Calculate Black Scholes Implied Volatility - Vectorwise

## Project description    # 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

## 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

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.

## Project details

This version 1.14.0 1.13.0 0.0.1