11308963957

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/ql/processes/g2process.cpp

/* -*- mode: c++; tab-width: 4; indent-tabs-mode: nil; c-basic-offset: 4 -*- */

/*
 Copyright (C) 2006 Banca Profilo S.p.A.

 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/g2process.hpp>
#include <ql/processes/eulerdiscretization.hpp>

namespace QuantLib {

    G2Process::G2Process(Real a, Real sigma, Real b, Real eta, Real rho)
    : a_(a), sigma_(sigma), b_(b), eta_(eta), rho_(rho),
      xProcess_(new QuantLib::OrnsteinUhlenbeckProcess(a, sigma, 0.0)),
      yProcess_(new QuantLib::OrnsteinUhlenbeckProcess(b, eta, 0.0)) {}

    Size G2Process::size() const {
        return 2;
    }

    Array G2Process::initialValues() const {
        return { x0_, y0_ };
    }

    Array G2Process::drift(Time t, const Array& x) const {
        return {
            xProcess_->drift(t, x[0]),
            yProcess_->drift(t, x[1])
        };
    }

    Matrix G2Process::diffusion(Time, const Array&) const {
        /* the correlation matrix is
           |  1   rho |
           | rho   1  |
           whose square root (which is used here) is
           |  1          0       |
           | rho   sqrt(1-rho^2) |
        */
        Matrix tmp(2,2);
        Real sigma1 = sigma_;
        Real sigma2 = eta_;
        tmp[0][0] = sigma1;       tmp[0][1] = 0.0;
        tmp[1][0] = rho_*sigma1;  tmp[1][1] = std::sqrt(1.0-rho_*rho_)*sigma2;
        return tmp;
    }

    Array G2Process::expectation(Time t0, const Array& x0,
                                 Time dt) const {
        return {
            xProcess_->expectation(t0, x0[0], dt),
            yProcess_->expectation(t0, x0[1], dt)
        };
    }

    Matrix G2Process::stdDeviation(Time t0, const Array& x0, Time dt) const {
        /* the correlation matrix is
           |  1   rho |
           | rho   1  |
           whose square root (which is used here) is
           |  1          0       |
           | rho   sqrt(1-rho^2) |
        */
        Matrix tmp(2,2);
        Real sigma1 = xProcess_->stdDeviation(t0, x0[0], dt);
        Real sigma2 = yProcess_->stdDeviation(t0, x0[1], dt);
        Real expa = std::exp(-a_*dt), expb = std::exp(-b_*dt);
        Real H = (rho_*sigma_*eta_)/(a_+b_)*(1-expa*expb);
        Real den =
            (0.5*sigma_*eta_)*std::sqrt((1-expa*expa)*(1-expb*expb)/(a_*b_));
        Real newRho = H/den;
        tmp[0][0] = sigma1;
        tmp[0][1] = 0.0;
        tmp[1][0] = newRho*sigma2;
        tmp[1][1] = std::sqrt(1.0-newRho*newRho)*sigma2;
        return tmp;
    }

    Matrix G2Process::covariance(Time t0, const Array& x0, Time dt) const {
        Matrix sigma = stdDeviation(t0, x0, dt);
        Matrix result = sigma*transpose(sigma);
        return result;
    }

    Real G2Process::x0() const {
        return x0_;
    }

    Real G2Process::y0() const {
        return y0_;
    }

    Real G2Process::a() const {
        return a_;
    }

    Real G2Process::sigma() const {
        return sigma_;
    }

    Real G2Process::b() const {
        return b_;
    }

    Real G2Process::eta() const {
        return eta_;
    }

    Real G2Process::rho() const {
        return rho_;
    }


    G2ForwardProcess::G2ForwardProcess(Real a, Real sigma, Real b, Real eta, Real rho)
    : a_(a), sigma_(sigma), b_(b), eta_(eta), rho_(rho),
      xProcess_(new QuantLib::OrnsteinUhlenbeckProcess(a, sigma, 0.0)),
      yProcess_(new QuantLib::OrnsteinUhlenbeckProcess(b, eta, 0.0)) {}

    Size G2ForwardProcess::size() const {
        return 2;
    }

    Array G2ForwardProcess::initialValues() const {
        return { x0_, y0_ };
    }

    Array G2ForwardProcess::drift(Time t, const Array& x) const {
        return {
            xProcess_->drift(t, x[0]) + xForwardDrift(t, T_),
            yProcess_->drift(t, x[1]) + yForwardDrift(t, T_)
        };
    }

