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)
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_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
)
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)
data['input'] = []
data['output'] = []
for i in range(TestCases):
F = _F[i]
K = _K[i]
sigma = _sigma[i]
T = _T[i]
q = _q[i]
z = _z[i]
N = _N[i]
black = lets_be_rational.black(F, K, sigma, T, q)
iv = lets_be_rational.implied_volatility_from_a_transformed_rational_guess(
black, F, K, T, q)
ivi = lets_be_rational.implied_volatility_from_a_transformed_rational_guess_with_limited_iterations(
black, F, K, T, q, N)
x = _x[i]
s = _s[i]
nblack = lets_be_rational.normalised_black(x, s, q)
nblackcall = lets_be_rational.normalised_black_call(x, s)
niv = lets_be_rational.normalised_implied_volatility_from_a_transformed_rational_guess(
nblack, x, q)
nivi = lets_be_rational.normalised_implied_volatility_from_a_transformed_rational_guess_with_limited_iterations(
nblack, x, q, N)
vega = lets_be_rational.normalised_vega(x, s)
norm_cdf = lets_be_rational.norm_cdf(z)
data['input'].append({
'F': F,
'K': K,
data = {}
data['input'] = []
data['output'] = []
for i in range(TestCases):
F = _F[i]
K = _K[i]
sigma = _sigma[i]
T = _T[i]
q = _q[i]
z = _z[i]
N = _N[i]
black = lets_be_rational.black(F, K, sigma, T, q)
iv = lets_be_rational.implied_volatility_from_a_transformed_rational_guess(black, F, K, T, q)
ivi = lets_be_rational.implied_volatility_from_a_transformed_rational_guess_with_limited_iterations(black, F, K, T, q, N)
x = _x[i]
s = _s[i]
nblack = lets_be_rational.normalised_black(x, s, q)
nblackcall = lets_be_rational.normalised_black_call(x, s)
niv = lets_be_rational.normalised_implied_volatility_from_a_transformed_rational_guess(nblack, x, q)
nivi = lets_be_rational.normalised_implied_volatility_from_a_transformed_rational_guess_with_limited_iterations(nblack, x, q, N)
vega = lets_be_rational.normalised_vega(x, s)
norm_cdf = lets_be_rational.norm_cdf(z)
data['input'].append({'F':F,
'K':K,
'sigma':sigma,
'T':T,
'q':q,
