Calculate Implied Volatility from option prices.

Implied Volatility

py_vollib_vectorized.implied_volatility.vectorized_implied_volatility(price, S, K, t, r, flag, q=None, *, on_error='warn', model='black_scholes', return_as='dataframe', dtype=<class 'numpy.float64'>, **kwargs)

An extremely fast, efficient and accurate Implied Volatility calculator for option/future contracts. Inputs can be lists, tuples, floats, pd.Series, or numpy.arrays. Broadcasting is applied on the inputs.

Parameters

  • price – The price of the option.

  • S – The price of the underlying asset.

  • 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.

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

  • q – The annualized continuous dividend yield.

  • on_error – Either “raise”, “warn” or “ignore”.

  • model – Must be one of “black_scholes” or “black_scholes_merton”. Use vectorized_implied_volatility_black for the Black model.

  • 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.

  • kwargs – Other keyword arguments are ignored.

Returns

pd.Series, pd.DataFrame or numpy.array object containing the implied volatility for each contract.

>>> import py_vollib.black_scholes_merton.implied_volatility
>>> import py_vollib_vectorized
>>> price = 0.10
>>> S = 95
>>> K = [100, 90]
>>> t = .2
>>> r = .2
>>> flag = ['c', 'p']
>>> py_vollib.black_scholes_merton.implied_volatility.implied_volatility(price, S, K, t, r, flag, q=0, return_as='numpy')
array([0.02621257, 0.12585767])
>>> py_vollib_vectorized.vectorized_implied_volatility(price, S, K, t, r, flag, q=0, model='black_scholes_merton',return_as='numpy')  # equivalent
array([0.02621257, 0.12585767])
py_vollib_vectorized.implied_volatility.vectorized_implied_volatility_black(price, F, K, r, t, flag, *, on_error='warn', return_as='dataframe', dtype=<class 'numpy.float64'>, **kwargs)

An extremely fast, efficient and accurate Implied Volatility calculator for option/future contracts. Inputs can be lists, tuples, floats, pd.Series, or numpy.arrays. Broadcasting is applied on the inputs. This method should only be used in the black model of pricing. Argument order is kept consistent with that of the py_vollib package.

Parameters

  • price – The price of the option.

  • F – The price of the underlying asset.

  • 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.

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

  • on_error – Either “raise”, “warn” or “ignore”.

  • 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.

  • kwargs – Other keyword arguments are ignored.

Returns

pd.Series, pd.DataFrame or numpy.array object containing the implied volatility for each contract.

>>> import py_vollib.black.implied_volatility
>>> import py_vollib_vectorized
>>> price = 0.10
>>> F = 95
>>> K = [100, 90]
>>> t = .2
>>> r = .2
>>> flag = ['c', 'p']
>>> py_vollib.black.implied_volatility.implied_volatility(price, F, K, r, t, flag, return_as='numpy')
array([0.02621257, 0.12585767])
>>> py_vollib_vectorized.vectorized_implied_volatility_black(price, F, K, r, t, flag, return_as='numpy')  # equivalent
array([0.02621257, 0.12585767])