swapforwardmappings.cpp

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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 Marco Bianchetti
Copyright (C) 2006 Giorgio Facchinetti
Copyright (C) 2006, 2008 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
<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/models/marketmodels/swapforwardmappings.hpp>
#include <ql/models/marketmodels/curvestate.hpp>
#include <ql/models/marketmodels/marketmodel.hpp>
#include <ql/models/marketmodels/evolutiondescription.hpp>
#include <ql/models/marketmodels/curvestates/lmmcurvestate.hpp>
#include <vector>
 
namespace QuantLib {
 
 
    Real SwapForwardMappings::annuity(const CurveState& cs,
                                      Size startIndex,
                                      Size endIndex,
                                      Size numeraireIndex)
    {
        Real annuity = 0.0;
        for (Size i=startIndex; i<endIndex; ++i)
            annuity += cs.rateTaus()[i]*cs.discountRatio(i+1, numeraireIndex);
        return annuity;
    }
 
    // compute derivative of swap-rate to underlying forward rate
    Real SwapForwardMappings::swapDerivative(const CurveState& cs,
                                             Size startIndex,
                                             Size endIndex,
                                             Size forwardIndex)
    {
        if (forwardIndex < startIndex)
            return 0.0;
        if (forwardIndex >= endIndex)
            return 0.0;
 
        Real numerator = cs.discountRatio(startIndex, endIndex)-1;
        Real swapAnnuity = annuity(cs, startIndex, endIndex,endIndex);
 
        Real ratio = cs.rateTaus()[forwardIndex] /
            (1 + cs.rateTaus()[forwardIndex] * cs.forwardRate(forwardIndex));
 
        Real part1 = ratio*(numerator+1)/swapAnnuity;
        Real part2 = numerator/(swapAnnuity*swapAnnuity);
 
        if (forwardIndex >=1)
            part2 *= ratio* annuity(cs, startIndex, forwardIndex, endIndex);
        else 
            part2 = 0.0;
 
        return part1-part2;
    }
 
    Matrix SwapForwardMappings::coterminalSwapForwardJacobian(const CurveState& cs)
    {
        Size n = cs.numberOfRates();
        const std::vector<Rate>& f = cs.forwardRates();
        const std::vector<Time>& tau = cs.rateTaus();
 
        // coterminal floating leg values
        std::vector<Real> a(n);
        for (Size k=0; k<n; ++k)
            a[k] = cs.discountRatio(k,n)-1.0;
        //p[k]-p[n];
 
        Matrix jacobian = Matrix(n, n, 0.0);
        for (Size i=0; i<n; ++i) {     // i = swap rate index
            for (Size j=i; j<n; ++j) { // j = forward rate index
                Real bi = cs.coterminalSwapAnnuity(n,i);
                Real bj = cs.coterminalSwapAnnuity(n,j);
                jacobian[i][j] =
                    //   p[j+1]*tau[j]/b[i] +
                    tau[j]/cs.coterminalSwapAnnuity(j+1,i) +
                    // tau[j]/(1.0+f[j]*tau[j]) *
                    tau[j]/(1.0+f[j]*tau[j]) *
                    //    (-a[j]*b[i]+a[i]*b[j])/(b[i]*b[i]);
                    (-a[j]*bi+a[i]*bj)/(bi*bi);
 
            }
        }
        return jacobian;
    }
 
    Matrix SwapForwardMappings::coterminalSwapZedMatrix(const CurveState& cs,
                                                        const Spread displacement) {
            Size n = cs.numberOfRates();
            Matrix zMatrix = coterminalSwapForwardJacobian(cs);
            const std::vector<Rate>& f = cs.forwardRates();
            const std::vector<Rate>& sr = cs.coterminalSwapRates();
            for (Size i=0; i<n; ++i)
                for (Size j=i; j<n; ++j)
                    zMatrix[i][j] *= (f[j]+displacement)/(sr[i]+displacement);
            return zMatrix;
    }
 
