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FRM Part I · FRM Exam Part I · Measuring Credit Risk

In the Merton structural model of default, a firm is financed by equity and a single zero-coupon bond maturing at time T. Which description of the equity of the firm is correct?

Equity in the Merton model is a European call option on the firm's assets with strike equal to the debt's face value, because shareholders receive the residual max(V - D, 0) at maturity and walk away with nothing if assets fall short of the debt.

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

Explanation

At maturity, shareholders receive max(V - D, 0), which is the payoff of a call on assets V with strike D. The put description fits the lenders' short position, not the equity. Lenders hold a risk-free bond minus a put on the assets.

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