30255006850

Committed 27 Jul 2026 09:41AM UTC coverage: 74.898% (-0.05%) from 74.944%

Build # 30255006850

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lballabio

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Avoid deprecated Ubuntu runner

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83.67

/ql/termstructures/volatility/abcdcalibration.cpp

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

/*
 Copyright (C) 2006, 2015 Ferdinando Ametrano
 Copyright (C) 2006 Cristina Duminuco
 Copyright (C) 2005, 2006 Klaus Spanderen
 Copyright (C) 2007 Giorgio Facchinetti
 Copyright (C) 2015 Paolo Mazzocchi

 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.
*/

#include <ql/math/distributions/normaldistribution.hpp>
#include <ql/math/interpolations/abcdinterpolation.hpp>
#include <ql/math/optimization/constraint.hpp>
#include <ql/math/optimization/levenbergmarquardt.hpp>
#include <ql/math/optimization/method.hpp>
#include <ql/pricingengines/blackformula.hpp>
#include <ql/termstructures/volatility/abcd.hpp>
#include <ql/termstructures/volatility/abcdcalibration.hpp>
#include <utility>

namespace QuantLib {

    // to constrained <- from unconstrained
    Array AbcdCalibration::AbcdParametersTransformation::direct(const Array& x) const {
        y_[1] = x[1];
        y_[2] = std::exp(x[2]);
        y_[3] = std::exp(x[3]);
        y_[0] = std::exp(x[0]) - y_[3];
        return y_;
    }

    // to unconstrained <- from constrained
    Array AbcdCalibration::AbcdParametersTransformation::inverse(const Array& x) const {
        y_[1] = x[1];
        y_[2] = std::log(x[2]);
        y_[3] = std::log(x[3]);
        y_[0] = std::log(x[0] + x[3]);
        return y_;
    }

    // to constrained <- from unconstrained

    AbcdCalibration::AbcdCalibration(const std::vector<Real>& t,
                                     const std::vector<Real>& blackVols,
                                     Real a,
                                     Real b,
                                     Real c,
                                     Real d,
                                     bool aIsFixed,
                                     bool bIsFixed,
                                     bool cIsFixed,
                                     bool dIsFixed,
                                     bool vegaWeighted,
                                     ext::shared_ptr<EndCriteria> endCriteria,
                                     ext::shared_ptr<OptimizationMethod> optMethod)
    : aIsFixed_(aIsFixed), bIsFixed_(bIsFixed), cIsFixed_(cIsFixed), dIsFixed_(dIsFixed), a_(a),
      b_(b), c_(c), d_(d), abcdEndCriteria_(EndCriteria::None),
      endCriteria_(std::move(endCriteria)), optMethod_(std::move(optMethod)),
      weights_(blackVols.size(), 1.0 / blackVols.size()), vegaWeighted_(vegaWeighted), times_(t),
      blackVols_(blackVols) {

        AbcdMathFunction::validate(a, b, c, d);

        QL_REQUIRE(blackVols.size()==t.size(),
                       "mismatch between number of times (" << t.size() <<
                       ") and blackVols (" << blackVols.size() << ")");

        // if no optimization method or endCriteria is provided, we provide one
        if (!optMethod_) {
            Real epsfcn = 1.0e-8;
            Real xtol = 1.0e-8;
            Real gtol = 1.0e-8;
            bool useCostFunctionsJacobian = false;
            optMethod_ = ext::make_shared<LevenbergMarquardt>(
                epsfcn, xtol, gtol, useCostFunctionsJacobian);
        }
        if (!endCriteria_) {
            Size maxIterations = 10000;
            Size maxStationaryStateIterations = 1000;
            Real rootEpsilon = 1.0e-8;
            Real functionEpsilon = 0.3e-4;     // Why 0.3e-4 ?
            Real gradientNormEpsilon = 0.3e-4; // Why 0.3e-4 ?
            endCriteria_ = ext::make_shared<EndCriteria>(maxIterations, maxStationaryStateIterations,
                            rootEpsilon, functionEpsilon, gradientNormEpsilon);
        }
    }

    void AbcdCalibration::compute() {
        if (vegaWeighted_) {
            Real weightsSum = 0.0;
            for (Size i=0; i<times_.size() ; i++) {
                Real stdDev = std::sqrt(blackVols_[i]* blackVols_[i]* times_[i]);
                // when strike==forward, the blackFormulaStdDevDerivative becomes
                weights_[i] = CumulativeNormalDistribution().derivative(.5*stdDev);
                weightsSum += weights_[i];
            }
            // weight normalization
            for (Size i=0; i<times_.size() ; i++) {
                weights_[i] /= weightsSum;
            }
        }

