Python Code: Geometric Brownian Motion - what's wrong?

Question

I\'m pretty new to Python, but for a paper in University I need to apply some models, using preferably Python. I spent a couple of days with the code I attached, but I can\'t re

Answer 1

According to Wikipedia,

So it appears that

X=(mu-0.5*sigma**2)*t+(sigma*W) ###geometric brownian motion#### 

rather than

X=(mu-0.5*sigma**2)*dt+(sigma*sqrt(dt)*W)

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Since T represents the time horizon, I think t should be

t = np.linspace(0, T, N)

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Now, according to these Matlab examples (here and here), it appears

W = np.random.standard_normal(size = N) 
W = np.cumsum(W)*np.sqrt(dt) ### standard brownian motion ###

not,

W=(standard_normal(size=Steps)+mu*t)

Please check the math, however, I could be wrong.

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So, putting it all together:

import matplotlib.pyplot as plt
import numpy as np

T = 2
mu = 0.1
sigma = 0.01
S0 = 20
dt = 0.01
N = round(T/dt)
t = np.linspace(0, T, N)
W = np.random.standard_normal(size = N) 
W = np.cumsum(W)*np.sqrt(dt) ### standard brownian motion ###
X = (mu-0.5*sigma**2)*t + sigma*W 
S = S0*np.exp(X) ### geometric brownian motion ###
plt.plot(t, S)
plt.show()

yields