How do I calculate Merton model distance to default step by step?

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AcadiFi · Accepted Answer

The Merton (1974) framework treats equity as a call option on firm assets struck at the face value of debt. Once you have asset value V, asset volatility sigma_V, debt face D, risk-free rate r, and horizon T, the distance to default is DD = [ln(V/D) + (r - 0.5 sigma_V^2) T] / (sigma_V sqrt(T)). Worked example: Orbitweld Industries has inferred asset value V = $640M, asset volatility 24% annualized, debt face D = $420M, r = 4%, T = 1 year. Then ln(640/420) = ln(1.5238) = 0.4215. Drift term = (0.04 - 0.5 * 0.0576) * 1 = 0.0112. Numerator = 0.4328. Denominator = 0.24 * 1 = 0.24. DD = 1.803. Risk-neutral PD = N(-DD) = N(-1.803) = 3.57%. The practical challenge is that V and sigma_V are unobservable. You solve a two-equation system simultaneously: the Black-Scholes-Merton call pricing equation linking equity E to V, and the volatility relationship sigma_E * E = sigma_V * V * N(d1). KMV iterates this numerically. ```mermaid flowchart TD A[Equity E
Equity vol] --> B[Solve BSM
system] B --> C[Asset V
Asset vol] C --> D[Compute DD] D --> E[Map to EDF] ``` For FRM exam watch for the Merton PD being risk-neutral versus the empirical EDF.

How do I calculate Merton model distance to default step by step?

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