#!/bin/python
# -*- coding: utf-8 -*-
from __future__ import division, print_function, absolute_import
import numpy as np
import scipy.optimize
import mafipy.function
[docs]def black_scholes_implied_vol(underlying,
strike,
rate,
maturity,
option_value,
vol_min=1e-4,
vol_max=6.0,
max_iter=2000):
"""black_scholes_implied_vol
calculates implied volatility of black schoels model by brent method.
:param float underlying:
:param float strike:
:param float rate:
:param float maturity:
:param float option_value: value of option.
:param float vol_min: lower bound of volatility. default value is 1e-4.
:param float vol_max: upper bound of volatility. default value is 6.0.
:param int max_iter: maximum number of iterations. default value is 2000.
:return: implied volatility.
:rtype: float.
"""
def objective_func(vol):
return (mafipy.function.black_scholes_call_formula(
underlying, strike, rate, maturity, vol) - option_value)
result = scipy.optimize.brentq(
objective_func,
vol_min,
vol_max,
xtol=4 * np.finfo(float).eps,
rtol=4 * np.finfo(float).eps,
maxiter=max_iter)
return result
[docs]def black_swaption_implied_vol(init_swap_rate,
option_strike,
swap_annuity,
option_maturity,
option_value,
vol_min=1e-4,
vol_max=6.0,
max_iter=2000):
"""black_swaption_implied_vol
calculates implied volatility of payer's swaption by brent method.
:param float init_swap_rate:
:param float option_strike:
:param float swap_annuity:
:param float option_maturity:
:param float option_value: value of option.
:param float vol_min: lower bound of volatility. default value is 1e-4.
:param float vol_max: upper bound of volatility. default value is 6.0.
:param int max_iter: maximum number of iterations. default value is 2000.
:return: implied volatility.
:rtype: float.
"""
def objective_func(vol):
return (mafipy.function.black_payers_swaption_value(
init_swap_rate, option_strike, swap_annuity, option_maturity, vol)
- option_value)
result = scipy.optimize.brentq(
objective_func,
vol_min,
vol_max,
xtol=4 * np.finfo(float).eps,
rtol=4 * np.finfo(float).eps,
maxiter=max_iter)
return result