Corporate Liabilities as Contingent Claims
In 1974, Robert Merton revolutionized credit risk by realizing that Equity and Debt are actually Options on the firm's assets. This is known as the Structural Approach to credit risk.
The Concept
Imagine a company with:
- Assets (V): value of the firm's business.
- Debt (D): face value of zero-coupon bond due at time T.
- Equity (E): residual claim.
At maturity (T):
- If Assets > Debt (V > D): Shareholders pay off the debt (D) and keep the remaining (V - D).
- If Assets < Debt (V < D): Shareholders have "Limited Liability". They walk away. Bondholders seize the Assets (V) and take a loss.
Equity as a Call Option
This payoff structure is exactly the same as a Call Option.
- Underlying: Firm Assets (V).
- Strike Price: Face Value of Debt (D).
- Payoff: Max(V - D, 0).
So, Equity = Call Option on Firm Value.
Debt as a Put Option
Bondholders effectively:
- Own the Risk-Free Assets.
- Sold a Put Option to shareholders. (The shareholders have the "right" to sell the assets to bondholders at price D by defaulting).
- Risky Debt = Risk Free Debt - Value of Put Option.
Note
Insight: This means we can use the Black-Scholes Model to value Corporate Debt and calculate the Probability of Default! If Volatility of Assets increases, the value of the Call Option (Equity) increases, but the value of Debt decreases. (High risk hurts bondholders, helps shareholders).
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