How does Moody's KMV calculate Expected Default Frequency (EDF)?

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AcadiFi · Accepted Answer

Moody's KMV estimates EDF through three steps grounded in Merton's 1974 model, which treats equity as a call option on firm assets struck at debt.

(1) Estimate asset value V and asset volatility sigma_V: observed equity value E and equity volatility sigma_E are used with Merton's equations E = V*N(d1) - D*exp(-rT)*N(d2) and sigma_E * E = sigma_V * V * N(d1) to back out V and sigma_V iteratively. For Thalassa Shipping, E = $820M, sigma_E = 42%, debt D = $1.4B, yields V = $2.15B, sigma_V = 16.5%.

(2) Compute distance-to-default (DD): DD = (V - default point)/(V * sigma_V). KMV defines the default point as short-term debt plus 50% of long-term debt, not total debt. With short-term debt $600M and long-term $800M, default point = $600M + $400M = $1.0B. DD = ($2.15B - $1.0B)/($2.15B * 0.165) = 3.24.

(3) Map DD to EDF via empirical calibration: KMV maintains a proprietary dataset of historical defaults and computes empirical default frequencies for each DD bucket. DD = 3.24 might map to EDF = 0.28%, meaningfully different from the theoretical Phi(-3.24) = 0.06% because real default distributions have fatter tails than normal.

This empirical mapping is KMV's secret sauce: theoretical structural models systematically understate default probabilities, so the database correction is essential. For FRM, distinguish between structural (Merton/KMV), reduced-form (hazard rate), and hybrid approaches.

How does Moody's KMV calculate Expected Default Frequency (EDF)?

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