calcbsimpvol¶
Calculate Black-Scholes Implied Volatility - Vectorwise
:)native python code:)lightweight footprint:)sample data included:(not suited for single / low number of options:(code reads un-pythonic:(not yet thoroughly tested
Getting started¶
Requirements¶
Python 3.x (currently) or PyPy3
NumPy
SciPy
(MatPlotLib to visualize results in some examples)
Installation¶
While the code consists of single digit functions, I recommend using the
pip install way to get the code. That way you would take advantage
of bug fixes, updates, and possible extensions.
$ pip install calcbsimpvol
Example¶
Pass your args bundled in a dict.
from calcbsimpvol import calcbsimpvol
import numpy as np
S = np.asarray(100)
K_value = np.arange(40, 160, 25)
K = np.ones((np.size(K_value), 1))
K[:, 0] = K_value
tau_value = np.arange(0.25, 1.01, 0.25)
tau = np.ones((np.size(tau_value), 1))
tau[:, 0] = tau_value
r = np.asarray(0.01)
q = np.asarray(0.03)
cp = np.asarray(1)
P = [[59.35, 34.41, 10.34, 0.50, 0.01],
[58.71, 33.85, 10.99, 1.36, 0.14],
[58.07, 33.35, 11.50, 2.12, 0.40],
[57.44, 32.91, 11.90, 2.77, 0.70]]
P = np.asarray(P)
[K, tau] = np.meshgrid(K, tau)
sigma = calcbsimpvol(dict(cp=cp, P=P, S=S, K=K, tau=tau, r=r, q=q))
print(sigma)
# [[ nan, nan, 0.20709362, 0.21820954, 0.24188675],
# [ nan, 0.22279836, 0.20240934, 0.21386148, 0.23738982],
# [ nan, 0.22442837, 0.1987048 , 0.21063506, 0.23450013],
# [ nan, 0.22188111, 0.19564657, 0.20798285, 0.23045406]]
More usage examples are available in example3.py (additional sample data required which is available at GitHub Repo
Performance¶
Design a test.
Get the results you want.
k_max = 10(default)tolerance = 10E-12(default)linear regression steps are commented out (default)
# assuming you did install it already
git clone https://github.com/erkandem/calcbsimpvol.git
cd calcbsimpvol
python examples/example3.py --steps 100 --mode reference
15 µs per option
41 ms per surface
tested with 3.6, 3.7 and PyPy3
matlab -nodisplay -nosplash -nodesktop -r "run('mlb_reference_example.m');"
12 µs per option
34 ms per surface
Obviously, these values are per core (i5 4210U 1.7 GHz).
Notes¶
Good Python code reads like a novel. Right? So should math. I preferred short math-like variable names in this case. That makes the code less readable compared to other Python code but the docstrings should make up for the lack of readability.
Originally, I left the camelCase function name and spelling in place but eventually got annoyed. > calcbsimpvol it is
Code Origin¶
first thought of by Li (2006) (see References)
implemented and published by Mark Whirdy as MATLAB .m-code (see References)
numpyified from
.mto.pyby me
Contact¶
email: erkan.dem@pm.me
documentation: erkandem.github.io/calcbsimpvol/
source: github.com/erkandem/calcbsimpvol
ToDos¶
make the code compatible with
Python 2make it
PyPycompatible
References¶
Li, 2006, “You Don’t Have to Bother Newton for Implied Volatility”
MATLAB source code available at:
https://www.mathworks.com/matlabcentral/fileexchange/41473-calcbsimpvol-cp-p-s-k-t-r-q