tsferro2 · March 10, 2022 15:56 · Mar 10, 2022
diff --git a/Square Root Diffusion time series simulation b/Square Root Diffusion time series simulation
@@ -0,0 +1,38 @@
+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');