py_vollib.ref_python.black_scholes_merton.implied_volatility

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.

py_vollib.ref_python is a pure python version of py_vollib without any dependence on LetsBeRational. It is provided purely as a reference implementation for sanity checking. It is not recommended for industrial use.

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)

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 = .02

>>> price = black_scholes_merton(flag, S, K, t, r, sigma, q)
>>> implied_volatility(price, S, K, t, r, q, flag)
0.20000000000000018

>>> flac = 'p'
>>> sigma = 0.3
>>> price = black_scholes_merton(flag, S, K, t, r, sigma, q)
>>> price
8.138101080183894
>>> implied_volatility(price, S, K, t, r, q, flag)
0.30000000000000027