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
|
=begin
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.
=end
# $Id: implied_volatility.rb,v 1.4 2002/01/16 15:17:06 nando Exp $
require 'QuantLib'
require 'runit/testcase'
require 'runit/testsuite'
require 'runit/cui/testrunner'
def pricer(type,underlying,strike,divCurve,rfCurve,exDate,volatility)
QuantLib::PlainOption.new(type,underlying,strike,divCurve,rfCurve,
exDate,volatility,QuantLib::EuropeanEngine.new)
end
def quote(value)
h = QuantLib::MarketElementHandle.new
h.linkTo QuantLib::SimpleMarketElement.new(value)
return h
end
def flatCurve(forward)
h = QuantLib::TermStructureHandle.new
h.linkTo QuantLib::FlatForward.new('EUR',
QuantLib::DayCounter.new('act/360'),
QuantLib::Date.new(12,10,2001),
QuantLib::Calendar.new('TARGET'), 2,
forward)
return h
end
class ImpliedVolatilityTest < RUNIT::TestCase
include QuantLib
def name
"Testing implied volatility calculation..."
end
def test
maxEval = 100
tol = 1.0e-6
[0.01, 0.05, 0.10].each { |qRate|
divCurve = flatCurve(qRate)
[0.01, 0.05, 0.10].each { |rRate|
rfCurve = flatCurve(rRate)
[0.01, 0.2, 0.3, 0.7, 0.9].each { |vol|
volatility = quote(vol)
[80, 95, 99.9, 100, 100.1, 105, 120].each { |under|
underlying = quote(under)
[1,36,180,360,1080].each { |days|
exDate = Date.new(16,10,2001) + days
[50, 99.5, 100, 100.5, 150].each { |strike|
['Call','Put','Straddle'].each { |type|
bsm = pricer(type,underlying,strike,
divCurve,rfCurve,exDate,volatility)
bsmValue = bsm.NPV
next if bsmValue == 0.0
[0.5, 0.999, 1.0, 1.001, 1.5].each { |dVol|
volatility2 = quote(vol*dVol)
bsm2 = pricer(type,underlying,strike,
divCurve,rfCurve,exDate,volatility2)
begin
implVol = bsm2.impliedVolatility(bsmValue,tol,maxEval)
rescue StandardError => e
assert_fail(<<-MESSAGE
Exception: #{e}
Option details: #{type} #{under} #{strike} #{qRate} #{rRate} #{days}
volatility: #{vol*dVol}
option value: #{bsm2.NPV}
while trying to calculate implied vol from value #{bsmValue}
MESSAGE
)
end
if (implVol-vol).abs > tol
volatility3 = quote(vol*dVol)
bsm3 = pricer(type,underlying,strike,
divCurve,rfCurve,exDate,volatility3)
bsm3Value = bsm3.NPV
unless (bsm3Value-bsmValue).abs/under <= 1.0e-3
assert_fail(<<-MESSAGE
Option details: #{type} #{under} #{strike} #{qRate} #{rRate} #{days}
at #{vol} vol the option value is #{bsmValue}
at #{vol+dVol} vol the option value is #{bsm2.NPV}
at #{bsmValue} value the implied vol is #{implVol}
at #{implVol} vol the option value is #{bsm3value}
which is #{(bsm3Value - bsmValue)} above target value
MESSAGE
)
end
end
}}}}}}}}
end
end
if $0 == __FILE__
RUNIT::CUI::TestRunner.run(ImpliedVolatilityTest.suite)
end
|
