merton.greeks.pd_sensitivity¶

Risk-neutral PD sensitivities (closed form).

Each sensitivity is the partial derivative of PD = Φ(-d₂) with respect to one input, evaluated at the supplied operating point.

Functions¶

`pd_leverage_sensitivity`(→ merton._typing.FloatArray)	∂PD/∂D = φ(-d₂) · 1 / (D · σ_A · √T).
`pd_vol_sensitivity`(→ merton._typing.FloatArray)	∂PD/∂σ_A in closed form.
`pd_rate_sensitivity`(→ merton._typing.FloatArray)	∂PD/∂r — typically negative: higher rates push the drift up, PD down.

Module Contents¶

merton.greeks.pd_sensitivity.pd_leverage_sensitivity(asset_value: merton._typing.ArrayLike, asset_vol: merton._typing.ArrayLike, debt: merton._typing.ArrayLike, rf: merton._typing.ArrayLike, T: merton._typing.ArrayLike, *, dividend_yield: merton._typing.ArrayLike = 0.0) → merton._typing.FloatArray[source]¶

∂PD/∂D = φ(-d₂) · 1 / (D · σ_A · √T).

Higher debt ⇒ higher PD. The sign is positive.

merton.greeks.pd_sensitivity.pd_vol_sensitivity(asset_value: merton._typing.ArrayLike, asset_vol: merton._typing.ArrayLike, debt: merton._typing.ArrayLike, rf: merton._typing.ArrayLike, T: merton._typing.ArrayLike, *, dividend_yield: merton._typing.ArrayLike = 0.0) → merton._typing.FloatArray[source]¶: ∂PD/∂σ_A in closed form.

merton.greeks.pd_sensitivity.pd_rate_sensitivity(asset_value: merton._typing.ArrayLike, asset_vol: merton._typing.ArrayLike, debt: merton._typing.ArrayLike, rf: merton._typing.ArrayLike, T: merton._typing.ArrayLike, *, dividend_yield: merton._typing.ArrayLike = 0.0) → merton._typing.FloatArray[source]¶: ∂PD/∂r — typically negative: higher rates push the drift up, PD down.