PyMPDATA_examples.Arabas_and_Farhat_2020.Black_Scholes_1973 

 1import numpy as np
 2from scipy.special import erf  # pylint: disable=no-name-in-module
 3
 4
 5def N(x: float):
 6    return (1 + erf(x / np.sqrt(2))) / 2
 7
 8
 9def c_euro(S: np.ndarray, K: float, T: float, r: float, b: float, sgma: float):
10    d1 = (np.log(S / K) + (b + sgma * sgma / 2) * T) / sgma / np.sqrt(T)
11    d2 = d1 - sgma * np.sqrt(T)
12    return S * np.exp(b - r) * N(d1) - K * np.exp(-r * T) * N(d2)
13
14
15def p_euro(S: np.ndarray, K: float, T: float, r: float, b: float, sgma: float):
16    d1 = (np.log(S / K) + (b + sgma * sgma / 2) * T) / sgma / np.sqrt(T)
17    d2 = d1 - sgma * np.sqrt(T)
18    return K * np.exp(-r * T) * N(-d2) - S * np.exp((b - r) * T) * N(-d1)
def N(x: float): 
6def N(x: float):
7    return (1 + erf(x / np.sqrt(2))) / 2
def c_euro( S: numpy.ndarray, K: float, T: float, r: float, b: float, sgma: float): 
10def c_euro(S: np.ndarray, K: float, T: float, r: float, b: float, sgma: float):
11    d1 = (np.log(S / K) + (b + sgma * sgma / 2) * T) / sgma / np.sqrt(T)
12    d2 = d1 - sgma * np.sqrt(T)
13    return S * np.exp(b - r) * N(d1) - K * np.exp(-r * T) * N(d2)
def p_euro( S: numpy.ndarray, K: float, T: float, r: float, b: float, sgma: float): 
16def p_euro(S: np.ndarray, K: float, T: float, r: float, b: float, sgma: float):
17    d1 = (np.log(S / K) + (b + sgma * sgma / 2) * T) / sgma / np.sqrt(T)
18    d2 = d1 - sgma * np.sqrt(T)
19    return K * np.exp(-r * T) * N(-d2) - S * np.exp((b - r) * T) * N(-d1)