Numba-vectorised Black-Scholes-Merton and Bachelier prices, Greeks, and implied-volatility fits over NumPy arrays for quantitative research pipelines

It is a focused, function-based numerical library, not a derivatives framework: callers supply forwards, discount factors, maturities, and market conventions.

Install: pip install vanilla-option-pricers · Import: vanilla_option_pricers · Status: Beta

Research pipelines often need focused pricing functions rather than a derivatives framework. This package provides forward-based Black-Scholes-Merton and Bachelier prices, Greeks, and implied-volatility inversion through scalar functions, aligned-array helpers, and per-expiry containers. The runtime dependency surface is limited to NumPy and Numba.

• Log-normal and absolute-normal models side by side. Black-Scholes-Merton and Bachelier functions share a forward-and-discount-factor interface. The Bachelier convention is annualised absolute normal volatility in the same units as the forward and strike.
• Implied volatility as a first-class fitter. Scalar, slice, and chain helpers recover model volatilities from caller-supplied option prices.
• Inverse-workflow branches. The 'IC' and 'IP' codes select branches used in coin-denominated inverse-option workflows. They do not perform every quote, numeraire, or payoff normalisation required by a market contract; callers remain responsible for those conversions. For the contract theory, see Lucic and Sepp (2024), Valuation and Hedging of Cryptocurrency Inverse Options, Quantitative Finance, 24(7), 851–869.
• Two runtime dependencies. NumPy and Numba; no object hierarchy, calendar, curve, pandas, or SciPy layer.

Use vanilla-option-pricers for forward-based vanilla prices, Greeks, and implied-volatility fits inside option-chain processing, volatility-surface preprocessing, simulation post-processing, or calibration objectives.

It is deliberately not a derivatives framework: it does not construct spots, forwards, discount curves, calendars, or settlement conventions, and it does not price American, exotic, or stochastic-volatility models. For pricing and calibration under stochastic volatility, use stochvolmodels; for portfolio-level analytics and reporting, use qis.

pip install vanilla-option-pricers

pip install --upgrade vanilla-option-pricers

• python >= 3.10
• numba >= 0.60.0
• numpy >= 2.0

The two runtime dependencies are NumPy and Numba. There is no dependency on any higher-level analytics package.

VanillaOptionPricers supports the following option types (passed as string parameters):

This scalar price-to-implied-volatility round trip works from any directory after installation:

from vanilla_option_pricers import compute_bsm_vanilla_price, infer_bsm_implied_vol

forward, discfactor, ttm, strike, vol = 101.25, 0.99, 0.25, 105.0, 0.20
price = compute_bsm_vanilla_price(forward, strike, ttm, vol, "C", discfactor)
implied_vol = infer_bsm_implied_vol(
    forward, ttm, strike, price, discfactor, "C"
)
print(f"call_price={price:.6f} implied_vol={implied_vol:.8f}")

call_price=2.481051 implied_vol=0.20000000

For arrays, chains, parity checks, and the Bachelier convention, clone the repository and use the authoritative deterministic workflow:

Use the authoritative, deterministic pricing and IV script. It prices one aligned BSM slice, recovers the input implied volatilities, checks put-call parity, demonstrates the absolute Bachelier volatility convention, and reports cold and warm execution separately.

python examples/getting_started/pricing_and_iv.py

The rendered quickstart includes that source directly and explains its inputs and output. The script requires no market data, network access, credentials, or optional dependencies.

The Colab entry point installs the latest release from public PyPI, reports its exact version and import path, and runs the same mechanically checked workflow with no saved notebook outputs.

Continue with the Bachelier convention, package-root API, and package comparison guides.

The public API has distinct execution paths:

• scalar pricing kernels are Numba dispatchers;
• slice, grid, and chain helpers use compiled loops over aligned inputs; and
• five *_vector convenience wrappers use numpy.vectorize.

The first Numba call includes compilation time. Runtime depends on input shape, dtype, machine, and whether the relevant signature has already been compiled; this README makes no universal timing or superiority claim.

The package is intended for:

• quantitative research using forward-based European vanilla prices and Greeks;
• option-chain and volatility-surface preprocessing;
• calibration or simulation post-processing that needs price/volatility inversion; and
• numerical experiments or teaching examples built around explicit model inputs.

This package is part of Artur Sepp's open-source Python stack for quantitative finance. The maintainer profile is the canonical ten-package catalogue.

vanilla-option-pricers is standalone and depends only on NumPy and Numba. It supplies the vanilla pricing layer used by option-chain-analytics and stochvolmodels; those packages own point-in-time chain workflows and stochastic-volatility models respectively.

• Bug or unsupported edge case: open the bug-report form with the package/Python versions, platform, quote convention, inputs, expected result, and actual result.
• Feature: open the feature-request form with the payoff, quote convention, or model edge case that is unsupported, your current workaround, and the smallest useful API.
• Contribution: read CONTRIBUTING.md, then browse good first issue or help wanted work.

A machine-readable citation is available in CITATION.cff.

If you use VanillaOptionPricers in your research, please cite it as:

@software{sepp2026vanillaoptionpricers,
  title={VanillaOptionPricers: Numba-vectorised Black-Scholes-Merton and Bachelier prices, Greeks, and implied-volatility fits over NumPy arrays},
  author={Sepp, Artur},
  year={2026},
  version={2.2.0},
  url={https://github.com/ArturSepp/VanillaOptionPricers},
  note={Python package for forward-based vanilla option pricing and implied-volatility fitting}
}

This project is licensed under the MIT License - see the LICENSE file for details.