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
|
/* -*- mode: c++; tab-width: 4; indent-tabs-mode: nil; c-basic-offset: 4 -*- */
/*
Copyright (C) 2016 Klaus Spanderen
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
<https://www.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.
*/
/*! \file normalclvmodel.hpp
\brief CLV model with a normally distributed kernel process
*/
#ifndef quantlib_normal_clv_model_hpp
#define quantlib_normal_clv_model_hpp
#include <ql/patterns/lazyobject.hpp>
#include <ql/math/interpolations/linearinterpolation.hpp>
#include <ql/math/interpolations/lagrangeinterpolation.hpp>
#include <ql/math/matrix.hpp>
#include <ql/time/date.hpp>
#include <functional>
namespace QuantLib {
/*! References:
A. Grzelak, 2016, The CLV Framework -
A Fresh Look at Efficient Pricing with Smile
http://papers.ssrn.com/sol3/papers.cfm?abstract_id=2747541
*/
class PricingEngine;
class GBSMRNDCalculator;
class OrnsteinUhlenbeckProcess;
class GeneralizedBlackScholesProcess;
class NormalCLVModel : public LazyObject {
public:
NormalCLVModel(const ext::shared_ptr<GeneralizedBlackScholesProcess>& bsProcess,
ext::shared_ptr<OrnsteinUhlenbeckProcess> ouProcess,
const std::vector<Date>& maturityDates,
Size lagrangeOrder,
Real pMax = Null<Real>(),
Real pMin = Null<Real>());
// cumulative distribution function of the BS process
Real cdf(const Date& d, Real x) const;
// inverse cumulative distribution function of the BS process
Real invCDF(const Date& d, Real q) const;
// collocation points of the Ornstein-Uhlenbeck process
Array collocationPointsX(const Date& d) const;
// collocation points for the underlying Y
Array collocationPointsY(const Date& d) const;
// CLV mapping function
std::function<Real(Time, Real)> g() const;
protected:
void performCalculations() const override;
private:
class MappingFunction {
public:
explicit MappingFunction(const NormalCLVModel& model);
Real operator()(Time t, Real x) const;
private:
mutable Array y_;
const Volatility sigma_;
const ext::shared_ptr<OrnsteinUhlenbeckProcess> ouProcess_;
struct InterpolationData {
explicit InterpolationData(const NormalCLVModel& model)
: s_(model.x_.size(), model.maturityDates_.size()),
x_(model.x_),
t_(model.maturityTimes_),
lagrangeInterpl_(x_.begin(), x_.end(), x_.begin()) {}
Matrix s_;
std::vector<LinearInterpolation> interpl_;
const Array x_;
const std::vector<Time> t_;
const LagrangeInterpolation lagrangeInterpl_;
};
const ext::shared_ptr<InterpolationData> data_;
};
const Array x_;
const Volatility sigma_;
const ext::shared_ptr<GeneralizedBlackScholesProcess> bsProcess_;
const ext::shared_ptr<OrnsteinUhlenbeckProcess> ouProcess_;
const std::vector<Date> maturityDates_;
const ext::shared_ptr<GBSMRNDCalculator> rndCalculator_;
std::vector<Time> maturityTimes_;
mutable std::function<Real(Time, Real)> g_;
};
}
#endif
|
