def undiscounted_black(F, K, sigma, t, flag):
"""Calculate the **undiscounted** Black option price.
:param F: underlying futures price
:type F: float
:param K: strike price
:type K: float
:param sigma: annualized standard deviation, or volatility
:type sigma: float
:param t: time to expiration in years
:type t: float
>>> F = 100
>>> K = 100
>>> sigma = .2
>>> flag = 'c'
>>> t = .5
>>> undiscounted_black(F, K, sigma, t, flag)
5.637197779701664
"""
q = binary_flag[flag]
F = float(F)
K = float(K)
sigma = float(sigma)
t = float(t)
return lets_be_rational.black(F, K, sigma, t, q)
def undiscounted_black(F, K, sigma, t, flag):
"""Calculate the **undiscounted** Black option price.
:param F: underlying futures price
:type F: float
:param K: strike price
:type K: float
:param sigma: annualized standard deviation, or volatility
:type sigma: float
:param t: time to expiration in years
:type t: float
>>> F = 100
>>> K = 100
>>> sigma = .2
>>> flag = 'c'
>>> t = .5
>>> undiscounted_black(F, K, sigma, t, flag)
5.637197779701664
"""
q = binary_flag[flag]
F = float(F)
K = float(K)
sigma = float(sigma)
t = float(t)
return lets_be_rational.black(F, K, sigma, t, q)
def black_scholes_merton(flag, S, K, t, r, sigma, q):
"""Return the Black-Scholes-Merton option price.
:param S: underlying asset price
:type S: float
:param K: strike price
:type K: float
:param sigma: annualized standard deviation, or volatility
:type sigma: float
:param t: time to expiration in years
:type t: float
:param r: risk-free interest rate
:type r: float
:param q: annualized continuous dividend rate
:type q: float
From Espen Haug, The Complete Guide To Option Pricing Formulas
Page 4
>>> S=100
>>> K=95
>>> q=.05
>>> t = 0.5
>>> r = 0.1
>>> sigma = 0.2
>>> p_published_value = 2.4648
>>> p_calc = black_scholes_merton('p', S, K, t, r, sigma, q)
>>> abs(p_published_value - p_calc) < 0.0001
True
>>> c1 = bsm_call(S, K, t, r, sigma, q)
>>> c2 = black_scholes_merton('c', S, K, t, r, sigma, q)
>>> abs(c1-c2) < .0001
True
"""
S = S * numpy.exp((r-q)*t)
p = black(S, K, sigma, t, binary_flag[flag])
conversion_factor = numpy.exp(-r*t)
return p * conversion_factor
_q = [-1 if random.randint(0, 1) == 0 else 1 for _ in range(TestCases)]
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 = {}
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,
