capletcoterminalswaptioncalibration.cpp

有很多的函数库

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

/*
 Copyright (C) 2007 Ferdinando Ametrano
 Copyright (C) 2007 Mark Joshi

 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
 <[e-mail]>. 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/models/marketmodels/models/capletcoterminalswaptioncalibration.hpp>
#include <ql/models/marketmodels/models/piecewiseconstantvariance.hpp>
#include <ql/models/marketmodels/models/pseudorootfacade.hpp>
#include <ql/models/marketmodels/models/cotswaptofwdadapter.hpp>
#include <ql/models/marketmodels/swapforwardmappings.hpp>
#include <ql/models/marketmodels/marketmodel.hpp>
#include <ql/math/matrixutilities/pseudosqrt.hpp>

namespace QuantLib {

    CapletCoterminalSwaptionCalibration::CapletCoterminalSwaptionCalibration(
                            const EvolutionDescription& evolution,
                            const boost::shared_ptr<PiecewiseConstantCorrelation>& corr,
                            const std::vector<boost::shared_ptr<
                                        PiecewiseConstantVariance> >&
                                                displacedSwapVariances,
                            const std::vector<Volatility>& mktCapletVols,
                            const boost::shared_ptr<CurveState>& cs,
                            Spread displacement)
    : evolution_(evolution),  corr_(corr),
      displacedSwapVariances_(displacedSwapVariances),
      mktCapletVols_(mktCapletVols),
      cs_(cs), displacement_(displacement), calibrated_(false) {}

    bool CapletCoterminalSwaptionCalibration::calibrationFunction(
                            const EvolutionDescription& evolution,
                            const PiecewiseConstantCorrelation& corr,
                            const std::vector<boost::shared_ptr<
                                PiecewiseConstantVariance> >&
                                    displacedSwapVariances,
                            const std::vector<Volatility>& capletVols,
                            const CurveState& cs,
                            const Spread displacement,
                            const Size numberOfFactors,
                            const std::vector<Real>& alpha,
                            const bool lowestRoot,
                            const bool useFullAprox,
                            std::vector<Matrix>& swapCovariancePseudoRoots,
                            Size& negativeDiscriminants) {

        negativeDiscriminants = 0;
        QL_REQUIRE(evolution.evolutionTimes()==corr.times(),
                   "evolutionTimes not equal to correlation times");

        Size numberOfRates = evolution.numberOfRates();
        QL_REQUIRE(numberOfFactors<=numberOfRates,
                   "number of factors (" << numberOfFactors <<
                   ") cannot be greater than numberOfRates (" <<
                   numberOfRates << ")");
        QL_REQUIRE(numberOfFactors>0,
                   "number of factors (" << numberOfFactors <<
                   ") must be greater than zero");

        QL_REQUIRE(numberOfRates==displacedSwapVariances.size(),
                   "mismatch between number of rates (" << numberOfRates <<
                   ") and displacedSwapVariances");

        QL_REQUIRE(numberOfRates==capletVols.size(),
                   "mismatch between number of rates (" << numberOfRates <<
                   ") and capletVols (" << capletVols.size() <<
                   ")");

        const std::vector<Time>& rateTimes = evolution.rateTimes();
        QL_REQUIRE(rateTimes==cs.rateTimes(),
                   "mismatch between EvolutionDescriptionand CurveState rate times ");
        QL_REQUIRE(numberOfRates==cs.numberOfRates(),
                   "mismatch between number of rates (" << numberOfRates <<
                   ") and CurveState");

        QL_REQUIRE(numberOfRates==alpha.size(),
                   "mismatch between number of rates (" << numberOfRates <<
                   ") and alphas (" << alpha.size() << ")");

        const std::vector<Time>& evolutionTimes = evolution.evolutionTimes();
        QL_REQUIRE(std::vector<Time>(rateTimes.begin(), rateTimes.end()-1)==evolutionTimes,
                   "mismatch between evolutionTimes and rateTimes");

        Real extraMultiplier =useFullAprox ? 1.0 : 0.0;

        Size numberOfSteps = evolution.numberOfSteps();

        // factor reduction
        std::vector<Matrix> corrPseudo(corr.times().size());
        for (Size i=0; i<corrPseudo.size(); ++i)
            corrPseudo[i] = rankReducedSqrt(corr.correlation(i),
                                            numberOfFactors, 1.0,
                                            SalvagingAlgorithm::None);

