Added Lab 11

Lab11/Lab11.py

@@ -0,0 +1,128 @@
+#!/usr/bin/env python
+# coding: utf-8
+
+# In[ ]:
+
+
+'''
+                                     MA374 | Lab 08
+                        Deepak Kumar Gouda | 160123054
+'''
+
+
+# In[1]:
+
+
+import numpy as np
+from numpy import exp,log
+from matplotlib import pyplot as plt
+
+
+# In[2]:
+
+
+from pylab import rcParams
+rcParams['figure.figsize'] = 10, 5
+
+
+# In[3]:
+
+
+def getVasicekYield(a, b, sigma, r, time_steps):
+    y = np.zeros(time_steps+1)
+    y[0] = r
+    for T in range(1,time_steps+1):
+        B = (1-exp(-a*T))/a
+        A = (B-T)*(a*b-0.5*sigma**2)/(a**2)-((a*B)**2)/(4*a) 
+        p = exp(A-B*r) 
+        y[T] = -1*log(p)/T
+    return y
+
+
+# In[4]:
+
+
+def getCIRYield(a,b,sigma,r,time_steps):
+    y = np.zeros(time_steps+1) 
+    y[0] = r
+    gamma = ((a)**2+2*(sigma**2))**0.5
+    for T in range(1,time_steps+1):
+        D = ((gamma+a)*(exp(gamma*T)-1)+2*gamma)
+        B = 2*(exp(gamma*T)-1)/D
+        A = (2*gamma*exp((a+gamma)*(T/2))/D)**(2*a*b/(sigma**2))
+
+        p = A*exp(-B*r)
+        y[T] = -1*log(p)/T
+    return y
+
+
+# In[5]:
+
+
+def getYieldPlot(model):
+    if model is 'Vasicek':
+        set1 = [5.9, 0.2, 0.3, 0.1,'blue']
+        set2 = [3.9, 0.1, 0.3, 0.2,'orange']
+        set3 = [0.1, 0.4, 0.11, 0.1,'green']
+    else:
+        set1 = [0.02, 0.7, 0.02, 0.1,'blue']
+        set2 = [0.7, 0.1, 0.3, 0.2,'orange']
+        set3 = [0.06, 0.09, 0.5, 0.02,'green']
+    sets = [set1, set2, set3]
+    time_steps = 10
+    plt.figure()
+
+    for set0 in sets:
+        beta, mu,sigma,r,col = set0
+        a = beta
+        b = beta * mu
+        if model is 'Vasicek':
+            y = getVasicekYield(a,b,sigma,r,time_steps)
+        elif model is 'CIR':
+            y = getCIRYield(a,b,sigma,r,time_steps)
+        plt.plot(y,color=col, label=set0[:-1])
+    plt.title(model+' Model')
+    plt.xlabel('T')
+    plt.ylabel('Yield')
+    plt.legend()
+    plt.show()
+
+    if model is 'CIR':
+        sets=[[0.02, 0.7, 0.02, 'orange']]
+        time_steps=600
+    else:
+        time_steps=500
+
+    for set0 in sets:
+        plt.figure()
+        for r1 in np.arange(0,1.1,0.1):
+            if model is 'Vasicek':
+                beta, mu, sigma, r, col = set0
+            else:
+                beta, mu, sigma, col = set0
+            a = beta
+            b = beta * mu
+            if model is 'Vasicek':
+                y = getVasicekYield(a,b,sigma,r1,time_steps)
+            elif model is 'CIR':
+                y = getCIRYield(a,b,sigma,r1,time_steps)
+
+            plt.plot(y,color=col)
+        plt.title(model+" Model with beta, mu,sigma = "+str(set0[:-2])+" r = 0.1 to 1")
+        plt.xlabel('T')
+        plt.ylabel('Yield')
+        plt.show()
+
+
+# In[6]:
+
+
+getYieldPlot('Vasicek')
+getYieldPlot('CIR')
+
+
+# In[ ]:
+
+
+
+