/// <summary>
/// Constructor for the Pelsser Calibration Problem based on caps matrices.
/// </summary>
/// <param name="project">The project where this calibration is being done.</param>
/// <param name="caplet">The Pelsser Caplet object to use.</param>
/// <param name="capMaturity">Vector of cap maturities.</param>
/// <param name="fwd">Forward with the deltaK step.</param>
/// <param name="capK">The caplet strike vector (columns).</param>
/// <param name="deltaK">Interval between caplets expressed in year.</param>
/// <param name="capMat">The caplet maturities.</param>
/// <param name="blackCaps">A Blacks caps matrix to use.</param>
internal PelsserCappletOptimizationProblem(ProjectROV project, Caplet caplet, Vector capMaturity, Vector fwd, Vector capK, double deltaK, Vector capMat, Matrix blackCaps)
{
this.project = project;
this.caplet = caplet;
this.capMaturity = capMaturity;
this.fwd = fwd;
this.capK = capK;
this.deltaK = deltaK;
this.capMat = capMat;
this.blackCaps = blackCaps;
Console.WriteLine("Pelsser Caps problem on " + this.capMaturity.Length + " x " + this.capK.Length + " elements");
}
/// <summary>
/// Attempts a calibration through <see cref="PelsserCappletOptimizationProblem"/>
/// using caps matrices.
/// </summary>
/// <param name="data">The data to be used in order to perform the calibration.</param>
/// <param name="settings">The parameter is not used.</param>
/// <param name="controller">The controller which may be used to cancel the process.</param>
/// <returns>The results of the calibration.</returns>
public EstimationResult Estimate(List <object> data, IEstimationSettings settings = null, IController controller = null, Dictionary <string, object> properties = null)
{
InterestRateMarketData dataset = data[0] as InterestRateMarketData;
MatrixMarketData normalVol = null;
if (data.Count > 1)
{
normalVol = (MatrixMarketData)data[1];
}
EstimationResult result;
if ((dataset.ZRMarket == null) || (dataset.CapVolatility == null))
{
result = new EstimationResult();
result.ErrorMessage = "Not enough data to calibrate.\n" +
"The estimator needs a ZRMarket and a CapVolatility " +
"defined inside InterestRateMarketData";
return(result);
}
// Backup the dates
DateTime effectiveDate = DateTime.Now.Date;
DateTime valuationDate = DateTime.Now.Date;
if (Document.ActiveDocument != null)
{
effectiveDate = Document.ActiveDocument.ContractDate;
valuationDate = Document.ActiveDocument.SimulationStartDate;
}
// Creates the Context.
Document doc = new Document();
ProjectROV prj = new ProjectROV(doc);
doc.Part.Add(prj);
Function zr = new PFunction(null);
zr.VarName = "zr";
// Load the zr.
double[,] zrvalue = (double[, ])ArrayHelper.Concat(dataset.ZRMarketDates.ToArray(), dataset.ZRMarket.ToArray());
zr.Expr = zrvalue;
prj.Symbols.Add(zr);
var bm = BlackModelFactory(zr);
if (bm is BachelierNormalModel)
{
(bm as BachelierNormalModel).Tenor = dataset.CapTenor;
}
double deltak = dataset.CapTenor;
Matrix capVol = normalVol != null ? normalVol.Values:dataset.CapVolatility;
Vector capMat = normalVol != null ? normalVol.RowValues: dataset.CapMaturity;
Vector capK = normalVol != null ? normalVol.ColumnValues: dataset.CapRate;
var preferences = settings as Fairmat.Calibration.CapVolatilityFiltering;
// Matrix calculated with black.
var blackCaps = new Matrix(capMat.Length, capK.Length);
for (int m = 0; m < capMat.Length; m++)
{
for (int s = 0; s < capK.Length; s++)
{
bool skip = false;
if (preferences != null)
{
if (capK[s] < preferences.MinCapRate || capK[s] > preferences.MaxCapRate ||
capMat[m] < preferences.MinCapMaturity || capMat[m] > preferences.MaxCapMaturity)
{
skip = true;
}
}
if (capVol[m, s] == 0 || skip)
{
blackCaps[m, s] = 0;
}
else
{
blackCaps[m, s] = bm.Cap(capK[s], capVol[m, s], deltak, capMat[m]);
}
}
}
if (blackCaps.IsNaN())
{
Console.WriteLine("Black caps matrix has non real values:");
Console.WriteLine(blackCaps);
throw new Exception("Cannot calculate Black caps");
}
// Maturity goes from 0 to the last item with step deltaK.
