#!/usr/bin/env python
# -*- coding: utf-8 -*-
# SPDX-License-Identifier: Unlicense
# http://www.h2t.ru/blog/9743.html
from __future__ import division
import numpy as np
import scipy.stats as ss
import datetime as dt
from matplotlib import pyplot as plt

def black_price_call(f, strike, sigma, t):
    d1 = (np.log(f / strike) + sigma * sigma * t / 2) / (sigma * np.sqrt(t))
    d2 = d1 - sigma * np.sqrt(t)
    return f * ss.norm.cdf(d1) - strike * ss.norm.cdf(d2)

def time_to_exp(now, exp):
    return (exp - now).total_seconds() / (60 * 60 * 24 * 365)

now = dt.datetime(2018,6,11,23,59,59)
exp = dt.datetime(2018,7,19,23,59,59)
t = time_to_exp(now, exp)
price = black_price_call(63456, 65000, 0.1536, t)
print price

x = []
y = []
d = now
while d < exp:
    price = black_price_call(63456, 65000, 0.1536, time_to_exp(d, exp))
    x.append(d)
    y.append(price)
    d += dt.timedelta(days=1)
fig = plt.figure()
graph = fig.add_subplot(111)
graph.plot(x, y)
plt.grid()
plt.show()