py_vollib.ref_python.black_scholes.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, flag)

Calculate the Black-Scholes implied volatility.

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

Calculate the Black-Scholes implied volatility.

Parameters:

• price (float) – the Black-Scholes option price

• S (float) – underlying asset price

• K (float) – strike price

• t (float) – time to expiration in years

• r (float) – risk-free interest rate

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

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

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

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

>>> abs(expected_price - price) < 0.00001
True
>>> abs(expected_iv - iv) < 0.01
True

>>> sigma = 0.3
>>> S, K, t, r, flag = 100.0, 1000.0, 0.5, 0.05, 'p'
>>> price = black_scholes(flag, S, K, t, r, sigma)
>>> print (price)
875.309912028
>>> iv = implied_volatility(price, S, K, t, r, flag)

>>> print (round(iv, 1))
0.0