets, so the put description applies to the debt's credit exposure, not equity.

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