 
    Matrix SwapForwardMappings::coinitialSwapForwardJacobian(const CurveState& cs)
    {
        Size n = cs.numberOfRates();
 
        Matrix jacobian = Matrix(n, n, 0.0);
        for (Size i=0; i<n; ++i)      // i = swap rate index
            for (Size j=0; j<n; ++j)  // j = forward rate index
                jacobian[i][j] =swapDerivative(cs, 0, i+1, j);
 
        return jacobian;
    }
 
    Matrix SwapForwardMappings::cmSwapForwardJacobian(const CurveState& cs,
                                                      const Size spanningForwards)
    {
        Size n = cs.numberOfRates();
 
        Matrix jacobian = Matrix(n, n, 0.0);
        for (Size i=0; i<n; ++i)      // i = swap rate index
            for (Size j=0; j<n; ++j)  // j = forward rate index
                jacobian[i][j] =swapDerivative(cs, i, std::min(n,i+spanningForwards), j);
 
        return jacobian;
    }
 
    Matrix SwapForwardMappings::coinitialSwapZedMatrix(const CurveState& cs,
                                                       const Spread displacement)
    {
        Size n = cs.numberOfRates();
        Matrix zMatrix = coinitialSwapForwardJacobian(cs);
        const std::vector<Rate>& f = cs.forwardRates();
        std::vector<Rate> sr(n);
 
        for (Size i=0; i<n; ++i)
            sr[i] = cs.cmSwapRate(0,i+1);
 
        for (Size i=0; i<n; ++i)
            for (Size j=i; j<n; ++j)
                zMatrix[i][j] *= (f[j]+displacement)/(sr[i]+displacement);
        return zMatrix;
    }
 
    Matrix SwapForwardMappings::cmSwapZedMatrix(const CurveState& cs,
                                                const Size spanningForwards,
                                                const Spread displacement)
    {
        Size n = cs.numberOfRates();
        Matrix zMatrix = cmSwapForwardJacobian(cs,spanningForwards);
        const std::vector<Rate>& f = cs.forwardRates();
        std::vector<Rate> sr(n);
 
        for (Size i=0; i<n; ++i)
            sr[i] = cs.cmSwapRate(i,spanningForwards);
 
        for (Size i=0; i<n; ++i)
            for (Size j=i; j<n; ++j)
                zMatrix[i][j] *= (f[j]+displacement)/(sr[i]+displacement);
        return zMatrix;
    }
 
    Real SwapForwardMappings::swaptionImpliedVolatility(const MarketModel& volStructure,
                                                        Size startIndex,
                                                        Size endIndex)
    {
          QL_REQUIRE(startIndex < endIndex, "start index must be before end index in swaptionImpliedVolatility");
 
          LMMCurveState cs(volStructure.evolution().rateTimes());
          cs.setOnForwardRates(volStructure.initialRates());
          Real displacement = volStructure.displacements()[0];
 
          Matrix cmsZed(cmSwapZedMatrix(cs, endIndex-startIndex,displacement));
 
          Real variance=0.0;
 
          Size index=0;
 
          const EvolutionDescription& evolution(volStructure.evolution());
          Size factors = volStructure.numberOfFactors();
 
          while (index < evolution.numberOfSteps() && startIndex >= evolution.firstAliveRate()[index] )
          {
              const Matrix& thisPseudo = volStructure.pseudoRoot(index);
              Real thisVariance =0.0;
              
              for (Size f=0; f < factors; ++f)
              {
                  Real sum=0.0;
 
                  for (Size j=startIndex; j < endIndex;++j)
                  {
                      sum += cmsZed[startIndex][j]*thisPseudo[j][f];
 
                  }
                  thisVariance += sum*sum;
 
              }
              variance += thisVariance;
              ++index;
 
          }
 
          Real expiry = evolution.rateTimes()[startIndex];
          return std::sqrt(variance/expiry);
 
    }
 
}