Vector maturity = new Vector((int)(1.0 + capMat[capMat.Length - 1] / deltak));
for (int l = 0; l < maturity.Length; l++)
{
maturity[l] = deltak * l;
}
Vector fwd = new Vector(maturity.Length - 1);
for (int i = 0; i < fwd.Length; i++)
{
fwd[i] = bm.Fk(maturity[i + 1], deltak);
}
// Creates a default Pelsser model.
Pelsser.SquaredGaussianModel model = new Pelsser.SquaredGaussianModel();
model.a1 = (ModelParameter)0.014;
model.sigma1 = (ModelParameter)0.001;
model.zr = (ModelParameter)"@zr";
StochasticProcessExtendible iex = new StochasticProcessExtendible(prj, model);
prj.Processes.AddProcess(iex);
prj.Parse();
DateTime t0 = DateTime.Now;
Caplet cp = new Caplet();
PelsserCappletOptimizationProblem problem = new PelsserCappletOptimizationProblem(prj, cp, maturity, fwd, capK, deltak, capMat, blackCaps);
IOptimizationAlgorithm solver = new QADE();
IOptimizationAlgorithm solver2 = new SteepestDescent();
DESettings o = new DESettings();
o.NP = 35;
o.TargetCost = 0.0025;
o.MaxIter = 10;
o.Verbosity = Math.Max(1, Engine.Verbose);
o.controller = controller;
// Parallel evaluation is not supported for this calibration.
o.Parallel = false;
o.Debug = true;
SolutionInfo solution = null;
Vector x0 = (Vector) new double[] { 0.1, 0.1 };
solution = solver.Minimize(problem, o, x0);
if (solution.errors)
{
return(new EstimationResult(solution.message));
}
o.epsilon = 10e-7;
o.h = 10e-7;
o.MaxIter = 1000;
o.Debug = true;
o.Verbosity = Math.Max(1, Engine.Verbose);
if (solution != null)
{
solution = solver2.Minimize(problem, o, solution.x);
}
else
{
solution = solver2.Minimize(problem, o, x0);
}
if (solution.errors)
{
return(new EstimationResult(solution.message));
}
Console.WriteLine(solution);
string[] names = new string[] { "alpha1", "sigma1" };
result = new EstimationResult(names, solution.x);
result.ZRX = (double[])dataset.ZRMarketDates.ToArray();
result.ZRY = (double[])dataset.ZRMarket.ToArray();
result.Objects = new object[1];
result.Objects[0] = solution.obj;
//result.Fit = solution.obj;//Uncomment in 1.6
// Restore the dates
if (Document.ActiveDocument != null)
{
Document.ActiveDocument.ContractDate = effectiveDate;
Document.ActiveDocument.SimulationStartDate = valuationDate;
}
return(result);
}
/// <summary>
/// Constructor for the Pelsser Calibration Problem based on caps matrices.
/// </summary>
/// <param name="project">The project where this calibration is being done.</param>
/// <param name="caplet">The Pelsser Caplet object to use.</param>
/// <param name="capMaturity">Vector of cap maturities.</param>
/// <param name="fwd">Forward with the deltaK step.</param>
/// <param name="capK">The caplet strike vector (columns).</param>
/// <param name="deltaK">Interval between caplets expressed in year.</param>
/// <param name="capMat">The caplet maturities.</param>
/// <param name="blackCaps">A Blacks caps matrix to use.</param>
internal PelsserCappletOptimizationProblem(ProjectROV project, Caplet caplet, Vector capMaturity, Vector fwd, Vector capK, double deltaK, Vector capMat, Matrix blackCaps)
{
this.project = project;
this.caplet = caplet;
this.capMaturity = capMaturity;
this.fwd = fwd;
this.capK = capK;
this.deltaK = deltaK;
this.capMat = capMat;
this.blackCaps = blackCaps;
Console.WriteLine("Pelsser Caps problem on " + this.capMaturity.Length + " x " + this.capK.Length + " elements");
}
public void Test()
{
Engine.MultiThread = true;
Document doc = new Document();
ProjectROV rov = new ProjectROV(doc);
doc.Part.Add(rov);
AFunction zerorate = new AFunction(rov);
zerorate.VarName = "zr";
zerorate.m_IndependentVariables = 1;
zerorate.m_Value = (RightValue)0.05;
rov.Symbols.Add(zerorate);
int n_sim = 4000;
double maturityOpt = 6.5;
// Simulation steps for a year. With stepPerYear = 150 the test will be passed.
