1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
41
42
43
44
45
46
47
48
49
50
51
52
53
54
55
56
57
58
59
60
61
62
63
64
65
66
67
68
69
70
71
72
73
74
75
76
77
78
79
80
81
82
83
84
85
86
87
88
89
90
91
92
93
94
95
96
97
98
99
100
101
102
103
104
105
106
107
108
109
110
111
112
113
114
115
116
117
118
119
120
121
122
123
124
125
126
127
128
129
130
131
132
133
134
135
136
137
138
139
140
141
142
143
144
|
#!/usr/bin/python
"""
Copyright (C) 2000, 2001, 2002 RiskMap srl
This file is part of QuantLib, a free-software/open-source library
for financial quantitative analysts and developers - http://quantlib.org/
QuantLib is free software: you can redistribute it and/or modify it under the
terms of the QuantLib license. You should have received a copy of the
license along with this program; if not, please email ferdinando@ametrano.net
The license is also available online at http://quantlib.org/html/license.html
This program is distributed in the hope that it will be useful, but WITHOUT
ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS
FOR A PARTICULAR PURPOSE. See the license for more details.
"""
__version__ = "$Revision: 1.14 $"
# $Source: /cvsroot/quantlib/QuantLib-Python/QuantLib/test/distributions.py,v $
import QuantLib
import unittest
from math import exp, sqrt, pi
# define a Gaussian
def gaussian(x, average, sigma):
normFact = sigma * sqrt( 2 * pi )
dx = x-average
return exp( -dx*dx/(2.0*sigma*sigma) ) / normFact
def gaussianDerivative(x, average, sigma):
normFact = sigma * sigma * sigma * sqrt( 2 * pi )
dx = x-average
return - dx * exp( -dx*dx/(2.0*sigma*sigma) ) / normFact
# define the norm of a discretized function
def norm(f,h):
# squared values
f2 = map(lambda x: x*x, f)
# numeric integral of f^2
I = h*(reduce(lambda x,y: x+y, f2)-0.5*f2[0]-0.5*f2[-1])
return sqrt(I)
class DistributionTest(unittest.TestCase):
def runTest(self):
"Testing distributions"
average = 0.0
sigma = 1.0
normal = QuantLib.NormalDistribution(average, sigma)
cum = QuantLib.CumulativeNormalDistribution(average, sigma)
invCum = QuantLib.InvCumulativeNormalDistribution(average, sigma)
xMin = average - 4*sigma
xMax = average + 4*sigma
# odd in include average
N = 10001
h = (xMax-xMin)/(N-1)
x = [0]*N # creates a list of N elements
for i in range(N):
x[i] = xMin+h*i
y = map(lambda x,average=average,sigma=sigma:
gaussian(x,average,sigma), x)
yIntegrated = map(cum, x)
yTemp = map(normal, x)
y2Temp = map(cum.derivative, x)
xTemp = map(invCum, yIntegrated)
yd = map(normal.derivative, x)
ydTemp = map(lambda x,average=average,sigma=sigma:
gaussianDerivative(x,average,sigma), x)
#check norm=gaussian
e = norm(map(lambda x,y:x-y,yTemp,y),h)
if not (e <= 1.0e-16):
self.fail("""
norm of C++ NormalDistribution minus analytic gaussian: %(e)5.2e
tolerance exceeded
""" % locals())
#check invCum(cum) = Identity
e = norm(map(lambda x,y:x-y,xTemp,x),h)
if not (e <= 1.0e-3):
self.fail("""
norm of C++ invCum(cum(.)) minus identity: %(e)5.2e
tolerance exceeded
""" % locals())
#check cum.derivative=normal
e = norm(map(lambda x,y:x-y,y2Temp,y),h)
if not (e <= 1.0e-16):
self.fail("""
norm of C++ Cumulative.derivative minus analytic gaussian: %(e)5.2e
tolerance exceeded
""" % locals())
#check normal.derivative=gaussianDerivative
e = norm(map(lambda x,y:x-y,ydTemp,yd),h)
if not (e <= 1.0e-16):
self.fail("""
norm of C++ NormalDist.derivative minus analytic gaussian.derivative: %(e)5.2e
tolerance exceeded
""" % locals())
# ... and now let's toy with finite difference
# define the first derivative operators
D = QuantLib.DZero(N,h)
D2 = QuantLib.DPlusDMinus(N,h)
# and calculate the derivatives
y3Temp = D.applyTo(yIntegrated)
yd2Temp = D2.applyTo(yIntegrated)
#check finite difference first order derivative operator = gaussian
e = norm(map(lambda x,y:x-y,y3Temp,y),h)
if not (e <= 1.0e-6):
self.fail("""
norm of C++ FD 1st deriv. of cum minus analytic gaussian: %(e)5.2e
tolerance exceeded
""" % locals())
# check finite difference second order derivative operator =
# normal.derivative
e = norm(map(lambda x,y:x-y,yd2Temp,yd),h)
if not (e <= 1.0e-4):
self.fail("""
norm of C++ FD 2nd deriv. of cum minus analytic gaussian.derivative: %(e)5.2e
tolerance exceeded
""" % locals())
if __name__ == '__main__':
print 'testing QuantLib', QuantLib.__version__, QuantLib.QuantLibc.__file__, QuantLib.__file__
import sys
suite = unittest.TestSuite()
suite.addTest(DistributionTest())
if sys.hexversion >= 0x020100f0:
unittest.TextTestRunner(verbosity=2).run(suite)
else:
unittest.TextTestRunner().run(suite)
raw_input('press any key to continue')
|
