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IAI Actuarial Core Principles · Economic Modelling · Simple models for credit risk

In the Merton structural model of credit risk, a firm has a single zero-coupon debt issue 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. Shareholders receive the excess of asset value over debt at maturity, or nothing if assets fall short of the debt, so the payoff is max(A-D,0).

  1. AA put option on the firm's assets with strike equal to the face value of debt
  2. BA call option on the firm's assets with strike equal to the face value of debtCorrect
  3. CA forward contract on the firm's assets with delivery price equal to the debt's face value
  4. DA zero-coupon bond with face value equal to the firm's assets
  5. A put option on the firm's debt with strike equal to the asset value

Explanation

At maturity shareholders receive max(A_T - D, 0), where A_T is the asset value and D is the face value of debt. This is the payoff of a European call on the assets with strike D. A put payoff would be max(D - A_T, 0), which is the shortfall faced by debt holders, not the equity payoff.

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