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lmmdriftcalculator.cpp

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

/*
 Copyright (C) 2007 Ferdinando Ametrano
 Copyright (C) 2006 Marco Bianchetti
 Copyright (C) 2006 Silvia Frasson
 Copyright (C) 2006 Mario Pucci
 Copyright (C) 2006 StatPro Italia srl

 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/driftcomputation/lmmdriftcalculator.hpp>
#include <ql/models/marketmodels/curvestates/lmmcurvestate.hpp>
#include <ql/models/marketmodels/duffsdeviceinnerproduct.hpp>

namespace QuantLib {

    LMMDriftCalculator::LMMDriftCalculator(
                                    const Matrix& pseudo,
                                    const std::vector<Spread>& displacements,
                                    const std::vector<Time>& taus,
                                    Size numeraire,
                                    Size alive)
    : numberOfRates_(taus.size()), numberOfFactors_(pseudo.columns()),
      isFullFactor_(numberOfFactors_==numberOfRates_ ? true : false),
      numeraire_(numeraire), alive_(alive),
      displacements_(displacements), oneOverTaus_(taus.size()),
      pseudo_(pseudo), tmp_(taus.size(), 0.0),
      e_(pseudo_.columns(), pseudo_.rows(), 0.0),
      downs_(taus.size()), ups_(taus.size()) {

        // Check requirements
        QL_REQUIRE(numberOfRates_>0, "Dim out of range");
        QL_REQUIRE(displacements.size() == numberOfRates_,
            "Displacements out of range");
        QL_REQUIRE(pseudo.rows()==numberOfRates_,
            "pseudo.rows() not consistent with dim");
        QL_REQUIRE(pseudo.columns()>0 && pseudo.columns()<=numberOfRates_,
            "pseudo.rows() not consistent with pseudo.columns()");
        QL_REQUIRE(alive<numberOfRates_, "Alive out of bounds");
        QL_REQUIRE(numeraire_<=numberOfRates_, "Numeraire larger than dim");
        QL_REQUIRE(numeraire_>=alive, "Numeraire smaller than alive");

        // Precompute 1/taus
        for (Size i=0; i<taus.size(); ++i)
            oneOverTaus_[i] = 1.0/taus[i];

        // Compute covariance matrix from pseudoroot
        const Disposable<Matrix> pT = transpose(pseudo_);
        C_ = pseudo_*pT;

        // Compute lower and upper extrema for (non reduced) drift calculation
        for (Size i=alive_; i<numberOfRates_; ++i) {
            downs_[i] = std::min(i+1, numeraire_);
            ups_[i]   = std::max(i+1, numeraire_);
        }
    }

00071     void LMMDriftCalculator::compute(const LMMCurveState& cs,
                                     std::vector<Real>& drifts) const {
        compute(cs.forwardRates(), drifts);
    }

    void LMMDriftCalculator::compute(const std::vector<Rate>& fwds,
                                     std::vector<Real>& drifts) const {
        #if defined(QL_EXTRA_SAFETY_CHECKS)
            QL_REQUIRE(fwds.size()==numberOfRates_, "numberOfRates <> dim");
            QL_REQUIRE(drifts.size()==numberOfRates_, "drifts.size() <> dim");
        #endif

        if (isFullFactor_)
            computePlain(fwds, drifts);
        else
            computeReduced(fwds, drifts);
    }

00089     void LMMDriftCalculator::computePlain(const LMMCurveState& cs,
                                          std::vector<Real>& drifts) const {
        computePlain(cs.forwardRates(), drifts);
    }

    void LMMDriftCalculator::computePlain(const std::vector<Rate>& forwards,
                                          std::vector<Real>& drifts) const {

        // Compute drifts without factor reduction,
        // using directly the covariance matrix.

        // Precompute forwards factor
        Size i;
        for(i=alive_; i<numberOfRates_; ++i)
            tmp_[i] = (forwards[i]+displacements_[i]) /
                      (oneOverTaus_[i]+forwards[i]);

        // Compute drifts
        for (i=alive_; i<numberOfRates_; ++i) {
            drifts[i] = std::inner_product(tmp_.begin()+downs_[i],
                                           tmp_.begin()+ups_[i],
                                           C_.row_begin(i)+downs_[i], 0.0);
            if (numeraire_>i+1)
                drifts[i] = -drifts[i];
        }
    }

00116     void LMMDriftCalculator::computeReduced(const LMMCurveState& cs,
                                            std::vector<Real>& drifts) const {
        computeReduced(cs.forwardRates(), drifts);
    }

    void LMMDriftCalculator::computeReduced(const std::vector<Rate>& forwards,
                                            std::vector<Real>& drifts) const {

        // Compute drifts with factor reduction,
        // using the pseudo square root of the covariance matrix.

        // Precompute forwards factor
        for (Size i=alive_; i<numberOfRates_; ++i)
            tmp_[i] = (forwards[i]+displacements_[i]) /
                (oneOverTaus_[i]+forwards[i]);

        // Enforce initialization
        for (Size r=0; r<numberOfFactors_; ++r)
            e_[r][std::max(0,static_cast<Integer>(numeraire_)-1)] = 0.0;

        // Now compute drifts: take the numeraire P_N (numeraire_=N)
        // as the reference point, divide the summation into 3 steps,
        // et impera:

        // 1st step: the drift corresponding to the numeraire P_N is zero.
        // (if N=0 no drift is null, if N=numberOfRates_ the last drift is null).
        if (numeraire_>0) drifts[numeraire_-1] = 0.0;

        // 2nd step: then, move backward from N-2 (included) back to
        // alive (included) (if N=0 jumps to 3rd step, if N=numberOfRates_ the
        // e_[r][N-1] are correctly initialized):

        for (Integer i=static_cast<Integer>(numeraire_)-2;
             i>=static_cast<Integer>(alive_); --i) {
            drifts[i] = 0.0;
            for (Size r=0; r<numberOfFactors_; ++r) {
                e_[r][i] = e_[r][i+1] + tmp_[i+1] * pseudo_[i+1][r];
                drifts[i] -= e_[r][i]*pseudo_[i][r];
            }

            /*
            Matrix::column_iterator p1 = e_.column_begin(i);
            Matrix::column_iterator end = e_.column_end(i);
            Matrix::const_column_iterator p2 = e_.column_begin(i+1);
            Matrix::const_row_iterator q1 = pseudo_.row_begin(i);
            Matrix::const_row_iterator q2 = pseudo_.row_begin(i+1);
            Real x = tmp_[i+1];
            while (p1 != end) {
                *p1 = *p2 + x*(*q2);
                drifts[i] -= *p1*(*q1);
                ++p1; ++p2; ++q1; ++q2;
            }
            */
        }

        // 3rd step: now, move forward from N (included) up to n (excluded)
        // (if N=0 this is the only relevant computation):
        for (Size i=numeraire_; i<numberOfRates_; ++i) {
            drifts[i] = 0.0;
            for (Size r=0; r<numberOfFactors_; ++r) {
                if (i==0)
                    e_[r][i] = tmp_[i] * pseudo_[i][r];
                else
                    e_[r][i] = e_[r][i-1] + tmp_[i] * pseudo_[i][r];
                drifts[i] += e_[r][i]*pseudo_[i][r];
            }
        }
    }

}

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