def implied_volatility(price, S, K, t, r, flag):
"""Calculate the Black-Scholes implied volatility.
:param price: the Black-Scholes option price
:type price: float
:param S: underlying asset price
:type S: float
:param K: strike price
:type K: float
:param t: time to expiration in years
:type t: float
:param r: risk-free interest rate
:type r: float
:param flag: 'c' or 'p' for call or put.
:type flag: str
>>> S = 100
>>> K = 100
>>> sigma = .2
>>> r = .01
>>> flag = 'c'
>>> t = .5
>>> price = black_scholes(flag, S, K, t, r, sigma)
>>> iv = implied_volatility(price, S, K, t, r, flag)
>>> print price, iv
5.87602423383 0.2
"""
adjusted_price = price / e**(-r * t)
return lets_be_rational.implied_volatility_from_a_transformed_rational_guess(
adjusted_price, forward_price(S, t, r), K, t, binary_flag[flag])
def implied_volatility_limited_iterations(price, S, K, t, r, flag, N):
"""Calculate the Black-Scholes implied volatility with limited iterations.
:param price: the Black-Scholes option price
:type price: float
:param S: underlying asset price
:type S: float
:param K: strike price
:type K: float
:param t: time to expiration in years
:type t: float
:param r: risk-free interest rate
:type r: float
:param flag: 'c' or 'p' for call or put.
:type flag: str
:param N: the maximum number of iterations to perform
:type N: int
>>> S = 100
>>> K = 100
>>> sigma = .232323232
>>> r = .01
>>> flag = 'c'
>>> t = .5
>>> price = black_scholes(flag, S, K, t, r, sigma)
>>> iv = implied_volatility_limited_iterations(price, S, K, t, r, flag,1)
>>> print price, iv
6.78242400926 0.232323232
"""
adjusted_price = price / e**(-r*t)
return lets_be_rational.implied_volatility_from_a_transformed_rational_guess_with_limited_iterations(
adjusted_price,
forward_price(S, t, r),
K,
t,
binary_flag[flag],
N
)
def implied_volatility(price, S, K, t, r, flag):
"""Calculate the Black-Scholes implied volatility.
:param price: the Black-Scholes option price
:type price: float
:param S: underlying asset price
:type S: float
:param K: strike price
:type K: float
:param t: time to expiration in years
:type t: float
:param r: risk-free interest rate
:type r: float
:param flag: 'c' or 'p' for call or put.
:type flag: str
>>> S = 100
>>> K = 100
>>> sigma = .2
>>> r = .01
>>> flag = 'c'
>>> t = .5
>>> price = black_scholes(flag, S, K, t, r, sigma)
>>> iv = implied_volatility(price, S, K, t, r, flag)
>>> print price, iv
5.87602423383 0.2
"""
adjusted_price = price / e**(-r*t)
return lets_be_rational.implied_volatility_from_a_transformed_rational_guess(
adjusted_price,
forward_price(S, t, r),
K,
t,
binary_flag[flag]
)
def implied_volatility_limited_iterations(price, S, K, t, r, flag, N):
"""Calculate the Black-Scholes implied volatility with limited iterations.
:param price: the Black-Scholes option price
:type price: float
:param S: underlying asset price
:type S: float
:param K: strike price
:type K: float
:param t: time to expiration in years
:type t: float
:param r: risk-free interest rate
:type r: float
:param flag: 'c' or 'p' for call or put.
:type flag: str
:param N: the maximum number of iterations to perform
:type N: int
>>> S = 100
>>> K = 100
>>> sigma = .232323232
>>> r = .01
>>> flag = 'c'
>>> t = .5
>>> price = black_scholes(flag, S, K, t, r, sigma)
>>> iv = implied_volatility_limited_iterations(price, S, K, t, r, flag,1)
>>> print price, iv
6.78242400926 0.232323232
"""
adjusted_price = price / e**(-r * t)
return lets_be_rational.implied_volatility_from_a_transformed_rational_guess_with_limited_iterations(
adjusted_price, forward_price(S, t, r), K, t, binary_flag[flag], N)