public LiborForwardModel(LiborForwardModelProcess process,
                                 LmVolatilityModel volaModel,
                                 LmCorrelationModel corrModel)
            : base(volaModel.parameters().Count + corrModel.parameters().Count)
        {
            f_             = new InitializedList <double>(process.size());
            accrualPeriod_ = new InitializedList <double>(process.size());
            covarProxy_    = new LfmCovarianceProxy(volaModel, corrModel);
            process_       = process;

            int k = volaModel.parameters().Count;

            for (int j = 0; j < k; j++)
            {
                arguments_[j] = volaModel.parameters()[j];
            }
            for (int j = 0; j < corrModel.parameters().Count; j++)
            {
                arguments_[j + k] = corrModel.parameters()[j];
            }

            for (int i = 0; i < process.size(); ++i)
            {
                accrualPeriod_[i] = process.accrualEndTimes()[i]
                                    - process.accrualStartTimes()[i];
                f_[i] = 1.0 / (1.0 + accrualPeriod_[i] * process_.initialValues()[i]);
            }
        }
Example #2
0
 public LfmHullWhiteParameterization(
     LiborForwardModelProcess process,
     OptionletVolatilityStructure capletVol)
     : this(process, capletVol, new Matrix(), 1)
 {
 }
Example #3
0
        public LfmHullWhiteParameterization(
            LiborForwardModelProcess process,
            OptionletVolatilityStructure capletVol,
            Matrix correlation, int factors)
            : base(process.size(), factors)
        {
            diffusion_   = new Matrix(size_ - 1, factors_);
            fixingTimes_ = process.fixingTimes();

            Matrix sqrtCorr = new Matrix(size_ - 1, factors_, 1.0);

            if (correlation.empty())
            {
                Utils.QL_REQUIRE(factors_ == 1, () => "correlation matrix must be given for multi factor models");
            }
            else
            {
                Utils.QL_REQUIRE(correlation.rows() == size_ - 1 &&
                                 correlation.rows() == correlation.columns(), () => "wrong dimesion of the correlation matrix");

                Utils.QL_REQUIRE(factors_ <= size_ - 1, () => "too many factors for given LFM process");

                Matrix tmpSqrtCorr = MatrixUtilitites.pseudoSqrt(correlation,
                                                                 MatrixUtilitites.SalvagingAlgorithm.Spectral);

                // reduce to n factor model
                // "Reconstructing a valid correlation matrix from invalid data"
                // (<http://www.quarchome.org/correlationmatrix.pdf>)
                for (int i = 0; i < size_ - 1; ++i)
                {
                    double d = 0;
                    tmpSqrtCorr.row(i).GetRange(0, factors_).ForEach((ii, vv) => d += vv * tmpSqrtCorr.row(i)[ii]);
                    for (int k = 0; k < factors_; ++k)
                    {
                        sqrtCorr[i, k] = tmpSqrtCorr.row(i).GetRange(0, factors_)[k] / Math.Sqrt(d);
                    }
                }
            }
            List <double> lambda      = new List <double>();
            DayCounter    dayCounter  = process.index().dayCounter();
            List <double> fixingTimes = process.fixingTimes();
            List <Date>   fixingDates = process.fixingDates();

            for (int i = 1; i < size_; ++i)
            {
                double cumVar = 0.0;
                for (int j = 1; j < i; ++j)
                {
                    cumVar += lambda[i - j - 1] * lambda[i - j - 1]
                              * (fixingTimes[j + 1] - fixingTimes[j]);
                }

                double vol = capletVol.volatility(fixingDates[i], 0.0, false);
                double var = vol * vol
                             * capletVol.dayCounter().yearFraction(fixingDates[0],
                                                                   fixingDates[i]);
                lambda.Add(Math.Sqrt((var - cumVar)
                                     / (fixingTimes[1] - fixingTimes[0])));
                for (int q = 0; q < factors_; ++q)
                {
                    diffusion_[i - 1, q] = sqrtCorr[i - 1, q] * lambda.Last();
                }
            }
            covariance_ = diffusion_ * Matrix.transpose(diffusion_);
        }