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
|
/* -*- mode: c++; tab-width: 4; indent-tabs-mode: nil; c-basic-offset: 4 -*- */
/*
Copyright (C) 2015 Johannes Göttker-Schnetmann
Copyright (C) 2015 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
<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/methods/finitedifferences/utilities/squarerootprocessrndcalculator.hpp>
#include <boost/math/distributions/non_central_chi_squared.hpp>
namespace QuantLib {
SquareRootProcessRNDCalculator::SquareRootProcessRNDCalculator(
Real v0, Real kappa, Real theta, Real sigma)
: v0_(v0), kappa_(kappa), theta_(theta),
d_(4*kappa/(sigma*sigma)), df_(d_*theta) { }
Real SquareRootProcessRNDCalculator::pdf(Real v, Time t) const {
const Real e = std::exp(-kappa_*t);
const Real k = d_/(1-e);
const Real ncp = k*v0_*e;
const boost::math::non_central_chi_squared_distribution<Real>
dist(df_, ncp);
return boost::math::pdf(dist, v*k) * k;
}
Real SquareRootProcessRNDCalculator::cdf(Real v, Time t) const {
const Real e = std::exp(-kappa_*t);
const Real k = d_/(1-e);
const Real ncp = k*v0_*e;
const boost::math::non_central_chi_squared_distribution<Real>
dist(df_, ncp);
return boost::math::cdf(dist, v*k);
}
Real SquareRootProcessRNDCalculator::invcdf(Real q, Time t) const {
const Real e = std::exp(-kappa_*t);
const Real k = d_/(1-e);
const Real ncp = k*v0_*e;
const boost::math::non_central_chi_squared_distribution<Real>
dist(df_, ncp);
return boost::math::quantile(dist, q) / k;
}
Real SquareRootProcessRNDCalculator::stationary_pdf(Real v) const {
const Real alpha = 0.5*df_;
const Real beta = alpha/theta_;
return std::pow(beta, alpha)*std::pow(v, alpha-1)
*std::exp(-beta*v-boost::math::lgamma(alpha));
}
Real SquareRootProcessRNDCalculator::stationary_cdf(Real v) const {
const Real alpha = 0.5*df_;
const Real beta = alpha/theta_;
return boost::math::gamma_p(alpha, beta*v);
}
Real SquareRootProcessRNDCalculator::stationary_invcdf(Real q) const {
const Real alpha = 0.5*df_;
const Real beta = alpha/theta_;
return boost::math::gamma_p_inv(alpha, q)/beta;
}
}
|
