Explanation

In structural models of credit risk (like the Merton model), the relationship between debt and equity can be interpreted using option pricing theory:

• Equity is a purchased call option on the assets: This is the correct interpretation. Shareholders have a call option on the firm's assets with a strike price equal to the face value of debt. If the asset value exceeds the debt value at maturity, shareholders exercise their option and keep the residual value.

• Debt is equivalent to a risk-free bond minus a put option: The correct interpretation is that debt holders are long a risk-free bond and short a put option on the assets. This means they receive the risk-free payment but have sold downside protection to shareholders.

• Option B is incorrect because it reverses the positions - debt is actually short a put option, not long one.

• Option C is incorrect because it doesn't accurately represent the option relationships in structural models.

The key insight is that shareholders have limited liability - they can't lose more than their investment, which gives them option-like characteristics.