// But notice that the price calculated through Monte Carlo is unstable when
// changing this value, even till 1000 steps per year.
int stepsPerYear = 150;
int n_steps = stepsPerYear * ((int)maturityOpt);
double strike = 0.01;
double tau = 0.5;
SquaredGaussianModel process = new SquaredGaussianModel();
process.a1 = (ModelParameter)0.1;
process.sigma1 = (ModelParameter)0.01;
process.zr = (ModelParameter)"@zr";
StochasticProcessExtendible s = new StochasticProcessExtendible(rov, process);
rov.Processes.AddProcess(s);
ModelParameter PT = new ModelParameter(maturityOpt, "TT");
PT.VarName = "TT";
rov.Symbols.Add(PT);
ModelParameter Ptau = new ModelParameter(tau, "tau");
Ptau.VarName = "tau";
rov.Symbols.Add(Ptau);
ModelParameter Pstrike = new ModelParameter(strike, "strike");
Pstrike.VarName = "strike";
rov.Symbols.Add(Pstrike);
// Set the discounting.
RiskFreeInfo rfi = rov.GetDiscountingModel() as RiskFreeInfo;
rfi.ActualizationType = EActualizationType.Stochastic;
rfi.m_deterministicRF = (ModelParameter)"@V1";
// Set the payoff.
OptionTree op = new OptionTree(rov);
op.PayoffInfo.PayoffExpression = "tau*max(rate(TT;tau;@v1) - strike; 0)";
op.PayoffInfo.Timing.EndingTime.m_Value = (RightValue)(maturityOpt + tau);
op.PayoffInfo.European = true;
rov.Map.Root = op;
rov.NMethods.Technology = ETechType.T_SIMULATION;
rov.NMethods.PathsNumber = n_sim;
rov.NMethods.SimulationSteps = n_steps;
ROVSolver solver = new ROVSolver();
solver.BindToProject(rov);
solver.DoValuation(-1);
if (rov.HasErrors)
{
rov.DisplayErrors();
}
Assert.IsFalse(rov.HasErrors);
ResultItem price = rov.m_ResultList[0] as ResultItem;
double mcPrice = price.value;
double mcDevST = price.stdDev / Math.Sqrt((double)n_sim);
Caplet cplt = new Caplet();
Vector Mat, fwd, Rk;
Vector capMatV;
double delta_k;
double capMat;
delta_k = 0.5;
capMat = maturityOpt + tau;
int nmat = 2 * ((int)capMat) + 1;
Mat = new Vector(nmat);
fwd = new Vector(nmat);
Mat[0] = 0;
fwd[0] = zerorate.Evaluate(0);
for (int k = 1; k < nmat; k++)
{
Mat[k] = tau * ((double)k);
fwd[k] = zerorate.Evaluate(Mat[k]) * Mat[k] - zerorate.Evaluate(Mat[k - 1]) * Mat[k - 1];
}
fwd = fwd / tau;
Rk = new Vector(1);
Rk[0] = strike;
capMatV = new Vector(2);
capMatV[0] = maturityOpt;
capMatV[1] = maturityOpt + tau;
Matrix caplet = cplt.PGSMCaplets(process, Mat, fwd, Rk, delta_k, capMatV);
double theoreticalPrice = caplet[1, 0] - caplet[0, 0];
Console.WriteLine("\nTheoretical Price = " + theoreticalPrice.ToString());
Console.WriteLine("Monte Carlo Price = " + mcPrice);
Console.WriteLine("Standard Deviation = " + mcDevST);
double tol = 4.0 * mcDevST;
Assert.Less(Math.Abs(theoreticalPrice - mcPrice), tol);
}
public void Test()
{
Engine.MultiThread = true;
Document doc = new Document();
ProjectROV rov = new ProjectROV(doc);
doc.Part.Add(rov);
AFunction zerorate = new AFunction(rov);
zerorate.VarName = "zr";
zerorate.m_IndependentVariables = 1;
zerorate.m_Value = (RightValue)0.05;
rov.Symbols.Add(zerorate);
int n_sim = 10000;
double maturityOpt = 6.5;
// Simulation steps for a year. With stepPerYear = 150 the test will be passed.