    Matrix G2ForwardProcess::diffusion(Time, const Array&) const {
        Matrix tmp(2,2);
        Real sigma1 = sigma_;
        Real sigma2 = eta_;
        tmp[0][0] = sigma1;       tmp[0][1] = 0.0;
        tmp[1][0] = rho_*sigma1;  tmp[1][1] = std::sqrt(1.0-rho_*rho_)*sigma2;
        return tmp;
    }

    Array G2ForwardProcess::expectation(Time t0, const Array& x0,
                                        Time dt) const {
        return {
            xProcess_->expectation(t0, x0[0], dt) - Mx_T(t0, t0+dt, T_),
            yProcess_->expectation(t0, x0[1], dt) - My_T(t0, t0+dt, T_)
        };
    }

    Matrix G2ForwardProcess::stdDeviation(Time t0, const Array& x0, Time dt) const {
        Matrix tmp(2,2);
        Real sigma1 = xProcess_->stdDeviation(t0, x0[0], dt);
        Real sigma2 = yProcess_->stdDeviation(t0, x0[1], dt);
        Real expa = std::exp(-a_*dt), expb = std::exp(-b_*dt);
        Real H = (rho_*sigma_*eta_)/(a_+b_)*(1-expa*expb);
        Real den =
            (0.5*sigma_*eta_)*std::sqrt((1-expa*expa)*(1-expb*expb)/(a_*b_));
        Real newRho = H/den;
        tmp[0][0] = sigma1;
        tmp[0][1] = 0.0;
        tmp[1][0] = newRho*sigma2;
        tmp[1][1] = std::sqrt(1.0-newRho*newRho)*sigma2;
        return tmp;
    }

    Matrix G2ForwardProcess::covariance(Time t0, const Array& x0, Time dt) const {
        Matrix sigma = stdDeviation(t0, x0, dt);
        Matrix result = sigma*transpose(sigma);
        return result;
    }

    Real G2ForwardProcess::xForwardDrift(Time t, Time T) const {
        Real expatT = std::exp(-a_*(T-t));
        Real expbtT = std::exp(-b_*(T-t));

        return -(sigma_*sigma_/a_) * (1-expatT)
              - (rho_*sigma_*eta_/b_) * (1-expbtT);
    }

    Real G2ForwardProcess::yForwardDrift(Time t, Time T) const {
        Real expatT = std::exp(-a_*(T-t));
        Real expbtT = std::exp(-b_*(T-t));

        return -(eta_*eta_/b_) * (1-expbtT)
              - (rho_*sigma_*eta_/a_) * (1-expatT);
    }

    Real G2ForwardProcess::Mx_T(Real s, Real t, Real T) const {
        Real M;
        M = ( (sigma_*sigma_)/(a_*a_) + (rho_*sigma_*eta_)/(a_*b_) )
          * (1-std::exp(-a_*(t-s)));
        M += -(sigma_*sigma_)/(2*a_*a_) *
              (std::exp(-a_*(T-t))-std::exp(-a_*(T+t-2*s)));
        M += -(rho_*sigma_*eta_)/(b_*(a_+b_))
            * (std::exp(-b_*(T-t)) -std::exp(-b_*T-a_*t+(a_+b_)*s));
        return M;
    }

    Real G2ForwardProcess::My_T(Real s, Real t, Real T) const {
        Real M;
        M = ( (eta_*eta_)/(b_*b_) + (rho_*sigma_*eta_)/(a_*b_) )
          * (1-std::exp(-b_*(t-s)));
        M += -(eta_*eta_)/(2*b_*b_) *
              (std::exp(-b_*(T-t))-std::exp(-b_*(T+t-2*s)));
        M += -(rho_*sigma_*eta_)/(a_*(a_+b_))
            * (std::exp(-a_*(T-t))-std::exp(-a_*T-b_*t+(a_+b_)*s));
        return M;
    }