        // do alpha part
        // first modify variances to take account of alpha
        // then rescale so total variance is unchanged
        Matrix swapTimeInhomogeneousVariances(numberOfSteps, numberOfRates, 0.0);
        std::vector<Real> originalVariances(numberOfRates, 0.0);
        std::vector<Real> modifiedVariances(numberOfRates, 0.0);
        for (Size i=0; i<numberOfSteps; ++i) {
            Real s = (i==0 ? 0.0 : evolutionTimes[i-1]);
            for (Size j=i; j<numberOfRates; ++j) {
                const std::vector<Real>& var = displacedSwapVariances[j]->variances();
                originalVariances[j]+=var[i];
                swapTimeInhomogeneousVariances[i][j] = var[i]/
                    ((1.0+alpha[j]*s)*(1.0+alpha[j]*s));
                modifiedVariances[j]+=swapTimeInhomogeneousVariances[i][j];
            }
        }

        for (Size i=0; i<numberOfSteps; ++i)
            for (Size j=i; j<numberOfRates; ++j)
                swapTimeInhomogeneousVariances[i][j] *= originalVariances[j]/
                                                        modifiedVariances[j];

        Matrix zedMatrix =
            SwapForwardMappings::coterminalSwapZedMatrix(cs, displacement);
        Matrix invertedZedMatrix = inverse(zedMatrix);


        // compute swap covariances for caplet approximation formula
        // without taking into account A and B
        std::vector<Matrix> CovarianceSwapPseudos(numberOfSteps);
        std::vector<Matrix> CovarianceSwapCovs(numberOfSteps); // this is total cov
        std::vector<Matrix> CovarianceSwapMarginalCovs(numberOfSteps); // this is cov for one step

        for (Size i=0; i<numberOfSteps; ++i) {
            CovarianceSwapPseudos[i] =  corrPseudo[i];
            for (Size j=0; j<numberOfRates; ++j)
                for (Size k=0; k < CovarianceSwapPseudos[i].columns();  ++k)
                    CovarianceSwapPseudos[i][j][k] *=
                            sqrt(swapTimeInhomogeneousVariances[i][j]);

            CovarianceSwapMarginalCovs[i] = CovarianceSwapPseudos[i] *
                                    transpose(CovarianceSwapPseudos[i]);

            CovarianceSwapCovs[i] = CovarianceSwapMarginalCovs[i];
            if (i>0)
                CovarianceSwapCovs[i]+= CovarianceSwapCovs[i-1];
        }

        // compute partial variances and covariances which will take A and B coefficients
        //const std::vector<Time>& taus = evolution.rateTaus();
        std::vector<Real> totVariance(numberOfRates, 0.0);
        std::vector<Real> almostTotVariance(numberOfRates, 0.0);
        std::vector<Real> almostTotCovariance(numberOfRates, 0.0);
        std::vector<Real> leftCovariance(numberOfRates, 0.0);
        for (Size i=0; i<numberOfRates; ++i) {
            for (Size j=0; j<=i; ++j)
                totVariance[i] += displacedSwapVariances[i]->variances()[j];
            for (Integer j=0; j<=static_cast<Integer>(i)-1; ++j)
                almostTotVariance[i] += swapTimeInhomogeneousVariances[j][i];
            Integer j=0;
            for (; j<=static_cast<Integer>(i)-2; ++j) {
                const Matrix& thisPseudo = corrPseudo[j];
                Real correlation = 0.0;
                for (Size k=0; k<numberOfFactors; ++k)
                    correlation += thisPseudo[i-1][k]*thisPseudo[i][k];
                almostTotCovariance[i] += correlation *
                    sqrt(swapTimeInhomogeneousVariances[j][i] *
                    swapTimeInhomogeneousVariances[j][i-1]);
            }
            if (i>0) {
                const Matrix& thisPseudo = corrPseudo[j];
                Real correlation = 0.0;
                for (Size k=0; k<numberOfFactors; ++k)
                    correlation += thisPseudo[i-1][k]*thisPseudo[i][k];
                leftCovariance[i] = correlation *
                    sqrt(swapTimeInhomogeneousVariances[j][i] *
                    swapTimeInhomogeneousVariances[j][i-1]);
            }
        }


        // multiplier up to rate reset previous time
        // the first element is not used
        std::vector<Real> a(numberOfSteps, 1.0);
        // multiplier afterward
        std::vector<Real> b(numberOfSteps);

        b[0]=displacedSwapVariances[0]->variances()[0]/swapTimeInhomogeneousVariances[0][0];
        // main loop where work is done
        for (Size i=1; i<numberOfSteps; ++i) {
            Integer j=0;
            // up date variances to take account of last a and b computed
            for (; j <= static_cast<Integer>(i)-2; j++)
                swapTimeInhomogeneousVariances[j][i-1]*= a[i-1]*a[i-1];
            swapTimeInhomogeneousVariances[j][i-1]*= b[i-1]*b[i-1];

            Real w0 = invertedZedMatrix[i-1][i-1];
            Real w1 = -invertedZedMatrix[i-1][i];
            Real v1t1 = capletVols[i-1]*capletVols[i-1]*rateTimes[i-1];