Structural Models of Credit Risk

Structural models (like Merton's) rely on the structure of the firm's balance sheet (Assets vs Liabilities) to predict default.

The Logic of Default

Default is not a random event. In Structural Models, default generally occurs Endogenously when the Value of Assets ($V_t$) falls below the Debt threshold ($D$).

Distance to Default (DD)

This is the key metric produced by Structural Models (like the Moody's KMV model). It measures: "How many standard deviations is the firm away from defaulting?"

Steps to Calculate DD:

1. Estimate Asset Value (V) and Asset Volatility: Since we can't see the market value of "Assets" directly (only Equity is traded), we use the Black-Scholes formula in reverse to back-solve for V and Sigma from the observed Stock Price (E) and Stock Volatility.
2. Determine Default Point: Usually taken as Short Term Debt + 0.5 * Long Term Debt.
3. Calculate Distance: (Asset Value - Default Point) / (Asset Volatility)

Interpreting DD

• High DD (e.g., 4 or 5): The firm is very safe. Assets are far above debt.
• Low DD (e.g., 1 or 2): The firm is risky. A small drop in asset value could trigger default.

Strengths & Weaknesses

Strengths

• Link to Fundamentals: Connects stock market (Equity) info to bond market (Credit) risk.
• Early Warning: Since stock prices often react first, a drop in stock price lowers DD, warning bondholders early.

Weaknesses

• Assumes Frictionless Markets: Real bankruptcy is messy (lawyers, restructuring costs).
• Assets are not liquid: You can't just "sell" a factory instantly to pay debt.

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