Exemplo n.º 1
0
        protected override void generateArguments()
        {
            double rho = arguments_[0].value(0.0);

            for (int i = 0; i < size_; ++i)
            {
                for (int j = i; j < size_; ++j)
                {
                    corrMatrix_[i, j] = corrMatrix_[j, i] = Math.Exp(-rho * Math.Abs((double)i - (double)j));
                }
            }
            pseudoSqrt_ = MatrixUtilitites.pseudoSqrt(corrMatrix_, MatrixUtilitites.SalvagingAlgorithm.Spectral);
        }
Exemplo n.º 2
0
        public StochasticProcessArray(List <StochasticProcess1D> processes, Matrix correlation)
        {
            processes_       = processes;
            sqrtCorrelation_ = MatrixUtilitites.pseudoSqrt(correlation, MatrixUtilitites.SalvagingAlgorithm.Spectral);

            Utils.QL_REQUIRE(processes.Count != 0, () => "no processes given");
            Utils.QL_REQUIRE(correlation.rows() == processes.Count, () =>
                             "mismatch between number of processes and size of correlation matrix");
            for (int i = 0; i < processes_.Count; i++)
            {
                processes_[i].registerWith(update);
            }
        }
Exemplo n.º 3
0
        protected override void generateArguments()
        {
            double rho  = arguments_[0].value(0.0);
            double beta = arguments_[1].value(0.0);

            for (int i = 0; i < size_; ++i)
            {
                for (int j = i; j < size_; ++j)
                {
                    corrMatrix_[i, j]             = corrMatrix_[j, i]
                                                  = rho + (1 - rho) * Math.Exp(-beta * Math.Abs((double)i - (double)j));
                }
            }

            pseudoSqrt_ = MatrixUtilitites.rankReducedSqrt(corrMatrix_, factors_, 1.0, MatrixUtilitites.SalvagingAlgorithm.None);
            corrMatrix_ = pseudoSqrt_ * Matrix.transpose(pseudoSqrt_);
        }
Exemplo n.º 4
0
        public StochasticProcessArray(List <StochasticProcess1D> processes, Matrix correlation)
        {
            processes_       = processes;
            sqrtCorrelation_ = MatrixUtilitites.pseudoSqrt(correlation, MatrixUtilitites.SalvagingAlgorithm.Spectral);

            if (processes.Count == 0)
            {
                throw new ApplicationException("no processes given");
            }
            if (correlation.rows() != processes.Count)
            {
                throw new ApplicationException("mismatch between number of processes and size of correlation matrix");
            }
            for (int i = 0; i < processes_.Count; i++)
            {
                processes_[i].registerWith(update);
            }
        }
Exemplo n.º 5
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())
            {
                if (!(factors_ == 1))
                {
                    throw new ApplicationException("correlation matrix must be given for " +
                                                   "multi factor models");
                }
            }
            else
            {
                if (!(correlation.rows() == size_ - 1 &&
                      correlation.rows() == correlation.columns()))
                {
                    throw new ApplicationException("wrong dimesion of the correlation matrix");
                }

                if (!(factors_ <= size_ - 1))
                {
                    throw new ApplicationException("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]);
                    //sqrtCorr.row(i).GetRange(0, factors_).ForEach((ii, vv) => sqrtCorr.row(i)[ii] = tmpSqrtCorr.row(i).GetRange(0, factors_)[ii] / Math.Sqrt(d));
                    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_);
        }
Exemplo n.º 6
0
 public virtual Matrix pseudoSqrt(double t, Vector x = null)
 {
     return(MatrixUtilitites.pseudoSqrt(this.correlation(t, x),
                                        MatrixUtilitites.SalvagingAlgorithm.Spectral));
 }