merton.core.physical

Risk-neutral ↔ physical probability-of-default conversion.

The Merton model under Black-Scholes assumptions produces risk-neutral PDs (Q-measure). For credit-loss forecasting, banks typically need physical PDs (P-measure). The two are related through the market price of risk:

\[DD_P = DD_Q + \lambda\, \sigma_A\, \sqrt{T}\]

where \(\lambda = (\mu - r) / \sigma_M\) is the (asset-class) Sharpe ratio. The physical PD is then \(\Phi(-DD_P)\).

Functions

physical_pd(→ merton._typing.FloatArray)

Convert a risk-neutral PD into a physical PD.

Module Contents

merton.core.physical.physical_pd(rn_pd: merton._typing.ArrayLike, asset_vol: merton._typing.ArrayLike, sharpe_ratio: merton._typing.ArrayLike, T: merton._typing.ArrayLike) → merton._typing.FloatArray[source]

Convert a risk-neutral PD into a physical PD.

Parameters:

  • rn_pd – Risk-neutral probability of default (decimal in [0, 1]).

  • asset_vol – Annualised asset volatility.

  • sharpe_ratio – Equity / asset-class Sharpe ratio λ = (μ - r) / σ.

  • T – Horizon (years).