KMV / Crosbie-Bohn adjustments

The KMV methodology (Crosbie & Bohn, 2003) tweaks the Merton model in two significant ways for practical PD estimation:

  1. Default point. Empirically, firms default when asset value falls below approximately \(\mathrm{ST} + 0.5 \cdot \mathrm{LT}\), where \(\mathrm{ST}\) and \(\mathrm{LT}\) are short- and long-term debt. The full nominal debt is too conservative; the short-only proxy is too aggressive.

  2. Empirical DD-to-EDF mapping. Rather than mapping \(\mathrm{DD}\) to PD via the normal CDF, KMV uses a non-parametric look-up table built from ~11,700 historical defaults. The resulting expected default frequency (EDF) is calibrated to actual default rates per DD bucket.

In merton, the KMV default point is selected via Firm(default_point="kmv") (this is the default). The empirical DD→EDF mapping ships in a later phase under merton.calibration.kmv_iterative().

Notes

  • KMV’s Sharpe-ratio adjustment to obtain physical PD is exposed via MertonModel(physical_measure=True, sharpe_ratio=...).

  • For real-world calibration you typically also blend implied volatility (when available) with historical equity volatility — see merton.calibration.implied_vol (Phase 0.7).