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py_lets_be_rational is a pure Python port of lets_be_rational. Below is a list of differences between the two:

Feature py_lets_be_rational lets_be_rational
Python Version Compatibility 2.7 and 3.x 2.7 only
Source Language Python C with Python SWIG Wrapper
Optional Dependencies Numba None
Installed Automatically by pip as part of py_vollib vollib

Execution Speed

Except for their source language, py_lets_be_rational and lets_be_rational are almost identical. Each is orders of magnitude faster than traditional implied volatility calculation libraries, thanks to the algorithms developed by Peter Jaeckel. However, py_lets_be_rational, without Numba installed, is about an order of magnitude slower than lets_be_rational. Numba helps to mitigate this speed gap considerably.

Numba Dependency

Numba is an optional dependency of py_lets_be_rational . Because Numba installation can be tricky and OS-dependent, we decided to leave it up to each user to decide how and whether to install Numba. If Numba is present, execution speed will be faster. If not, the code will still run -- just slower.

Installing numba

py_lets_be_rational optionally depends on numba which in turn depends on llvm-lite. llvm-lite wants LLVM 3.9 being installed. On Mac OSX, use the latest version of HomeBrew to install numba's dependencies as shown below:

brew install llvm@3.9
LLVM_CONFIG=/usr/local/opt/llvm@3.9/bin/llvm-config pip install llvmlite==0.16.0
pip install numba==0.31.0

For other operating systems, please refer to the llvm-lite and numba documentation.


Fork our repository, and make the changes on your local copy:

git clone
cd py_lets_be_rational
pip install -e .
pip install -r dev-requirements.txt

When you are done, push the changes, and create a pull request on your repo.

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

    Copyright © 2013-2014 Peter Jäckel.

    Permission to use, copy, modify, and distribute this software is freely granted,
    provided that this notice is preserved.

    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.


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