py_vollib.black.greeks package

Submodules

py_vollib.black.greeks.analytical module

py_vollib.black.greeks.analytical

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:© 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.
========================================================================================
py_vollib.black.greeks.analytical.delta(flag, F, K, t, r, sigma)[source]

Returns the Black delta of an option.

Parameters:
  • flag (str) – ‘c’ or ‘p’ for call or put.
  • F (float) – underlying futures price
  • K (float) – strike price
  • t (float) – time to expiration in years
  • r (float) – annual risk-free interest rate
  • sigma (float) – volatility
Returns:

float

>>> F = 49
>>> K = 50 
>>> r = .05
>>> t = 0.3846
>>> sigma = 0.2
>>> flag = 'c'
>>> v1 = delta(flag, F, K, t, r, sigma)
>>> v2 = 0.45107017482201828
>>> abs(v1-v2) < .000001
True
py_vollib.black.greeks.analytical.gamma(flag, F, K, t, r, sigma)[source]

Returns the Black gamma of an option.

Parameters:
  • flag (str) – ‘c’ or ‘p’ for call or put.
  • F (float) – underlying futures price
  • K (float) – strike price
  • t (float) – time to expiration in years
  • r (float) – annual risk-free interest rate
  • sigma (float) – volatility
Returns:

float

>>> F = 49
>>> K = 50 
>>> r = .05
>>> t = 0.3846
>>> sigma = 0.2
>>> flag = 'c'
>>> v1 = gamma(flag, F, K, t, r, sigma)
>>> # 0.0640646705882
>>> v2 = 0.0640646705882
>>> abs(v1-v2) < .000001
True
py_vollib.black.greeks.analytical.rho(flag, F, K, t, r, sigma)[source]

Returns the Black rho of an option.

Parameters:
  • flag (str) – ‘c’ or ‘p’ for call or put.
  • F (float) – underlying futures price
  • K (float) – strike price
  • t (float) – time to expiration in years
  • r (float) – annual risk-free interest rate
  • sigma (float) – volatility
Returns:

float

==========================================================
The text book analytical formula does not multiply by .01,
but in practice rho is defined as the change in price
for each 1 percent change in r, hence we multiply by 0.01.
==========================================================
>>> F = 49
>>> K = 50 
>>> r = .05
>>> t = 0.3846
>>> sigma = 0.2
>>> flag = 'c'
>>> v1 = rho(flag, F, K, t, r, sigma)
>>> v2 = -0.0074705380059582258
>>> abs(v1-v2) < .000001
True
>>> flag = 'p'
>>> v1 = rho(flag, F, K, t, r, sigma)
>>> v2 = -0.011243286001308292
>>> abs(v1-v2) < .000001
True
py_vollib.black.greeks.analytical.theta(flag, F, K, t, r, sigma)[source]

Returns the Black theta of an option.

Parameters:
  • flag (str) – ‘c’ or ‘p’ for call or put.
  • F (float) – underlying futures price
  • K (float) – strike price
  • t (float) – time to expiration in years
  • r (float) – annual risk-free interest rate
  • sigma (float) – volatility
Returns:

float

>>> F = 49
>>> K = 50 
>>> r = .05
>>> t = 0.3846
>>> sigma = 0.2
>>> flag = 'c'
>>> v1 = theta(flag, F, K, t, r, sigma)
>>> v2 = -0.00816236877462
>>> abs(v1-v2) < .000001
True
>>> flag = 'p'
>>> v1 = theta(flag, F, K, t, r, sigma)
>>> v2 = -0.00802799155312
>>> abs(v1-v2) < .000001
True
py_vollib.black.greeks.analytical.vega(flag, F, K, t, r, sigma)[source]

Returns the Black vega of an option.

Parameters:
  • flag (str) – ‘c’ or ‘p’ for call or put.
  • F (float) – underlying futures price
  • K (float) – strike price
  • t (float) – time to expiration in years
  • r (float) – annual risk-free interest rate
  • sigma (float) – volatility
Returns:

float

==========================================================
Note: The text book analytical formula does not multiply by .01,
but in practice vega is defined as the change in price
for each 1 percent change in IV, hence we multiply by 0.01.
==========================================================
>>> F = 49
>>> K = 50 
>>> r = .05
>>> t = 0.3846
>>> sigma = 0.2
>>> flag = 'c'
>>> v1 = vega(flag, F, K, t, r, sigma)
>>> # 0.118317785624
>>> v2 = 0.118317785624
>>> abs(v1-v2) < .000001
True

py_vollib.black.greeks.numerical module

py_vollib.black.greeks.numerical

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:© 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.
========================================================================================
py_vollib.black.greeks.numerical.delta(flag, F, K, t, r, sigma)[source]

Returns the Black delta of an option.

