# -*- coding: utf-8 -*-
"""
vollib.black.implied_volatility
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
A library for option pricing, implied volatility, and
greek calculation. vollib is based on lets_be_rational,
a Python wrapper for LetsBeRational by Peter Jaeckel as
described below.
:copyright: © 2015 Iota Technologies Pte Ltd
: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.
======================================================================================
"""
# -----------------------------------------------------------------------------
# IMPORTS
# Standard library imports
from math import e
# Related third party imports
import lets_be_rational
import numpy
# Local application/library specific imports
from vollib.black import black
from vollib.black import undiscounted_black
from vollib.black import normalised_black
# -----------------------------------------------------------------------------
# DATA
CALL = 'c'
PUT = 'p'
binary_flag = {CALL:1,PUT:-1}
# -----------------------------------------------------------------------------
# FUNCTIONS - IMPLIED VOLATILITY
[docs]def normalised_implied_volatility(beta, x, flag):
"""Calculate the normalised Black implied volatility,
a time invariant transformation
of Black implied volatility.
Keyword arguments:
:param x: ln(F/K) where K is the strike price, and F is the futures price
:type x: float
:param beta: the normalized Black price
:type beta: float
:param flag: 'p' or 'c' for put or call
:type flag: str
>>> beta_call = normalised_black(0.0, 0.2, 'c')
>>> beta_put = normalised_black(0.1,0.23232323888,'p')
>>> normalized_b76_iv_call = normalised_implied_volatility(beta_call, 0.0, 'c')
>>> normalized_b76_iv_put = normalised_implied_volatility(beta_put, 0.1, 'p')
>>> print beta_call, normalized_b76_iv_call
0.0796556745541 0.2
>>> print beta_put, normalized_b76_iv_put
0.0509710222785 0.23232323888
"""
q = binary_flag[flag]
return lets_be_rational.normalised_implied_volatility_from_a_transformed_rational_guess(
beta, x, q)
[docs]def normalised_implied_volatility_limited_iterations(beta, x, flag, N):
"""Calculate the normalised Black implied volatility,
with limited iterations.
:param x: ln(F/K) where K is the strike price, and F is the futures price
:type x: float
:param beta: the normalized Black price
:type beta: float
:param flag: 'p' or 'c' for put or call
:type flag: str
>>> beta_call = normalised_black(0.0, 0.2, 'c')
>>> beta_put = normalised_black(0.1,0.23232323888,'p')
>>> normalized_b76_iv_call = normalised_implied_volatility_limited_iterations(beta_call, 0.0, 'c',1)
>>> normalized_b76_iv_put = normalised_implied_volatility_limited_iterations(beta_put, 0.1, 'p',1)
>>> print beta_call, normalized_b76_iv_call
0.0796556745541 0.2
>>> print beta_put, normalized_b76_iv_put
0.0509710222785 0.23232323888
"""
q = binary_flag[flag]
return lets_be_rational.normalised_implied_volatility_from_a_transformed_rational_guess_with_limited_iterations(
beta, x, q, N)
[docs]def implied_volatility_of_undiscounted_option_price(undiscounted_option_price, F, K, t, flag):
"""Calculate the implied volatility of the undiscounted Black option price
:param undiscounted_option_price: undiscounted Black price of a futures option
:type undiscounted_option_price: float
:param F: underlying futures price
:type F: float
:param K: strike price
:type K: float
:param t: time to expiration in years
:type t: float
>>> F = 100
>>> K = 100
>>> sigma = .2
>>> flag = 'c'
>>> t = .5
>>> undiscounted_call_price = undiscounted_black(F, K, sigma, t, flag)
>>> iv = implied_volatility_of_undiscounted_option_price(
... undiscounted_call_price, F, K, t, flag)
>>> print undiscounted_call_price, iv
5.6371977797 0.2
"""
return lets_be_rational.implied_volatility_from_a_transformed_rational_guess(
undiscounted_option_price,
F,
K,
t,
binary_flag[flag]
)
[docs]def implied_volatility_of_discounted_option_price(discounted_option_price, F, K, r, t, flag):
"""Calculate the implied volatility of the Black option price
:param discounted_option_price: discounted Black price of a futures option
:type discounted_option_price: float
:param F: underlying futures price
:type F: float
:param K: strike price
:type K: float
:param r: the risk-free interest rate
:type r: float
:param t: time to expiration in years
:type t: float
:param flag: 'p' or 'c' for put or call
:type flag: str
>>> F = 100
>>> K = 100
>>> sigma = .2
>>> flag = 'c'
>>> t = .5
>>> r = .02
>>> discounted_call_price = black(flag, F, K, t, r, sigma)
>>> iv = implied_volatility_of_discounted_option_price(
... discounted_call_price, F, K, r, t, flag)
>>> print discounted_call_price, iv
5.5811067246 0.2
"""
discount_factor = numpy.exp(-r*t)
undiscounted_option_price = discounted_option_price / discount_factor
return lets_be_rational.implied_volatility_from_a_transformed_rational_guess(
undiscounted_option_price,
F,
K,
t,
binary_flag[flag]
)
[docs]def implied_volatility_of_undiscounted_option_price_limited_iterations(
undiscounted_option_price, F, K, t, flag, N):
"""Calculate implied volatility of the undiscounted Black
option price with limited iterations.
:param undiscounted_option_price: undiscounted Black price of a futures option
:type undiscounted_option_price: float
:param F: underlying futures price
:type F: float
:param K: strike price
:type K: float
:param t: time to expiration in years
:type t: float
>>> F = 100
>>> K = 100
>>> sigma = .232323232
>>> flag = 'c'
>>> t = .5
>>> price = undiscounted_black(F, K, sigma, t, flag)
>>> iv = implied_volatility_of_undiscounted_option_price_limited_iterations(
... price, F, K, t, flag, 1)
>>> print price, iv
6.54635543387 0.232323232
"""
return lets_be_rational.implied_volatility_from_a_transformed_rational_guess_with_limited_iterations(
undiscounted_option_price,
F,
K,
t,
binary_flag[flag],
N
)
# -----------------------------------------------------------------------------
# MAIN
if __name__=='__main__':
import doctest
if not doctest.testmod().failed:
print "Doctest passed"