merton.calibration.naive

Naive calibration (Bharath-Shumway 2008).

Closed-form approximation that skips the two-equation calibration entirely:

A   ≈ E + D
σ_D ≈ 0.05 + 0.25 · σ_E                 (proxy for debt volatility)
σ_A ≈ (E / (E + D)) · σ_E + (D / (E + D)) · σ_D

Empirically (Bharath-Shumway 2008, RFS), this estimator forecasts default about as well as the full Merton solution while costing essentially nothing to evaluate.

References

Bharath & Shumway (2008). Forecasting Default with the Merton Distance to Default Model. Review of Financial Studies 21 (3), 1339-1369.

Classes

NaiveCalibrator

OO interface to naive().

Functions

naive(→ merton.calibration.base.CalibrationResult)

Closed-form Bharath-Shumway naive estimator.

Module Contents

merton.calibration.naive.naive(equity: merton._typing.ArrayLike, equity_vol: merton._typing.ArrayLike, debt: merton._typing.ArrayLike, rf: merton._typing.ArrayLike, T: merton._typing.ArrayLike) → merton.calibration.base.CalibrationResult

Closed-form Bharath-Shumway naive estimator.

Parameters:

• equity – Market value of equity and the default threshold.

• debt – Market value of equity and the default threshold.

• equity_vol – Annualised equity volatility.

• rf – Risk-free rate and horizon (used for the parent MertonResult only — not inside the naive math).

• T – Risk-free rate and horizon (used for the parent MertonResult only — not inside the naive math).

class merton.calibration.naive.NaiveCalibrator

Bases: merton.calibration.base.Calibrator

OO interface to naive().

method = 'naive'

fit(firm)

Infer asset value & volatility for firm.