vollib.black_scholes_merton package

Subpackages

Submodules

vollib.black_scholes_merton.implied_volatility module

vollib.black_scholes_merton.implied_volatility

Copyright © 2017 Gammon Capital LLC

A library for option pricing, implied volatility, and greek calculation. vollib is based on lets_be_rational, a Python wrapper for LetsBeRational by Peter Jaeckel as described below.

copyright:

© 2017 Gammon Capital LLC

license:

MIT, see LICENSE for more details.

About LetsBeRational:

The source code of LetsBeRational resides at www.jaeckel.org/LetsBeRational.7z .

========================================================================================
Copyright © 2013-2014 Peter Jäckel.

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

WARRANTY DISCLAIMER
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.
========================================================================================
vollib.black_scholes_merton.implied_volatility.implied_volatility(price, S, K, t, r, q, flag)[source]

Calculate the Black-Scholes-Merton implied volatility.

Parameters:

  • S (float) – underlying asset price

  • K (float) – strike price

  • t (float) – time to expiration in years

  • r (float) – risk-free interest rate

  • q (float) – annualized continuous dividend rate

  • flag (str) – ‘c’ or ‘p’ for call or put.

>>> S = 100
>>> K = 100
>>> sigma = .2
>>> r = .01
>>> flag = 'c'
>>> t = .5
>>> q = 0

>>> price = black_scholes_merton(flag, S, K, t, r, sigma, q)
>>> iv = implied_volatility(price, S, K, t, r, q, flag)

>>> expected_price = 5.87602423383
>>> expected_iv = 0.2

>>> abs(expected_price - price) < 0.00001
True
>>> abs(expected_iv - iv) < 0.00001
True

Module contents

vollib.black_scholes_merton

A library for option pricing, implied volatility, and greek calculation. vollib is based on lets_be_rational, a Python wrapper for LetsBeRational by Peter Jaeckel as described below.

copyright:

© 2017 Gammon Capital LLC

license:

MIT, see LICENSE for more details.

About LetsBeRational:

The source code of LetsBeRational resides at www.jaeckel.org/LetsBeRational.7z .

========================================================================================
Copyright © 2013-2014 Peter Jäckel.

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

WARRANTY DISCLAIMER
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.
========================================================================================
vollib.black_scholes_merton.black_scholes_merton(flag, S, K, t, r, sigma, q)[source]

Return the Black-Scholes-Merton option price.

Parameters:

  • S (float) – underlying asset price

  • K (float) – strike price; must be strictly positive.

  • sigma (float) – annualized standard deviation, or volatility

  • t (float) – time to expiration in years

  • r (float) – risk-free interest rate

  • q (float) – annualized continuous dividend rate

From Espen Haug, The Complete Guide To Option Pricing Formulas Page 4

>>> S=100
>>> K=95
>>> q=.05
>>> t = 0.5
>>> r = 0.1
>>> sigma = 0.2

>>> p_published_value = 2.4648
>>> p_calc = black_scholes_merton('p', S, K, t, r, sigma, q)
>>> abs(p_published_value - p_calc) < 0.0001
True