About vollib
vollib is a python library for calculating option prices, implied volatility and greeks. At its core is
Peter Jäckel’s source code for LetsBeRational, an extremely fast and accurate algorithm for obtaining Black’s
implied volatility from option prices.
Building on this solid foundation, vollib provides functions to calculate option prices, implied volatility and
greeks using Black, Black-Scholes, and Black-Scholes-Merton. vollib implements both analytical and numerical
greeks for each of the three pricing formulae.
Input domain
Strike prices (K) must be strictly positive for the Black, Black-Scholes, and Black-Scholes-Merton pricing
functions. A zero strike call has a well-defined mathematical limit, but vollib does not special-case that
boundary; it preserves the domain and behavior of the underlying LetsBeRational implementation. If an application
wants to support K = 0, handle that boundary before calling vollib.
This domain requirement applies equally to calls and puts:
Strike input |
Calls |
Puts |
|---|---|---|
|
raises |
raises |
|
raises |
raises |
Package history and compatibility
Feature |
|
|
|
|---|---|---|---|
Python Version Compatibility |
3.9 through 3.12 |
2.7 and 3.x |
2.7 only |
Source Language |
Python |
Python |
C with Python SWIG Wrapper |
Core Dependency (automatically installed by pip) |
|
|
|
The original vollib 0.1.x package was the Python 2.7/C-SWIG implementation. It remains available on PyPI
for pinned legacy installs, but it is deprecated.
The py_vollib 1.0.x package name was introduced for the pure-Python implementation with Python 3 support.
Starting with vollib 1.0.7, the canonical package name is again vollib.
About the reference Python implementation
vollib contains vollib.ref_python, a pure python version of the functions in vollib.*, except
without any dependency on lets_be_rational or py_lets_be_rational. It is provided purely as a reference
implementation for sanity checking. It is not recommended for serious use.
Dependencies
vollib 1.0.7 supports Python 3.9 through 3.12. Its core dependency is py_lets_be_rational,
a pure python implementation of Peter Jäckel’s original C source code.
To install via pip, type the following:
pip install vollib
Installing vollib via pip will automatically install the necessary dependencies,
except for pip, and Python.
Python, and pip must be installed prior to installing vollib.
Migration from py_vollib
The canonical Python package is now vollib. Existing py_vollib.* imports remain available as a
compatibility namespace for this transition release, but they are deprecated. New code should import from
vollib:
from vollib.black_scholes import black_scholes
Existing code like this will continue to work for now:
from py_vollib.black_scholes import black_scholes
The temporary vollib-test package was a bridge while the official package release path was being repaired.
It is superseded by the official vollib package.
Implied volatility from option price
vollib can calculate implied volatility from a known option price. For example, using Black-Scholes:
from vollib.black_scholes import black_scholes
from vollib.black_scholes.implied_volatility import implied_volatility
flag = "c"
S = 100
K = 100
t = 0.5
r = 0.01
sigma = 0.2
price = black_scholes(flag, S, K, t, r, sigma)
iv = implied_volatility(price, S, K, t, r, flag)
The same pattern is available for Black and Black-Scholes-Merton through their respective
implied_volatility modules.
About “Let’s be Rational”
“Let’s Be Rational” is a paper by Peter Jäckel showing “how Black’s volatility can be implied from option prices with as little as two iterations to maximum attainable precision on standard (64 bit floating point) hardware for all possible inputs.”
The paper is accompanied by the full C source code, which resides at www.jaeckel.org/LetsBeRational.7z.
Copyright © 2013-2014 Peter Jäckel.
Permission to use, copy, modify, and distribute this software is freely granted,
provided that this notice is preserved.
WARRANTY DISCLAIMER
The Software is provided "as is" without warranty of any kind, either express or implied,
including without limitation any implied warranties of condition, uninterrupted use,
merchantability, fitness for a particular purpose, or non-infringement.
Links
Development
Fork the GitHub repository. This will make it available under your username e.g. https://github.com/YOUR-USERNAME/py_vollib.
Clone that repo on your computer, change the code as you wish. Commit and push it, and create a pull request. That’s all.
Generate documentation
cd docs
sphinx-apidoc -f -o apidoc ../vollib
make html