}


1	/* -- mode: c++; tab-width: 4; indent-tabs-mode: nil; c-basic-offset: 4 -- */
2
3	/*
4	Copyright (C) 2006 Banca Profilo S.p.A.
5
6	This file is part of QuantLib, a free-software/open-source library
7	for financial quantitative analysts and developers - http://quantlib.org/
8
9	QuantLib is free software: you can redistribute it and/or modify it
10	under the terms of the QuantLib license. You should have received a
11	copy of the license along with this program; if not, please email
12	<quantlib-dev@lists.sf.net>. The license is also available online at
13	<http://quantlib.org/license.shtml>.
14
15	This program is distributed in the hope that it will be useful, but WITHOUT
16	ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS
17	FOR A PARTICULAR PURPOSE. See the license for more details.
18	*/
19
20	#include <ql/processes/g2process.hpp>
21	#include <ql/processes/eulerdiscretization.hpp>
22
23	namespace QuantLib {
24
25	G2Process::G2Process(Real a, Real sigma, Real b, Real eta, Real rho)	×
26	: a_(a), sigma_(sigma), b_(b), eta_(eta), rho_(rho),	×
27	xProcess_(new QuantLib::OrnsteinUhlenbeckProcess(a, sigma, 0.0)),	×
28	yProcess_(new QuantLib::OrnsteinUhlenbeckProcess(b, eta, 0.0)) {}	×
29
30	Size G2Process::size() const {	×
31	return 2;	×
32	}
33
34	Array G2Process::initialValues() const {	×
35	return { x0_, y0_ };	×
36	}
37
38	Array G2Process::drift(Time t, const Array& x) const {	×
39	return {
40	xProcess_->drift(t, x[0]),	×
41	yProcess_->drift(t, x[1])	×
42	};	×
43	}
44
45	Matrix G2Process::diffusion(Time, const Array&) const {	×
46	/* the correlation matrix is
47	\| 1 rho \|
48	\| rho 1 \|
49	whose square root (which is used here) is
50	\| 1 0 \|
51	\| rho sqrt(1-rho^2) \|
52	*/
53	Matrix tmp(2,2);
54	Real sigma1 = sigma_;	×
55	Real sigma2 = eta_;	×
56	tmp[0][0] = sigma1; tmp[0][1] = 0.0;	×
57	tmp[1][0] = rho_sigma1; tmp[1][1] = std::sqrt(1.0-rho_rho_)*sigma2;	×
58	return tmp;	×
59	}
60
61	Array G2Process::expectation(Time t0, const Array& x0,	×
62	Time dt) const {
63	return {
64	xProcess_->expectation(t0, x0[0], dt),	×
65	yProcess_->expectation(t0, x0[1], dt)	×
66	};	×
67	}
68
69	Matrix G2Process::stdDeviation(Time t0, const Array& x0, Time dt) const {	×
70	/* the correlation matrix is
71	\| 1 rho \|
72	\| rho 1 \|
73	whose square root (which is used here) is
74	\| 1 0 \|
75	\| rho sqrt(1-rho^2) \|
76	*/
77	Matrix tmp(2,2);
78	Real sigma1 = xProcess_->stdDeviation(t0, x0[0], dt);	×
79	Real sigma2 = yProcess_->stdDeviation(t0, x0[1], dt);	×
80	Real expa = std::exp(-a_dt), expb = std::exp(-b_dt);	×
81	Real H = (rho_sigma_eta_)/(a_+b_)(1-expaexpb);	×
82	Real den =
83	(0.5sigma_eta_)std::sqrt((1-expaexpa)(1-expbexpb)/(a_*b_));	×
84	Real newRho = H/den;	×
85	tmp[0][0] = sigma1;	×
86	tmp[0][1] = 0.0;	×
87	tmp[1][0] = newRho*sigma2;	×
88	tmp[1][1] = std::sqrt(1.0-newRhonewRho)sigma2;	×
89	return tmp;	×
90	}
91
92	Matrix G2Process::covariance(Time t0, const Array& x0, Time dt) const {	×
93	Matrix sigma = stdDeviation(t0, x0, dt);	×
94	Matrix result = sigma*transpose(sigma);	×
95	return result;	×
96	}
97
98	Real G2Process::x0() const {	×
99	return x0_;	×
100	}
101
102	Real G2Process::y0() const {	×
103	return y0_;	×
104	}
105
106	Real G2Process::a() const {	×
107	return a_;	×
108	}
109
110	Real G2Process::sigma() const {	×
111	return sigma_;	×
112	}
113
114	Real G2Process::b() const {	×
115	return b_;	×
116	}
117
118	Real G2Process::eta() const {	×
119	return eta_;	×
