lmmnormaldriftcalculator.cpp

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/* -*- mode: c++; tab-width: 4; indent-tabs-mode: nil; c-basic-offset: 4 -*- */
 
/*
  Copyright (C) 2007 Giorgio Facchinetti
  Copyright (C) 2007 Chiara Fornarola
 
 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/lmmnormaldriftcalculator.hpp>
 
namespace QuantLib {
 
    LMMNormalDriftCalculator::LMMNormalDriftCalculator(const Matrix& pseudo,
                                                       const std::vector<Time>& taus,
                                                       Size numeraire,
                                                       Size alive)
    : numberOfRates_(taus.size()), numberOfFactors_(pseudo.columns()),
      isFullFactor_(numberOfFactors_ == numberOfRates_), numeraire_(numeraire), alive_(alive),
      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(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
        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_);
        }
    }
 
    void LMMNormalDriftCalculator::compute(const LMMCurveState& cs,
                                           std::vector<Real>& drifts) const {
        compute(cs.forwardRates(), drifts);
    }
 
    void LMMNormalDriftCalculator::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);
    }
 
    void LMMNormalDriftCalculator::computePlain(const LMMCurveState& cs,
                                                std::vector<Real>& drifts) const {
        computePlain(cs.forwardRates(), drifts);
    }
 
    void LMMNormalDriftCalculator::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] = 1.0/(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], Real(0.0));
            if (numeraire_>i+1)
                drifts[i] = -drifts[i];
        }
    }
 
    void LMMNormalDriftCalculator::computeReduced(const LMMCurveState& cs,
                                                std::vector<Real>& drifts) const {
        computeReduced(cs.forwardRates(), drifts);
    }
 
    void LMMNormalDriftCalculator::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] = 1.0/(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];
            }
 
        }
 
        // 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];
            }
        }
    }
 
}