py_vollib.black_scholes_merton.implied_volatility

Copyright © 2023 Larry Richards

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

copyright:

© 2023 Larry Richards

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.
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Module Contents

Functions

implied_volatility(price, S, K, t, r, q, flag)

Calculate the 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

  • 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

  • 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