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]); } }
public LfmHullWhiteParameterization( LiborForwardModelProcess process, OptionletVolatilityStructure capletVol) : this(process, capletVol, new Matrix(), 1) { }
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_); }