import random
import time

start_time = time.time()

S0 = 100
K = 110
N = 36
n = 10000

rez = 0.

pas = vsp = [1]
while len(pas) != N + 1:
    for i in range(1, len(vsp)):
        pas[i] = vsp[i] + vsp[i - 1]
    pas.append(1)
    vsp = [i for i in pas]

for t in range(n):
    d = 1 - random.uniform(0.07, 0.1)
    u = 1 + random.uniform(0.08, 0.12)
    p = random.uniform(0.4, 0.7)

    for i in range(N + 1):
        r = S0 * d**i * u**(N - i) - K
        if r > 0:
            rez += r * (1 - p)**(N - i) * p**i * pas[i]

print("Calculating example option price:")
print(rez / n)

print("Time taken:", time.time() - start_time)