merton.core.distance

Distance-to-default and probability-of-default primitives.

These are the most-called functions in the whole package. They accept any combination of scalar and array inputs (NumPy-style broadcasting) and dispatch to the fastest available backend.

Examples

>>> from merton import distance_to_default, prob_of_default
>>> dd = distance_to_default(100, 0.25, 60, 0.04, 1.0)
>>> float(round(dd, 4))
2.0783
>>> float(round(prob_of_default(dd), 6))
0.018841

Functions

distance_to_default(→ merton._typing.FloatArray)	Compute Merton's distance-to-default DD = d_2.
prob_of_default(→ merton._typing.FloatArray)	Risk-neutral probability of default given the distance-to-default.

Module Contents

merton.core.distance.distance_to_default(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, backend: str | None = None, validate: bool = True) → merton._typing.FloatArray

Compute Merton’s distance-to-default DD = d_2.

\[DD = \frac{\ln(A/D) + (r - q - \sigma_A^2 / 2)\, T}{\sigma_A \sqrt{T}}\]

Parameters:

• asset_value – Firm asset value(s) A (strictly positive).

• asset_vol – Annualised asset volatility σ_A (strictly positive).

• debt – Default threshold D (strictly positive). For real firms this is typically computed via merton.core.compute_default_point().

• rf – Risk-free rate r (decimal).

• T – Horizon in years (strictly positive).

• dividend_yield – Continuous dividend yield q. Defaults to 0.

• backend – Force a particular backend.

• validate – If True, check for non-finite and out-of-domain inputs.

Returns:

DD — number of asset-volatility standard deviations between the log of assets and the log of the default threshold.

Return type:

FloatArray

References

Merton (1974). Vassalou & Xing (2004). Crosbie & Bohn (2003).

Examples

>>> import numpy as np
>>> dd = distance_to_default(
...     asset_value=np.array([100.0, 150.0]),
...     asset_vol=0.25,
...     debt=60.0,
...     rf=0.04,
...     T=1.0,
... )
>>> dd.shape
(2,)

merton.core.distance.prob_of_default(dd: merton._typing.ArrayLike, *, backend: str | None = None) → merton._typing.FloatArray

Risk-neutral probability of default given the distance-to-default.

\[\text{PD} = \Phi(-DD)\]

where \(\Phi\) is the standard-normal CDF.

Examples

>>> import numpy as np
>>> float(round(prob_of_default(2.5), 5))
0.00621