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/* -*- mode: c++; tab-width: 4; indent-tabs-mode: nil; c-basic-offset: 4 -*- */
/*
Copyright (C) 2006 Ferdinando Ametrano
Copyright (C) 2006 Cristina Duminuco
Copyright (C) 2005, 2006 Klaus Spanderen
Copyright (C) 2007 Giorgio Facchinetti
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/termstructures/volatility/abcdcalibration.hpp>
#include <ql/math/optimization/method.hpp>
#include <ql/math/optimization/constraint.hpp>
#include <ql/math/optimization/levenbergmarquardt.hpp>
#include <ql/pricingengines/blackformula.hpp>
#include <ql/termstructures/volatility/abcd.hpp>
#include <ql/math/distributions/normaldistribution.hpp>
#include <ql/math/interpolations/abcdinterpolation.hpp>
namespace QuantLib {
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,
const boost::shared_ptr<EndCriteria>& endCriteria,
const boost::shared_ptr<OptimizationMethod>& optMethod)
: aIsFixed_(aIsFixed), bIsFixed_(bIsFixed),
cIsFixed_(cIsFixed), dIsFixed_(dIsFixed),
a_(a), b_(b), c_(c), d_(d),
abcdEndCriteria_(EndCriteria::None), endCriteria_(endCriteria),
optMethod_(optMethod), weights_(blackVols.size(), 1.0/blackVols.size()),
vegaWeighted_(vegaWeighted),
times_(t), blackVols_(blackVols) {
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_)
optMethod_ = boost::shared_ptr<OptimizationMethod>(new
LevenbergMarquardt(1e-8, 1e-8, 1e-8));
//method_ = boost::shared_ptr<OptimizationMethod>(new
// Simplex(0.01));
if (!endCriteria_)
//endCriteria_ = boost::shared_ptr<EndCriteria>(new
// EndCriteria(60000, 100, 1e-8, 1e-8, 1e-8));
endCriteria_ = boost::shared_ptr<EndCriteria>(new
EndCriteria(1000, 100, 1.0e-8, 0.3e-4, 0.3e-4)); // Why 0.3e-4 ?
}
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_ = boost::shared_ptr<ParametersTransformation>(new
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);
a_ = result[0];
b_ = result[1];
c_ = result[2];
d_ = result[3];
validateAbcdParameters(a_, b_, c_, d_);
}
}
Real AbcdCalibration::a() const {
return a_;
}
Real AbcdCalibration::b() const {
return b_;
}
Real AbcdCalibration::c() const {
return c_;
}
Real AbcdCalibration::d() const {
return d_;
}
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
Disposable<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_;
}
}
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