ex02.py

import numpy as np
import importlib 
import time
import matplotlib.pyplot as plt
import pylab
pylab.ion()
pylab.show()
import sys
import seaborn as sns
sns.set()
'''
BRIEF DESCRIPTION:
This is an example file associated with the code library for Chapter 2. In 
this example, we use the functions in binomialPoissonModels.py to simulate
the binomial and Poisson independent-default models, print the results and
graph the tail probabilities.
-----------------
David Jamieson Bolder, February 2018
'''
# This is the base location for your code implementation
# You'll need to change this to reflect your own personal location
myHome = "/home/djb/Work/cmBook/GitHub/"
# These are the exposure and default-probability files
dpFile = myHome+"defaultProbabilties.npy"
expFile = myHome+"exposures.npy"
# Loading the necessary libraries
#sys.path.insert(0, myHome + "cmLib")
import cmUtilities as util
import binomialPoissonModels as bp
importlib.reload(util)
importlib.reload(bp)
plt.close('all')
# Key inputs and parameters
c = np.load(expFile)  
p = np.load(dpFile)
N = len(c)
myRho = 0.05  
portfolioSize = np.sum(c)
myC = portfolioSize/N
M = 1000000
numberOfModels = 2
alpha = np.array([0.95,0.97,0.99,0.995,0.999,0.9997,0.9999])
myP = np.mean(p)
myC = np.mean(c)
# Set aside some memory
el = np.zeros([numberOfModels])
ul = np.zeros([numberOfModels])
var = np.zeros([len(alpha),numberOfModels])
es = np.zeros([len(alpha),numberOfModels])
cTime = np.zeros(numberOfModels)
# Binomial model
startTime = time.clock() 
el[0],ul[0],var[:,0],es[:,0] = bp.independentBinomialSimulation(N,M,p,c,alpha)
cTime[0] = (time.clock() - startTime)
# Poisson model
startTime = time.clock() 
el[1],ul[1],var[:,1],es[:,1] = bp.independentPoissonSimulation(N,M,p,c,alpha)
cTime[1] = (time.clock() - startTime)
# =====================
# TABLE: Key Model results
# =====================
print("Alpha\t VaR_b\t ES_b\t VaR_p\t ES_p")
for n in range(0,len(alpha)):
    print("%0.2fth\t %0.1f\t %0.1f\t %0.1f\t %0.1f" % (1e2*alpha[n],var[n,0],es[n,0],var[n,1],es[n,1]))
print("Expected loss: %0.1f vs. %0.1f" % (el[0],el[1]))
print("Loss volatility: %0.1f vs. %0.1f" % (ul[0],ul[1]))
print("CPU Time: %0.1f vs. %0.1f" % (cTime[0],cTime[1]))
# =====================
plt.figure(1) # Plot the independent default simulation results
# =====================
plt.plot(var[:,0],alpha,color='red',linestyle='-',label='Binomial')
plt.plot(var[:,1],alpha,color='blue',linestyle='--',label='Poisson')
plt.xlabel('USD')
plt.ylabel('Quantile')
plt.legend(loc=4)