        // there is nothing to optimize
        if (aIsFixed_ && bIsFixed_ && cIsFixed_ && dIsFixed_) {
            abcdEndCriteria_ = EndCriteria::None;
            //error_ = interpolationError();
            //maxError_ = interpolationMaxError();
            return;
        } else {

            AbcdError costFunction(this);
            transformation_ = ext::make_shared<AbcdParametersTransformation>();

            Array guess(4);
            guess[0] = a_;
            guess[1] = b_;
            guess[2] = c_;
            guess[3] = d_;

            std::vector<bool> parameterAreFixed(4);
            parameterAreFixed[0] = aIsFixed_;
            parameterAreFixed[1] = bIsFixed_;
            parameterAreFixed[2] = cIsFixed_;
            parameterAreFixed[3] = dIsFixed_;

            Array inversedTransformatedGuess(transformation_->inverse(guess));

            ProjectedCostFunction projectedAbcdCostFunction(costFunction,
                            inversedTransformatedGuess, parameterAreFixed);

            Array projectedGuess
                (projectedAbcdCostFunction.project(inversedTransformatedGuess));

            NoConstraint constraint;
            Problem problem(projectedAbcdCostFunction, constraint, projectedGuess);
            abcdEndCriteria_ = optMethod_->minimize(problem, *endCriteria_);
            Array projectedResult(problem.currentValue());
            Array transfResult(projectedAbcdCostFunction.include(projectedResult));

            Array result = transformation_->direct(transfResult);
            AbcdMathFunction::validate(a_, b_, c_, d_);
            a_ = result[0];
            b_ = result[1];
            c_ = result[2];
            d_ = result[3];

        }
    }

    Real AbcdCalibration::value(Real x) const {
        return abcdBlackVolatility(x,a_,b_,c_,d_);
    }

    std::vector<Real> AbcdCalibration::k(const std::vector<Real>& t,
                                         const std::vector<Real>& blackVols) const {
        QL_REQUIRE(blackVols.size()==t.size(),
               "mismatch between number of times (" << t.size() <<
               ") and blackVols (" << blackVols.size() << ")");
        std::vector<Real> k(t.size());
        for (Size i=0; i<t.size() ; i++) {
            k[i]=blackVols[i]/value(t[i]);
        }
        return k;
    }

    Real AbcdCalibration::error() const {
        Size n = times_.size();
        Real error, squaredError = 0.0;
        for (Size i=0; i<times_.size() ; i++) {
            error = (value(times_[i]) - blackVols_[i]);
            squaredError += error * error * weights_[i];
        }
        return std::sqrt(n*squaredError/(n-1));
    }

    Real AbcdCalibration::maxError() const {
        Real error, maxError = QL_MIN_REAL;
        for (Size i=0; i<times_.size() ; i++) {
            error = std::fabs(value(times_[i]) - blackVols_[i]);
            maxError = std::max(maxError, error);
        }
        return maxError;
    }

    // calculate weighted differences
    Array AbcdCalibration::errors() const {
        Array results(times_.size());
        for (Size i=0; i<times_.size() ; i++) {
            results[i] = (value(times_[i]) - blackVols_[i])* std::sqrt(weights_[i]);
        }
        return results;
    }

    EndCriteria::Type AbcdCalibration::endCriteria() const{
        return abcdEndCriteria_;
    }

