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Calculate Black Scholes Implied Volatility - Vectorwise

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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 .m to .py by me

Contact

ToDos

  • make the code compatible with Python 2
  • make it PyPy compatible

References

  1. Li, 2006, "You Don't Have to Bother Newton for Implied Volatility"

    http://papers.ssrn.com/sol3/papers.cfm?abstract_id=952727

  2. MATLAB source code available at:

    https://www.mathworks.com/matlabcentral/fileexchange/41473-calcbsimpvol-cp-p-s-k-t-r-q

License

The included Python code is licensed under MIT License

The Code by Mark Whirdy is licensed under MIT License

The translation is not related or endorsed by the original author.

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