lbriv 1.0.0

Black-76 pricing and Let's-Be-Rational implied volatility (Cython port of Peter Jaeckel's LetsBeRational)

lbriv

Black-76 pricing and implied volatility for European options, with the implied-vol inversion done by a Cython port of Peter Jaeckel's LetsBeRational algorithm (~2 Householder steps per quote to machine precision, nogil batch loops).

Everything works in the T=1, r=0 convention: prices are undiscounted (premium / discount factor) and vols are Black total vols (raw IV at T=1). Rescale externally for other maturities. q = +1 for calls, -1 for puts.

Install

pip install lbriv

Prebuilt wheels cover CPython 3.11+ on Linux (x86_64, aarch64), Windows (x86_64), and macOS (arm64, x86_64). On anything else pip falls back to the sdist, which needs a C compiler — the compiled extension is required, there is no pure-Python fallback.

To work on the package itself, either install from a checkout:

pip install .

or build in place and put the repo root on PYTHONPATH:

python setup.py build_ext --inplace

Usage

import numpy as np
from lbriv import black76_undiscounted, vectorized_implied_vol_strikes

forward = 100.0
strikes = np.array([80.0, 100.0, 120.0])
prices = black76_undiscounted(forward, strikes, np.array([0.25, 0.20, 0.22]), q=1)

iv = vectorized_implied_vol_strikes(prices, forward, strikes, q=1)
# -> array([0.25, 0.20, 0.22])

Unsolvable quotes (at/below intrinsic, or at/above the vol→∞ bound) come back as NaN.

API

Function	Purpose
black76_undiscounted(F, K, total_vol, q)	vectorised Black-76 price
black76_vega(F, K, total_vol)	d(price)/d(total_vol)
implied_vol(price, F, K, q)	scalar IV (returns 0.0 on unsolvable)
vectorized_implied_vol_strikes(prices, F, K[], q)	IV across strikes, NaN on unsolvable
vectorized_implied_vol(prices[], F[], K, q)	IV across a time series, one strike
black_delta / black_gamma / black_vega	scalar Black greeks (T=1, r=0)
compute_trades_greeks(...)	batch IV + delta/gamma/vega over mixed trades

Tests

pip install -e .[test]
pytest

License

MIT. The implied-vol solver is a port of Peter Jäckel's LetsBeRational reference implementation, whose permissive notice is preserved in LICENSE.