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

A risk analyst applies the Merton structural model to a firm financed by equity and a single zero-coupon debt issue maturing in one year. Under the model, how is the firm's equity value best described?

Equity is a European call option on the firm's assets with the strike equal to the face value of debt, because shareholders receive the asset value above the debt owed at maturity and nothing if assets fall short of the debt.

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

Explanation

In the Merton model, shareholders hold a residual claim: they receive max(V - D, 0) at debt maturity, which is the payoff of a European call on assets with strike D. Debt is equivalent to a risk-free bond less a put on assets, so the put-based descriptions apply to debt holders, not equity.

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