// But notice that the price calculated through Monte Carlo is unstable when
// changing this value, even till 1000 steps per year.
int stepsPerYear = 500;
int n_steps = stepsPerYear * ((int)maturityOpt);
double strike = 100.0;
double tau = 0.5;
SquaredGaussianModel process = new SquaredGaussianModel();
process.a1 = (ModelParameter)0.1;
process.sigma1 = (ModelParameter)0.01;
process.zr = (ModelParameter)"@zr";
StochasticProcessExtendible s = new StochasticProcessExtendible(rov, process);
rov.Processes.AddProcess(s);
ModelParameter PT = new ModelParameter(maturityOpt, "TT");
PT.VarName = "TT";
rov.Symbols.Add(PT);
ModelParameter Ptau = new ModelParameter(tau, "tau");
Ptau.VarName = "tau";
rov.Symbols.Add(Ptau);
ModelParameter Pstrike = new ModelParameter(strike, "strike");
Pstrike.VarName = "strike";
rov.Symbols.Add(Pstrike);
// Set the discounting.
RiskFreeInfo rfi = rov.GetDiscountingModel() as RiskFreeInfo;
rfi.ActualizationType = EActualizationType.Stochastic;
rfi.m_deterministicRF = (ModelParameter)"@V1";
// Set the payoff.
OptionTree op = new OptionTree(rov);
op.PayoffInfo.PayoffExpression = "max(strike - Bond(TT;TT+tau;@v1); 0)";
op.PayoffInfo.Timing.EndingTime.m_Value = (RightValue)maturityOpt;
op.PayoffInfo.European = true;
rov.Map.Root = op;
rov.NMethods.Technology = ETechType.T_SIMULATION;
rov.NMethods.PathsNumber = n_sim;
rov.NMethods.SimulationSteps = n_steps;
ROVSolver solver = new ROVSolver();
solver.BindToProject(rov);
solver.DoValuation(-1);
if (rov.HasErrors)
{
Console.WriteLine(rov.m_RuntimeErrorList[0]);
}
Assert.IsFalse(rov.HasErrors);
ResultItem price = rov.m_ResultList[0] as ResultItem;
double mcPrice = price.value;
double mcDevST = price.stdDev / Math.Sqrt(2.0 * ((double)n_sim));
Caplet cplt = new Caplet();
Vector Mat;
Vector fwd;
Vector Rk;
Vector capMatV;
double deltaK;
double capMat;
deltaK = 0.5;
capMat = maturityOpt + tau;
int nmat = 2 * ((int)capMat) + 1;
Mat = new Vector(nmat);
fwd = new Vector(nmat);
Mat[0] = 0;
fwd[0] = zerorate.Evaluate(0);
for (int k = 1; k < nmat; k++)
{
Mat[k] = tau * ((double)k);
fwd[k] = zerorate.Evaluate(Mat[k]) * Mat[k] - zerorate.Evaluate(Mat[k - 1]) * Mat[k - 1];
}
fwd = fwd / tau;
Rk = new Vector(1);
Rk[0] = (1 / strike - 1.0) / tau;
capMatV = new Vector(2);
capMatV[0] = maturityOpt;
capMatV[1] = maturityOpt + tau;
Matrix caplet = cplt.PGSMCaplets(process, Mat, fwd, Rk, deltaK, capMatV);
Console.WriteLine("rows = " + caplet.R);
Console.WriteLine("columns = " + caplet.C);
double theoreticalPrice = caplet[1, 0] - caplet[0, 0];
Console.WriteLine("\nTheoretical Price = " + theoreticalPrice.ToString());
Console.WriteLine("Monte Carlo Price = " + mcPrice);
Console.WriteLine("Standard Deviation = " + mcDevST);
double tol = 4.0 * mcDevST;
Assert.Less(Math.Abs(theoreticalPrice - mcPrice), tol);
}
/// <summary>
/// Attempts a calibration through <see cref="PelsserCappletOptimizationProblem"/>
/// using caps matrices.
/// </summary>
/// <param name="data">The data to be used in order to perform the calibration.</param>
/// <param name="settings">The parameter is not used.</param>
/// <param name="controller">The controller which may be used to cancel the process.</param>
/// <returns>The results of the calibration.</returns>
public EstimationResult Estimate(List<object> data, IEstimationSettings settings = null, IController controller = null, Dictionary<string, object> properties = null)
{
InterestRateMarketData dataset = data[0] as InterestRateMarketData;
EstimationResult result;
if ((dataset.ZRMarket == null) || (dataset.CapVolatility == null))
{
result = new EstimationResult();
result.ErrorMessage = "Not enough data to calibrate.\n" +
"The estimator needs a ZRMarket and a CapVolatility " +
"defined inside InterestRateMarketData";
return result;
}
// Backup the dates
DateTime effectiveDate = DateTime.Now.Date;
DateTime valuationDate = DateTime.Now.Date;
if (Document.ActiveDocument != null)
{
effectiveDate = Document.ActiveDocument.ContractDate;
valuationDate = Document.ActiveDocument.SimulationStartDate;
}
// Creates the Context.