120	}
121
122	Real G2Process::rho() const {	×
123	return rho_;	×
124	}
125
126
127	G2ForwardProcess::G2ForwardProcess(Real a, Real sigma, Real b, Real eta, Real rho)	×
128	: a_(a), sigma_(sigma), b_(b), eta_(eta), rho_(rho),	×
129	xProcess_(new QuantLib::OrnsteinUhlenbeckProcess(a, sigma, 0.0)),	×
130	yProcess_(new QuantLib::OrnsteinUhlenbeckProcess(b, eta, 0.0)) {}	×
131
132	Size G2ForwardProcess::size() const {	×
133	return 2;	×
134	}
135
136	Array G2ForwardProcess::initialValues() const {	×
137	return { x0_, y0_ };	×
138	}
139
140	Array G2ForwardProcess::drift(Time t, const Array& x) const {	×
141	return {
142	xProcess_->drift(t, x[0]) + xForwardDrift(t, T_),	×
143	yProcess_->drift(t, x[1]) + yForwardDrift(t, T_)	×
144	};	×
145	}
146
147	Matrix G2ForwardProcess::diffusion(Time, const Array&) const {	×
148	Matrix tmp(2,2);
149	Real sigma1 = sigma_;	×
150	Real sigma2 = eta_;	×
151	tmp[0][0] = sigma1; tmp[0][1] = 0.0;	×
152	tmp[1][0] = rho_sigma1; tmp[1][1] = std::sqrt(1.0-rho_rho_)*sigma2;	×
153	return tmp;	×
154	}
155
156	Array G2ForwardProcess::expectation(Time t0, const Array& x0,	×
157	Time dt) const {
158	return {
159	xProcess_->expectation(t0, x0[0], dt) - Mx_T(t0, t0+dt, T_),	×
160	yProcess_->expectation(t0, x0[1], dt) - My_T(t0, t0+dt, T_)	×
161	};	×
162	}
163
164	Matrix G2ForwardProcess::stdDeviation(Time t0, const Array& x0, Time dt) const {	×
165	Matrix tmp(2,2);
166	Real sigma1 = xProcess_->stdDeviation(t0, x0[0], dt);	×
167	Real sigma2 = yProcess_->stdDeviation(t0, x0[1], dt);	×
168	Real expa = std::exp(-a_dt), expb = std::exp(-b_dt);	×
169	Real H = (rho_sigma_eta_)/(a_+b_)(1-expaexpb);	×
170	Real den =
171	(0.5sigma_eta_)std::sqrt((1-expaexpa)(1-expbexpb)/(a_*b_));	×
172	Real newRho = H/den;	×
173	tmp[0][0] = sigma1;	×
174	tmp[0][1] = 0.0;	×
175	tmp[1][0] = newRho*sigma2;	×
176	tmp[1][1] = std::sqrt(1.0-newRhonewRho)sigma2;	×
177	return tmp;	×
178	}
179
180	Matrix G2ForwardProcess::covariance(Time t0, const Array& x0, Time dt) const {	×
181	Matrix sigma = stdDeviation(t0, x0, dt);	×
182	Matrix result = sigma*transpose(sigma);	×
183	return result;	×
184	}
185
186	Real G2ForwardProcess::xForwardDrift(Time t, Time T) const {	×
187	Real expatT = std::exp(-a_*(T-t));	×
188	Real expbtT = std::exp(-b_*(T-t));	×
189
190	return -(sigma_sigma_/a_) (1-expatT)	×
191	- (rho_sigma_eta_/b_) * (1-expbtT);	×
192	}
193
194	Real G2ForwardProcess::yForwardDrift(Time t, Time T) const {	×
195	Real expatT = std::exp(-a_*(T-t));	×
196	Real expbtT = std::exp(-b_*(T-t));	×
197
198	return -(eta_eta_/b_) (1-expbtT)	×
199	- (rho_sigma_eta_/a_) * (1-expatT);	×
200	}
201
202	Real G2ForwardProcess::Mx_T(Real s, Real t, Real T) const {	×
203	Real M;
204	M = ( (sigma_sigma_)/(a_a_) + (rho_sigma_eta_)/(a_*b_) )	×
205	* (1-std::exp(-a_*(t-s)));	×
206	M += -(sigma_sigma_)/(2a_a_)	×
207	(std::exp(-a_(T-t))-std::exp(-a_(T+t-2*s)));	×
208	M += -(rho_sigma_eta_)/(b_*(a_+b_))	×
209	* (std::exp(-b_(T-t)) -std::exp(-b_T-a_t+(a_+b_)s));	×
210	return M;	×
211	}
212
213	Real G2ForwardProcess::My_T(Real s, Real t, Real T) const {	×
214	Real M;
215	M = ( (eta_eta_)/(b_b_) + (rho_sigma_eta_)/(a_*b_) )	×
216	* (1-std::exp(-b_*(t-s)));	×
217	M += -(eta_eta_)/(2b_b_)	×
218	(std::exp(-b_(T-t))-std::exp(-b_(T+t-2*s)));	×
219	M += -(rho_sigma_eta_)/(a_*(a_+b_))	×
220	* (std::exp(-a_(T-t))-std::exp(-a_T-b_t+(a_+b_)s));	×
221	return M;	×
222	}
223
224	}
225

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