py_vollib.ref_python.black

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.

Subpackages

Submodules

Package Contents

Functions

d1(F, K, t, r, sigma)

Calculate the d1 component of the Black PDE.

d2(F, K, t, r, sigma)

Calculate the d2 component of the Black PDE.

black_call(F, K, t, r, sigma)

Calculate the price of a call using Black. (Python

black_put(F, K, t, r, sigma)

Calculate the price of a put using Black. (Python

black(flag, F, K, t, r, sigma)

Calculate the (discounted) Black option price.

Attributes

N

From John C. Hull, "Options, Futures and Other Derivatives,"
N

From John C. Hull, “Options, Futures and Other Derivatives,” 7th edition, Chapter 16.8, page 342

d1(F, K, t, r, sigma)[source]

Calculate the d1 component of the Black PDE.

Parameters:

  • F (float) – underlying futures 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

Doctest using Hull, page 343, example 16.6

>>> F = 20
>>> K = 20
>>> r = .09
>>> t = 4/12.0
>>> sigma = 0.25

>>> calculated_value = d1(F, K, t, r, sigma)
>>> #0.0721687836487
>>> text_book_value = 0.07216
>>> abs(calculated_value - text_book_value) < .00001
True
d2(F, K, t, r, sigma)[source]

Calculate the d2 component of the Black PDE.

Parameters:

  • F (float) – underlying futures 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

Hull, page 343, example 16.6

>>> F = 20
>>> K = 20
>>> r = .09
>>> t = 4/12.0
>>> sigma = 0.25

>>> calculated_value = d2(F, K, t, r, sigma)
>>> #-0.0721687836487
>>> text_book_value = -0.07216
>>> abs(calculated_value - text_book_value) < .00001
True
black_call(F, K, t, r, sigma)[source]

Calculate the price of a call using Black. (Python implementation for reference.)

Parameters:

  • F (float) – underlying futures 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

Hull, page 343, example 16.7

>>> F = 620
>>> K = 600
>>> r = .05
>>> sigma = .2
>>> t = 0.5
>>> calculated_value = black_call(F, K, t, r, sigma)
>>> #44.1868533121
>>> text_book_value = 44.19
>>> abs(calculated_value - text_book_value) < .01
True
black_put(F, K, t, r, sigma)[source]

Calculate the price of a put using Black. (Python implementation for reference.)

Parameters:

  • F (float) – underlying futures 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

Hull, page 338, example 16.6

>>> F = 20
>>> K = 20
>>> r = .09
>>> sigma = .25
>>> t = 4/12.0
>>> calculated_value = black_put(F, K, t, r, sigma)
>>> # 1.11664145656
>>> text_book_value = 1.12
>>> abs(calculated_value - text_book_value) < .01
True
black(flag, F, K, t, r, sigma)[source]

Calculate the (discounted) Black option price.

Parameters:

  • F (float) – underlying futures price

  • K (float) – strike price

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

  • t (float) – time to expiration in years

>>> F = 100
>>> K = 100
>>> sigma = .2
>>> flag = 'c'
>>> r = .02
>>> t = .5

>>> expected = 5.5811067246048118
>>> actual = black(flag, F, K, t, r, sigma)
>>> abs(expected - actual) < 1e-12
True