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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.

.. code:: bash

   $ pip install calcbsimpvol

Example
~~~~~~~

Pass your ``args`` bundled in a ``dict``.

.. code:: python

   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 <https://github.com/erkandem/calcbsimpvol>`__ (additional
sample data required which is available at `GitHub
Repo <https://github.com/erkandem/calcbsimpvol>`__

Performance
-----------

::

   Design a test. 
   Get the results you want.

-  ``k_max = 10`` (default)
-  ``tolerance = 10E-12`` (default)
-  linear regression steps are commented out (default)

.. code:: bash

   # 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

.. code:: bash

   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
-------

-  email: erkan.dem@pm.me
-  documentation:
   `erkandem.github.io/calcbsimpvol/ <https://erkandem.github.io/calcbsimpvol/>`__
-  source:
   `github.com/erkandem/calcbsimpvol <https://github.com/erkandem/calcbsimpvol>`__
-  issues:
   `github.com/erkandem/calcbsimpvol/issues <https://github.com/erkandem/calcbsimpvol/issues>`__

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 <https://github.com/calcbsimpvol/calcbsimpvol/LICENCE>`__

The Code by Mark Whirdy is licensed under ``MIT``
`License <https://github.com/erkandem/calcbsimpvol/calcBSImpVol_mlab/LICENSE>`__

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

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