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I read this:

Equity in a corporation is essentially a call option on the enterprise value (the sum of all the firm’s assets) with a strike price equal to the firm’s debt. The firm’s bonds are a risk-free bond with a short put option where the strike price again equals the debt face value.

Which later mentioned the Merton Model, which I think is over my head, but can someone explain to me the intuition behind this? The short-put kind of makes sense, since if the assets fall behind the debt a business is likely to go bankrupt, but I don't really understand the equity being like a call option at all.

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  • I keep misreading "short put" as "shot put"...
    – keshlam
    Oct 15, 2023 at 0:07
  • FWIW, for me that comparison adds more confusion than it resolves. Usually it's more useful to explain more complicated or less common things in terms of simple ones rather than the reverse.
    – keshlam
    Oct 15, 2023 at 15:04

1 Answer 1

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Let A = assets (enterprise value) and D = debt.

If A > D, then the firm is solvent: Bonds have the full value D, and equity has the value A - D.

If A < D, then the firm is bankrupt: Bondholders receive A (a loss of D - A), and equity is wiped out.

So the value of equity = max(A - D, 0), which corresponds to a call option with strike D.

And the loss by bondholders = max(D - A, 0), which corresponds to a put option with strike D.

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