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tsferro2/Geometric Brownian Motion time series simulation

Created March 10, 2022 15:51
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Geometric Brownian Motion time series simulation
import math
import numpy as np
import numpy.random as npr
from pylab import plt, mpl
# Geometric Brownian Motion (granual/steps)
S0 = 100 # starting price
r = 0.05 # short rate
sigma = 0.25 # vol
I = 10000 # simulations
M = 50 # steps per sim
dt = T / M
S = np.zeros((M + 1, I))
S[0] = S0
for t in range(1, M + 1):
S[t] = S[t - 1] * np.exp((r - 0.5 * sigma ** 2) * dt +
sigma * math.sqrt(dt) * npr.standard_normal(I))
plt.figure(figsize=(10, 6))
plt.hist(S[-1], bins=50)
plt.xlabel('index level')
plt.ylabel('frequency');
plt.figure(figsize=(10, 6))
plt.plot(S[:, :10], lw=1.5)
plt.xlabel('time')
plt.ylabel('index level');
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