Parameters:
  • flag (str) – ‘c’ or ‘p’ for call or put.
  • F (float) – underlying futures price
  • K (float) – strike price
  • t (float) – time to expiration in years
  • r (float) – annual risk-free interest rate
  • sigma (float) – volatility
Returns:

float

py_vollib.black.greeks.numerical.f(flag, F, K, t, r, sigma, b)
py_vollib.black.greeks.numerical.gamma(flag, F, K, t, r, sigma)[source]

Returns the Black gamma of an option.

Parameters:
  • flag (str) – ‘c’ or ‘p’ for call or put.
  • F (float) – underlying futures price
  • K (float) – strike price
  • t (float) – time to expiration in years
  • r (float) – annual risk-free interest rate
  • sigma (float) – volatility
Returns:

float

py_vollib.black.greeks.numerical.rho(flag, F, K, t, r, sigma)[source]

Returns the Black rho of an option.

Parameters:
  • flag (str) – ‘c’ or ‘p’ for call or put.
  • F (float) – underlying futures price
  • K (float) – strike price
  • t (float) – time to expiration in years
  • r (float) – annual risk-free interest rate
  • sigma (float) – volatility
Returns:

float

py_vollib.black.greeks.numerical.test()[source]

Tests by comparing the analytical and numerical greek values.

>>> S =  49
>>> K = 50 
>>> r = .05
>>> t = 0.3846
>>> sigma = 0.2
>>> flag = 'c'
>>> epsilon = .0001
>>> v1 = delta(flag, S, K, t, r, sigma)
>>> v2 = adelta(flag, S, K, t, r, sigma)
>>> abs(v1-v2)<epsilon
True
>>> v1 = gamma(flag, S, K, t, r, sigma)
>>> v2 = agamma(flag, S, K, t, r, sigma)
>>> abs(v1-v2)<epsilon
True
>>> v1 = rho(flag, S, K, t, r, sigma)
>>> v2 = arho(flag, S, K, t, r, sigma)
>>> abs(v1-v2)<epsilon
True
>>> v1 = vega(flag, S, K, t, r, sigma)
>>> v2 = avega(flag, S, K, t, r, sigma)
>>> abs(v1-v2)<epsilon
True
>>> v1 = theta(flag, S, K, t, r, sigma)
>>> v2 = atheta(flag, S, K, t, r, sigma)
>>> abs(v1-v2)<epsilon
True

Test PUT flag

>>> flag = 'p'
>>> v1 = delta(flag, S, K, t, r, sigma)
>>> v2 = adelta(flag, S, K, t, r, sigma)
>>> abs(v1-v2)<epsilon
True
>>> v1 = gamma(flag, S, K, t, r, sigma)
>>> v2 = agamma(flag, S, K, t, r, sigma)
>>> abs(v1-v2)<epsilon
True
>>> v1 = rho(flag, S, K, t, r, sigma)
>>> v2 = arho(flag, S, K, t, r, sigma)
>>> abs(v1-v2)<epsilon
True
>>> v1 = vega(flag, S, K, t, r, sigma)
>>> v2 = avega(flag, S, K, t, r, sigma)
>>> abs(v1-v2)<epsilon
True
>>> v1 = theta(flag, S, K, t, r, sigma)
>>> v2 = atheta(flag, S, K, t, r, sigma)
>>> abs(v1-v2)<epsilon
True
py_vollib.black.greeks.numerical.theta(flag, F, K, t, r, sigma)[source]

Returns the Black theta of an option.

Parameters:
  • flag (str) – ‘c’ or ‘p’ for call or put.
  • F (float) – underlying futures price
  • K (float) – strike price
  • t (float) – time to expiration in years
  • r (float) – annual risk-free interest rate
  • sigma (float) – volatility
Returns:

float

py_vollib.black.greeks.numerical.vega(flag, F, K, t, r, sigma)[source]

Returns the Black vega of an option.

Parameters:
  • flag (str) – ‘c’ or ‘p’ for call or put.
  • F (float) – underlying futures price
  • K (float) – strike price
  • t (float) – time to expiration in years
  • r (float) – annual risk-free interest rate
  • sigma (float) – volatility
Returns:

float

Module contents

py_vollib

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:© 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.
========================================================================================