}

1	/* -- mode: c++; tab-width: 4; indent-tabs-mode: nil; c-basic-offset: 4 -- */
2
3	/*
4	Copyright (C) 2006, 2015 Ferdinando Ametrano
5	Copyright (C) 2006 Cristina Duminuco
6	Copyright (C) 2005, 2006 Klaus Spanderen
7	Copyright (C) 2007 Giorgio Facchinetti
8	Copyright (C) 2015 Paolo Mazzocchi
9
10	This file is part of QuantLib, a free-software/open-source library
11	for financial quantitative analysts and developers - http://quantlib.org/
12
13	QuantLib is free software: you can redistribute it and/or modify it
14	under the terms of the QuantLib license. You should have received a
15	copy of the license along with this program; if not, please email
16	<quantlib-dev@lists.sf.net>. The license is also available online at
17	<https://www.quantlib.org/license.shtml>.
18
19	This program is distributed in the hope that it will be useful, but WITHOUT
20	ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS
21	FOR A PARTICULAR PURPOSE. See the license for more details.
22	*/
23
24	#include <ql/math/distributions/normaldistribution.hpp>
25	#include <ql/math/interpolations/abcdinterpolation.hpp>
26	#include <ql/math/optimization/constraint.hpp>
27	#include <ql/math/optimization/levenbergmarquardt.hpp>
28	#include <ql/math/optimization/method.hpp>
29	#include <ql/pricingengines/blackformula.hpp>
30	#include <ql/termstructures/volatility/abcd.hpp>
31	#include <ql/termstructures/volatility/abcdcalibration.hpp>
32	#include <utility>
33
34	namespace QuantLib {
35
36	// to constrained <- from unconstrained
37	Array AbcdCalibration::AbcdParametersTransformation::direct(const Array& x) const {	19✔
38	y_[1] = x[1];	19✔
39	y_[2] = std::exp(x[2]);	19✔
40	y_[3] = std::exp(x[3]);	19✔
41	y_[0] = std::exp(x[0]) - y_[3];	19✔
42	return y_;	19✔
43	}
44
45	// to unconstrained <- from constrained
46	Array AbcdCalibration::AbcdParametersTransformation::inverse(const Array& x) const {	1✔
47	y_[1] = x[1];	1✔
48	y_[2] = std::log(x[2]);	1✔
49	y_[3] = std::log(x[3]);	1✔
50	y_[0] = std::log(x[0] + x[3]);	1✔
51	return y_;	1✔
52	}
53
54	// to constrained <- from unconstrained
55
56	AbcdCalibration::AbcdCalibration(const std::vector<Real>& t,	1✔
57	const std::vector<Real>& blackVols,
58	Real a,
59	Real b,
60	Real c,
61	Real d,
62	bool aIsFixed,
63	bool bIsFixed,
64	bool cIsFixed,
65	bool dIsFixed,
66	bool vegaWeighted,
67	ext::shared_ptr<EndCriteria> endCriteria,
68	ext::shared_ptr<OptimizationMethod> optMethod)	1✔
69	: aIsFixed_(aIsFixed), bIsFixed_(bIsFixed), cIsFixed_(cIsFixed), dIsFixed_(dIsFixed), a_(a),	1✔
70	b_(b), c_(c), d_(d), abcdEndCriteria_(EndCriteria::None),	1✔
71	endCriteria_(std::move(endCriteria)), optMethod_(std::move(optMethod)),
72	weights_(blackVols.size(), 1.0 / blackVols.size()), vegaWeighted_(vegaWeighted), times_(t),	1✔
73	blackVols_(blackVols) {	1✔
74
75	AbcdMathFunction::validate(a, b, c, d);	1✔
76
77	QL_REQUIRE(blackVols.size()==t.size(),	1✔
78	"mismatch between number of times (" << t.size() <<
79	") and blackVols (" << blackVols.size() << ")");
80
81	// if no optimization method or endCriteria is provided, we provide one
82	if (!optMethod_) {	1✔
83	Real epsfcn = 1.0e-8;	1✔
84	Real xtol = 1.0e-8;	1✔
85	Real gtol = 1.0e-8;	1✔
86	bool useCostFunctionsJacobian = false;	1✔
87	optMethod_ = ext::make_shared<LevenbergMarquardt>(	2✔
88	epsfcn, xtol, gtol, useCostFunctionsJacobian);	1✔
89	}
90	if (!endCriteria_) {	1✔
91	Size maxIterations = 10000;	1✔
92	Size maxStationaryStateIterations = 1000;	1✔
93	Real rootEpsilon = 1.0e-8;	1✔
94	Real functionEpsilon = 0.3e-4; // Why 0.3e-4 ?	1✔
95	Real gradientNormEpsilon = 0.3e-4; // Why 0.3e-4 ?	1✔
96	endCriteria_ = ext::make_shared<EndCriteria>(maxIterations, maxStationaryStateIterations,	2✔
97	rootEpsilon, functionEpsilon, gradientNormEpsilon);	1✔