Document doc = new Document();
ProjectROV prj = new ProjectROV(doc);
doc.Part.Add(prj);
Function zr = new PFunction(null);
zr.VarName = "zr";
// Load the zr.
double[,] zrvalue = (double[,])ArrayHelper.Concat(dataset.ZRMarketDates.ToArray(), dataset.ZRMarket.ToArray());
zr.Expr = zrvalue;
prj.Symbols.Add(zr);
BlackModel bm = new BlackModel(zr);
double deltak = dataset.CapTenor;
Matrix capVol = dataset.CapVolatility;
Vector capMat = dataset.CapMaturity;
Vector capK = dataset.CapRate;
var preferences = settings as Fairmat.Calibration.CapVolatilityFiltering;
// Matrix calculated with black.
Matrix blackCaps = new Matrix(capMat.Length, capK.Length);
for (int m = 0; m < capMat.Length; m++)
{
for (int s = 0; s < capK.Length; s++)
{
bool skip = false;
if (preferences != null)
{
if (capK[s] < preferences.MinCapRate || capK[s] > preferences.MaxCapRate ||
capMat[m] < preferences.MinCapMaturity || capMat[m] > preferences.MaxCapMaturity)
{skip = true; }
}
if (capVol[m, s] == 0 || skip)
blackCaps[m, s] = 0;
else
blackCaps[m, s] = bm.Cap(capK[s], capVol[m, s], deltak, capMat[m]);
}
}
if (blackCaps.IsNAN())
{
Console.WriteLine("Black caps matrix has non real values:");
Console.WriteLine(blackCaps);
throw new Exception("Cannot calculate Black caps");
}
// Maturity goes from 0 to the last item with step deltaK.
Vector maturity = new Vector((int)(1.0 + capMat[capMat.Length - 1] / deltak));
for (int l = 0; l < maturity.Length; l++)
maturity[l] = deltak * l;
Vector fwd = new Vector(maturity.Length - 1);
for (int i = 0; i < fwd.Length; i++)
{
fwd[i] = bm.Fk(maturity[i + 1], deltak);
}
// Creates a default Pelsser model.
Pelsser.SquaredGaussianModel model = new Pelsser.SquaredGaussianModel();
model.a1 = (ModelParameter)0.014;
model.sigma1 = (ModelParameter)0.001;
model.zr = (ModelParameter)"@zr";
StochasticProcessExtendible iex = new StochasticProcessExtendible(prj, model);
prj.Processes.AddProcess(iex);
prj.Parse();
DateTime t0 = DateTime.Now;
Caplet cp = new Caplet();
PelsserCappletOptimizationProblem problem = new PelsserCappletOptimizationProblem(prj, cp, maturity, fwd, capK, deltak, capMat, blackCaps);
IOptimizationAlgorithm solver = new QADE();
IOptimizationAlgorithm solver2 = new SteepestDescent();
DESettings o = new DESettings();
o.NP = 35;
o.TargetCost = 0.0025;
o.MaxIter = 10;
o.Verbosity = Math.Max(1, Engine.Verbose);
o.controller = controller;
// Parallel evaluation is not supported for this calibration.
o.Parallel = false;
o.Debug = true;
SolutionInfo solution = null;
Vector x0 = (Vector)new double[] { 0.1, 0.1 };
solution = solver.Minimize(problem, o, x0);
if (solution.errors)
return new EstimationResult(solution.message);
o.epsilon = 10e-7;
o.h = 10e-7;
o.MaxIter = 1000;
o.Debug = true;
o.Verbosity = Math.Max(1, Engine.Verbose);
if (solution != null)
solution = solver2.Minimize(problem, o, solution.x);
else
solution = solver2.Minimize(problem, o, x0);
if (solution.errors)
return new EstimationResult(solution.message);
Console.WriteLine(solution);
string[] names = new string[] { "alpha1", "sigma1" };
result = new EstimationResult(names, solution.x);
result.ZRX = (double[])dataset.ZRMarketDates.ToArray();
result.ZRY = (double[])dataset.ZRMarket.ToArray();
result.Objects = new object[1];
result.Objects[0] = solution.obj;
//result.Fit = solution.obj;//Uncomment in 1.6
// Restore the dates
if (Document.ActiveDocument != null)
{
Document.ActiveDocument.ContractDate = effectiveDate;
Document.ActiveDocument.SimulationStartDate = valuationDate;
}
return result;
}
