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tsferro2/Square Root Diffusion time series simulation

Created March 10, 2022 15:56
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Square Root Diffusion time series simulation
import math
import numpy as np
import numpy.random as npr
from pylab import plt, mpl
# Square-Root Diffusion (mean-reverting process)-------------------------------
# widely used for short rates & volatility
x0 = 1.00 # starting value
kappa = 3.0 # mean-reversion paramater
theta = 1.00 # long term mean
sigma = 0.1
I = 10000
M = 365
dt = T / M
def srd_euler():
xh = np.zeros((M + 1, I))
x = np.zeros_like(xh)
xh[0] = x0
x[0] = x0
for t in range(1, M + 1):
xh[t] = (xh[t - 1] +
kappa * (theta - np.maximum(xh[t - 1], 0)) * dt +
sigma * np.sqrt(np.maximum(xh[t - 1], 0)) *
math.sqrt(dt) * npr.standard_normal(I))
x = np.maximum(xh, 0)
return x
x1 = srd_euler()
plt.figure(figsize=(10, 6))
plt.hist(x1[-1], bins=50)
plt.xlabel('value')
plt.ylabel('frequency');
plt.figure(figsize=(10, 6))
plt.plot(x1[:, :10], lw=1.5)
plt.xlabel('time')
plt.ylabel('index level');
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