merton.greeks.autodiff

Autodiff Greeks via JAX.

Each Greek is computed by composing jax.grad() with the BSM equity or PD expression, then jax.vmap() to vectorise across input arrays and jax.jit() to compile the result. This is useful for:

• Validating the closed-form Greeks in merton.greeks.equity and merton.greeks.pd_sensitivity (they should agree to ~1e-7).

• Differentiating novel BSM extensions where deriving Greeks by hand is error-prone.

The module is only importable when merton[jax] is installed; importing it without JAX raises a clean ImportError.

Examples

>>> from merton.greeks import autodiff
>>> import numpy as np
>>> A = np.array([100.0, 150.0, 80.0])
>>> autodiff.equity_delta_ad(A, 0.25, 60.0, 0.04, 1.0)

Functions

equity_delta_ad(asset_value, asset_vol, debt, rf, T, *)	∂E/∂A via JAX autodiff.
equity_vega_ad(asset_value, asset_vol, debt, rf, T, *)	∂E/∂σ_A via JAX autodiff.
equity_gamma_ad(asset_value, asset_vol, debt, rf, T, *)	∂²E/∂A² via JAX autodiff (gradient of the delta).
equity_theta_ad(asset_value, asset_vol, debt, rf, T, *)	Theta as ∂E/∂t (i.e. -∂E/∂T) — matches the option-pricing
equity_rho_ad(asset_value, asset_vol, debt, rf, T, *)	∂E/∂r via JAX autodiff.
pd_leverage_sensitivity_ad(asset_value, asset_vol, ...)	∂PD/∂D via JAX autodiff.
pd_vol_sensitivity_ad(asset_value, asset_vol, debt, ...)	∂PD/∂σ_A via JAX autodiff.
pd_rate_sensitivity_ad(asset_value, asset_vol, debt, ...)	∂PD/∂r via JAX autodiff.

Module Contents

merton.greeks.autodiff.equity_delta_ad(asset_value, asset_vol, debt, rf, T, *, dividend_yield=0.0)

∂E/∂A via JAX autodiff.

merton.greeks.autodiff.equity_vega_ad(asset_value, asset_vol, debt, rf, T, *, dividend_yield=0.0)

∂E/∂σ_A via JAX autodiff.

merton.greeks.autodiff.equity_gamma_ad(asset_value, asset_vol, debt, rf, T, *, dividend_yield=0.0)

∂²E/∂A² via JAX autodiff (gradient of the delta).

merton.greeks.autodiff.equity_theta_ad(asset_value, asset_vol, debt, rf, T, *, dividend_yield=0.0)

Theta as ∂E/∂t (i.e. -∂E/∂T) — matches the option-pricing convention used by merton.greeks.equity_theta() so the autodiff and closed-form columns line up sign-wise.

merton.greeks.autodiff.equity_rho_ad(asset_value, asset_vol, debt, rf, T, *, dividend_yield=0.0)

∂E/∂r via JAX autodiff.

merton.greeks.autodiff.pd_leverage_sensitivity_ad(asset_value, asset_vol, debt, rf, T, *, dividend_yield=0.0)

∂PD/∂D via JAX autodiff.

merton.greeks.autodiff.pd_vol_sensitivity_ad(asset_value, asset_vol, debt, rf, T, *, dividend_yield=0.0)

∂PD/∂σ_A via JAX autodiff.

merton.greeks.autodiff.pd_rate_sensitivity_ad(asset_value, asset_vol, debt, rf, T, *, dividend_yield=0.0)

∂PD/∂r via JAX autodiff.