Vectorized implementation of the Black model for option pricing on futures, the Black-Scholes model for option pricing, and its extension to dividend stocks, the Black-Scholes-Merton model.

Models

py_vollib_vectorized.models.vectorized_black(flag, F, K, t, r, sigma, *, return_as='dataframe', dtype=<class 'numpy.float64'>)

Price a Future option using the Black model. Broadcasting is applied on the inputs.

Parameters

  • F – The price of the underlying asset.

  • K – The strike price.

  • sigma – The Implied Volatility (as a decimal, i.e. 0.10 for 10%).

  • t – The annualized time to expiration. Must be positive. For small TTEs, use a small value (1e-3).

  • flag – For each contract, this should be specified as c for a call option and p for a put option.

  • return_as – To return as a pd.Series object, use “series”. To return as a pd.DataFrame object, use “dataframe”. Any other value will return a numpy.array object.

  • dtype – Data type.

Returns

The price of the option.

>>> import py_vollib.black
>>> import py_vollib_vectorized
>>> flag = ['c', 'p']
>>> F = 95
>>> K = [100, 90]
>>> t = .2
>>> r = .2
>>> sigma = .2
>>> py_vollib.black.black(flag, F, K, t, r, sigma, return_as='numpy')
array([1.53408169, 1.38409245])
>>> py_vollib_vectorized.vectorized_black(flag, F, K, t, r, sigma, return_as='numpy')  # equivalent
array([1.53408169, 1.38409245])
py_vollib_vectorized.models.vectorized_black_scholes(flag, S, K, t, r, sigma, *, return_as='dataframe', dtype=<class 'numpy.float64'>)

Price an option using the Black-Scholes model. Broadcasting is applied on the inputs.

Parameters

  • flag – For each contract, this should be specified as c for a call option and p for a put option.

  • S – The underlying asset price

  • K – The strike price.

  • t – The annualized time to expiration. Must be positive. For small TTEs, use a small value (1e-3).

  • r – The interest free rate.

  • sigma – The Implied Volatility (as a decimal, i.e. 0.10 for 10%).

  • return_as – To return as a pd.Series object, use “series”. To return as a pd.DataFrame object, use “dataframe”. Any other value will return a numpy.array object.

  • dtype – Data type.

Returns

The price of the option.

>>> import py_vollib.black_scholes
>>> import py_vollib_vectorized
>>> flag = ['c', 'p']
>>> S = 95
>>> K = [100, 90]
>>> t = .2
>>> r = .2
>>> sigma = .2
>>> py_vollib.black_scholes.black_scholes(flag, S, K, t, r, sigma, return_as='numpy')
array([2.89558836, 0.61109351])
>>> py_vollib_vectorized.vectorized_black_scholes(flag, S, K, t, r, sigma, return_as='numpy')  # equivalent
array([2.89558836, 0.61109351])
py_vollib_vectorized.models.vectorized_black_scholes_merton(flag, S, K, t, r, sigma, q, *, return_as='dataframe', dtype=<class 'numpy.float64'>)

Price an option using the Black-Scholes-Merton model. Broadcasting is applied on the inputs.

Parameters

  • flag – For each contract, this should be specified as c for a call option and p for a put option.

  • S – The underlying asset price

  • K – The strike price.

  • t – The annualized time to expiration. Must be positive. For small TTEs, use a small value (1e-3).

  • r – The interest free rate.

  • sigma – The Implied Volatility (as a decimal, i.e. 0.10 for 10%).

  • q – The annualized continuous dividend yield.

  • return_as – To return as a pd.Series object, use “series”. To return as a pd.DataFrame object, use “dataframe”. Any other value will return a numpy.array object.

  • dtype – Data type.

Returns

The price of the option.

>>> import py_vollib.black_scholes_merton
>>> import py_vollib_vectorized
>>> flag = ['c', 'p']
>>> S = [95, 99]
>>> K = [100, 90]
>>> t = .2
>>> r = .2
>>> sigma = .2
>>> q = 0
>>> py_vollib.black_scholes_merton.black_scholes_merton(flag, S, K, t, r, sigma, q, return_as='numpy')
array([2.89558836, 0.23536284])
>>> py_vollib_vectorized.vectorized_black_scholes_merton(flag, S, K, t, r, sigma, q, return_as='numpy')  # equivalent
array([2.89558836, 0.23536284])