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.
1 maintainer
Release files for lbriv 1.0.0
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Built distributions (wheels)
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