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
145
146
147
148
149
150
151
152
153
154
155
156
157
158
159
160
161
162
163
164
165
166
167
168
169
170
171
172
173
174
175
176
177
178
179
180
181
182
183
184
185
186
187
188
189
190
191
192
193
194
195
196
197
198
199
200
|
/* -*- mode: c++; tab-width: 4; indent-tabs-mode: nil; c-basic-offset: 4 -*- */
/*
Copyright (C) 2003 Ferdinando Ametrano
Copyright (C) 2001, 2002, 2003 Sadruddin Rejeb
Copyright (C) 2004, 2005, 2006, 2007 StatPro Italia 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
<quantlib-dev@lists.sf.net>. The license is also available online at
<http://quantlib.org/license.shtml>.
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.
*/
#include <ql/processes/blackscholesprocess.hpp>
#include <ql/termstructures/volatility/equityfx/localvolsurface.hpp>
#include <ql/termstructures/volatility/equityfx/localvolcurve.hpp>
#include <ql/termstructures/volatility/equityfx/localconstantvol.hpp>
#include <ql/termstructures/yield/flatforward.hpp>
#include <ql/time/calendars/nullcalendar.hpp>
#include <ql/time/daycounters/actual365fixed.hpp>
namespace QuantLib {
GeneralizedBlackScholesProcess::GeneralizedBlackScholesProcess(
const Handle<Quote>& x0,
const Handle<YieldTermStructure>& dividendTS,
const Handle<YieldTermStructure>& riskFreeTS,
const Handle<BlackVolTermStructure>& blackVolTS,
const boost::shared_ptr<discretization>& disc)
: StochasticProcess1D(disc), x0_(x0), riskFreeRate_(riskFreeTS),
dividendYield_(dividendTS), blackVolatility_(blackVolTS),
updated_(false) {
registerWith(x0_);
registerWith(riskFreeRate_);
registerWith(dividendYield_);
registerWith(blackVolatility_);
}
Real GeneralizedBlackScholesProcess::x0() const {
return x0_->value();
}
Real GeneralizedBlackScholesProcess::drift(Time t, Real x) const {
Real sigma = diffusion(t,x);
// we could be more anticipatory if we know the right dt
// for which the drift will be used
Time t1 = t + 0.0001;
return riskFreeRate_->forwardRate(t,t1,Continuous,NoFrequency,true)
- dividendYield_->forwardRate(t,t1,Continuous,NoFrequency,true)
- 0.5 * sigma * sigma;
}
Real GeneralizedBlackScholesProcess::diffusion(Time t, Real x) const {
return localVolatility()->localVol(t, x, true);
}
Real GeneralizedBlackScholesProcess::apply(Real x0, Real dx) const {
return x0 * std::exp(dx);
}
Real GeneralizedBlackScholesProcess::expectation(Time,
Real,
Time) const {
QL_FAIL("not implemented");
}
Real GeneralizedBlackScholesProcess::evolve(Time t0, Real x0,
Time dt, Real dw) const {
return apply(x0, discretization_->drift(*this,t0,x0,dt) +
stdDeviation(t0,x0,dt)*dw);
}
Time GeneralizedBlackScholesProcess::time(const Date& d) const {
return riskFreeRate_->dayCounter().yearFraction(
riskFreeRate_->referenceDate(), d);
}
void GeneralizedBlackScholesProcess::update() {
updated_ = false;
StochasticProcess1D::update();
}
const Handle<Quote>&
GeneralizedBlackScholesProcess::stateVariable() const {
return x0_;
}
const Handle<YieldTermStructure>&
GeneralizedBlackScholesProcess::dividendYield() const {
return dividendYield_;
}
const Handle<YieldTermStructure>&
GeneralizedBlackScholesProcess::riskFreeRate() const {
return riskFreeRate_;
}
const Handle<BlackVolTermStructure>&
GeneralizedBlackScholesProcess::blackVolatility() const {
return blackVolatility_;
}
const Handle<LocalVolTermStructure>&
GeneralizedBlackScholesProcess::localVolatility() const {
if (!updated_) {
// constant Black vol?
boost::shared_ptr<BlackConstantVol> constVol =
boost::dynamic_pointer_cast<BlackConstantVol>(
*blackVolatility());
if (constVol) {
// ok, the local vol is constant too.
localVolatility_.linkTo(
boost::shared_ptr<LocalVolTermStructure>(new
LocalConstantVol(constVol->referenceDate(),
constVol->blackVol(0.0, x0_->value()),
constVol->dayCounter())));
updated_ = true;
return localVolatility_;
}
// ok, so it's not constant. Maybe it's strike-independent?
boost::shared_ptr<BlackVarianceCurve> volCurve =
boost::dynamic_pointer_cast<BlackVarianceCurve>(
*blackVolatility());
if (volCurve) {
// ok, we can use the optimized algorithm
localVolatility_.linkTo(
boost::shared_ptr<LocalVolTermStructure>(
new LocalVolCurve(
Handle<BlackVarianceCurve>(volCurve))));
updated_ = true;
return localVolatility_;
}
// ok, so it's strike-dependent. Never mind.
localVolatility_.linkTo(
boost::shared_ptr<LocalVolTermStructure>(
new LocalVolSurface(blackVolatility_, riskFreeRate_,
dividendYield_, x0_->value())));
updated_ = true;
return localVolatility_;
} else {
return localVolatility_;
}
}
// specific models
BlackScholesProcess::BlackScholesProcess(
const Handle<Quote>& x0,
const Handle<YieldTermStructure>& riskFreeTS,
const Handle<BlackVolTermStructure>& blackVolTS,
const boost::shared_ptr<discretization>& d)
: GeneralizedBlackScholesProcess(
x0,
// no dividend yield
Handle<YieldTermStructure>(boost::shared_ptr<YieldTermStructure>(
new FlatForward(0, NullCalendar(), 0.0, Actual365Fixed()))),
riskFreeTS,
blackVolTS,
d) {}
BlackScholesMertonProcess::BlackScholesMertonProcess(
const Handle<Quote>& x0,
const Handle<YieldTermStructure>& dividendTS,
const Handle<YieldTermStructure>& riskFreeTS,
const Handle<BlackVolTermStructure>& blackVolTS,
const boost::shared_ptr<discretization>& d)
: GeneralizedBlackScholesProcess(x0,dividendTS,riskFreeTS,blackVolTS,d) {}
BlackProcess::BlackProcess(const Handle<Quote>& x0,
const Handle<YieldTermStructure>& riskFreeTS,
const Handle<BlackVolTermStructure>& blackVolTS,
const boost::shared_ptr<discretization>& d)
: GeneralizedBlackScholesProcess(x0,riskFreeTS,riskFreeTS,blackVolTS,d) {}
GarmanKohlagenProcess::GarmanKohlagenProcess(
const Handle<Quote>& x0,
const Handle<YieldTermStructure>& foreignRiskFreeTS,
const Handle<YieldTermStructure>& domesticRiskFreeTS,
const Handle<BlackVolTermStructure>& blackVolTS,
const boost::shared_ptr<discretization>& d)
: GeneralizedBlackScholesProcess(x0,foreignRiskFreeTS,domesticRiskFreeTS,
blackVolTS,d) {}
}
|