98	}
99	}	1✔
100
101	void AbcdCalibration::compute() {	1✔
102	if (vegaWeighted_) {	1✔
103	Real weightsSum = 0.0;
104	for (Size i=0; i<times_.size() ; i++) {	×
105	Real stdDev = std::sqrt(blackVols_[i]* blackVols_[i]* times_[i]);	×
106	// when strike==forward, the blackFormulaStdDevDerivative becomes
107	weights_[i] = CumulativeNormalDistribution().derivative(.5*stdDev);	×
108	weightsSum += weights_[i];	×
109	}
110	// weight normalization
111	for (Size i=0; i<times_.size() ; i++) {	×
112	weights_[i] /= weightsSum;	×
113	}
114	}
115
116	// there is nothing to optimize
117	if (aIsFixed_ && bIsFixed_ && cIsFixed_ && dIsFixed_) {	1✔
118	abcdEndCriteria_ = EndCriteria::None;	×
119	//error_ = interpolationError();
120	//maxError_ = interpolationMaxError();
121	return;	×
122	} else {
123
124	AbcdError costFunction(this);
125	transformation_ = ext::make_shared<AbcdParametersTransformation>();	2✔
126
127	Array guess(4);
128	guess[0] = a_;	1✔
129	guess[1] = b_;	1✔
130	guess[2] = c_;	1✔
131	guess[3] = d_;	1✔
132
133	std::vector<bool> parameterAreFixed(4);	×
134	parameterAreFixed[0] = aIsFixed_;	1✔
135	parameterAreFixed[1] = bIsFixed_;	1✔
136	parameterAreFixed[2] = cIsFixed_;	1✔
137	parameterAreFixed[3] = dIsFixed_;	1✔
138
139	Array inversedTransformatedGuess(transformation_->inverse(guess));	1✔
140
141	ProjectedCostFunction projectedAbcdCostFunction(costFunction,
142	inversedTransformatedGuess, parameterAreFixed);	1✔
143
144	Array projectedGuess
145	(projectedAbcdCostFunction.project(inversedTransformatedGuess));	1✔
146
147	NoConstraint constraint;	1✔
148	Problem problem(projectedAbcdCostFunction, constraint, projectedGuess);	1✔
149	abcdEndCriteria_ = optMethod_->minimize(problem, *endCriteria_);	1✔
150	Array projectedResult(problem.currentValue());	1✔
151	Array transfResult(projectedAbcdCostFunction.include(projectedResult));	1✔
152
153	Array result = transformation_->direct(transfResult);	1✔
154	AbcdMathFunction::validate(a_, b_, c_, d_);	1✔
155	a_ = result[0];	1✔
156	b_ = result[1];	1✔
157	c_ = result[2];	1✔
158	d_ = result[3];	1✔
159
160	}
161	}
162
163	Real AbcdCalibration::value(Real x) const {	189✔
164	return abcdBlackVolatility(x,a_,b_,c_,d_);	189✔
165	}
166
167	std::vector<Real> AbcdCalibration::k(const std::vector<Real>& t,	1✔
168	const std::vector<Real>& blackVols) const {
169	QL_REQUIRE(blackVols.size()==t.size(),	1✔
170	"mismatch between number of times (" << t.size() <<
171	") and blackVols (" << blackVols.size() << ")");
172	std::vector<Real> k(t.size());	1✔
173	for (Size i=0; i<t.size() ; i++) {	10✔
174	k[i]=blackVols[i]/value(t[i]);	9✔
175	}
176	return k;	1✔
177	}	×
178
179	Real AbcdCalibration::error() const {	3✔
180	Size n = times_.size();
181	Real error, squaredError = 0.0;
182	for (Size i=0; i<times_.size() ; i++) {	30✔
183	error = (value(times_[i]) - blackVols_[i]);	27✔
184	squaredError += error * error * weights_[i];	27✔
185	}
186	return std::sqrt(n*squaredError/(n-1));	3✔
187	}
188
189	Real AbcdCalibration::maxError() const {	×
190	Real error, maxError = QL_MIN_REAL;	×
191	for (Size i=0; i<times_.size() ; i++) {	×
192	error = std::fabs(value(times_[i]) - blackVols_[i]);	×
193	maxError = std::max(maxError, error);	×
194	}
195	return maxError;	×
196	}
197
198	// calculate weighted differences
199	Array AbcdCalibration::errors() const {	17✔
200	Array results(times_.size());	17✔
201	for (Size i=0; i<times_.size() ; i++) {	170✔
202	results[i] = (value(times_[i]) - blackVols_[i])* std::sqrt(weights_[i]);	153✔
203	}
204	return results;	17✔
205	}
206
207	EndCriteria::Type AbcdCalibration::endCriteria() const{	1✔
208	return abcdEndCriteria_;	1✔
209	}
210
211	}

lballabio / QuantLib / 30255006850

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