geometric-brownian-motion.py

import matplotlib.pyplot as plt
import numpy as np

def geometric_brownian(years, drift, sigma, startPrice):
	T=years
	mu = drift
	simga = sigma
	S0 = startPrice
	dt = 0.01
	
	N = round(T/dt)
	t = np.linspace(0, T, N)
	print(len(t))
	W = np.random.standard_normal(size = N)
	W = np.cumsum(W)*np.sqrt(dt)
	X = (mu-0.5*sigma**2)*t + sigma*W
	S = S0*np.exp(X)
	
	return t, S

t1, S1 = geometric_brownian(10, 0, 0, 100)
plt.plot(t1, S1)

t1, S1 = geometric_brownian(10, -0.1, 0.02, 100)
plt.plot(t1, S1)

t1, S1 = geometric_brownian(10, 0, 0.05, 100)
plt.plot(t1, S1)

t1, S1 = geometric_brownian(10, 0.1, 0.1, 100)
plt.plot(t1, S1)

plt.show()