/// <summary>
/// Creates a representation of the Pelsser constraints.
/// </summary>
/// <remarks>
/// The method is static in order to be used by other classes.
/// </remarks>
/// <param name="project">The project where to evaluate the constraints.</param>
/// <param name="x">The vector of x values.</param>
/// <param name="maturity">The cap maturity to use to evaluate the constraints.</param>
/// <returns>
/// A vector with the representation of the Pelsser constraints.
/// </returns>
public static DVPLI.Vector PelsserConstraint(ProjectROV project, DVPLI.Vector x, double maturity)
{
// This is modeled as a one-dimensional bound.
SquaredGaussianModel model = Assign(project, x);
Vector res = new Vector(1);
double dt = 1.0 / (252);
for (double t = 0; t <= maturity; t += dt)
{
res[0] += Math.Max(0, -model.F2(t, dt)); // The square of F.
}
/*
* dt = .1317;
* for (double t = 0; t <= 2; t += dt)
* res[0] +=Math.Max(0,-model.F2(t, dt)); // The square of F.
*
*
* dt = .25;
* for (double t = 0; t <= 2; t += dt)
* res[0] +=Math.Max(0,-model.F2(t, dt)); // The square of F.
*/
return(res);
}
public void Test()
{
ProjectROV r = HullAndWhite1("bond(t;2;@V1)", 1, 1, .05);
r.Container.NMethods.Technology = ETechType.T_SIMULATION;
r.Container.NMethods.m_UseRepeatableSequence = true;
r.Initialize();
AnalysisValuation valuator = new AnalysisValuation();
valuator.BindToProject(r);
valuator.RunAnalysis(-1);
if (r.HasErrors)
{
r.DisplayErrors();
}
Assert.IsFalse(r.HasErrors);
double v = r.m_ResultList[0].value;
Console.WriteLine("v = " + v.ToString());
Assert.AreEqual(0.9134, v, 0.0001);
}
public static void Calculate(double t1, double t2, double simEnd, int numSim, int numSteps, out double val, out double stDev)
{
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);
// To be changed to 350000.
int n_sim = numSim;
int n_steps = numSteps;
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);
// Set the discounting.
RiskFreeInfo rfi = rov.GetDiscountingModel() as RiskFreeInfo;
rfi.ActualizationType = EActualizationType.RiskFree;
rfi.m_deterministicRF = 0.0;
OptionTree op = new OptionTree(rov);
op.PayoffInfo.PayoffExpression = "bond(" + t1.ToString() + ";" + t2.ToString() + ";@v1)";
// Here we put the simulation maturity.
op.PayoffInfo.Timing.EndingTime.m_Value = (RightValue)simEnd;
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]);
}
ResultItem price = rov.m_ResultList[0] as ResultItem;
val = price.value;
stDev = price.stdDev / Math.Sqrt((double)numSim);
}
/// <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()
{
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 = 5000;
int n_steps = 900;
SquaredGaussianModel process = new SquaredGaussianModel();
process.a1 = (ModelParameter)0.0704877770928728;
process.sigma1 = (ModelParameter)0.116251516678772;
process.zr = (ModelParameter)"@zr";
StochasticProcessExtendible s = new StochasticProcessExtendible(rov, process);
rov.Processes.AddProcess(s);
OptionTree op = new OptionTree(rov);
op.PayoffInfo.PayoffExpression = "bond(t;10;@v1)";
// Set the simulation maturity.
op.PayoffInfo.Timing.EndingTime.m_Value = (RightValue)2.0;
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);
}
private static ProjectROV HullAndWhite1(string payoff, double maturity, double a1, double sigma1)
{
Document doc = new Document();
ProjectROV rov1 = new ProjectROV(doc);
doc.Part.Add(rov1);
// Create the zero rate curve
double a = 0.08;
double b = 0.05;
double c = -0.18;
string zr = string.Format("{0} - {1}*exp({2}*x1)", a, b, c);
AFunction zero_rate = new AFunction(rov1);
zero_rate.VarName = "ZeroRate";
zero_rate.m_IndependentVariables = 1;
zero_rate.m_Value = new RightValueExpression(zr);
// Add to the project the created zero rate curve.
rov1.Symbols.Add(zero_rate);
RiskFreeInfo rfi = rov1.GetDiscountingModel() as RiskFreeInfo;
rfi.ActualizationType = EActualizationType.ZeroCoupond;
rfi.m_deterministicRF.m_Value = (RightValue)"exp( -ZeroRate(t)*t)";
// Create the short rate process.
HW1 hw1 = new HW1(a1, sigma1, "@ZeroRate");
StochasticProcessExtendible hw = new StochasticProcessExtendible(rov1, hw1);
rov1.Processes.AddProcess(hw);
OptionTree ot = new OptionTree(rov1);
ot.European = true;
ot.PayoffInfo.PayoffExpression = payoff;
ot.PayoffInfo.Timing.EndingTime.m_Value = (RightValue)maturity;
rov1.Map.Root = ot;
return(rov1);
}
private static ProjectROV HullAndWhite1(string payoff, double maturity, double a1, double sigma1)
{
Document doc = new Document();
ProjectROV rov1 = new ProjectROV(doc);
doc.Part.Add(rov1);
// Create the zero rate curve
double a = 0.08;
double b = 0.05;
double c = -0.18;
string zr = string.Format("{0} - {1}*exp({2}*x1)", a, b, c);
AFunction zero_rate = new AFunction(rov1);
zero_rate.VarName = "ZeroRate";
zero_rate.m_IndependentVariables = 1;
zero_rate.m_Value = new RightValueExpression(zr);
// Add to the project the created zero rate curve.
rov1.Symbols.Add(zero_rate);
RiskFreeInfo rfi = rov1.GetDiscountingModel() as RiskFreeInfo;
rfi.ActualizationType = EActualizationType.ZeroCoupond;
rfi.m_deterministicRF.m_Value = (RightValue)"exp( -ZeroRate(t)*t)";
// Create the short rate process.
HW1 hw1 = new HW1(a1, sigma1, "@ZeroRate");
StochasticProcessExtendible hw = new StochasticProcessExtendible(rov1, hw1);
rov1.Processes.AddProcess(hw);
OptionTree ot = new OptionTree(rov1);
ot.European = true;
ot.PayoffInfo.PayoffExpression = payoff;
ot.PayoffInfo.Timing.EndingTime.m_Value = (RightValue)maturity;
rov1.Map.Root = ot;
return rov1;
}
/// <summary>
/// Assigns new trial values for x in order to use it
/// for the evaluation of the constraints and the objective function.
/// </summary>
/// <param name="project">The project where to evaluate.</param>
/// <param name="x">The vector of x values.</param>
/// <returns>A <see cref="SquaredGaussianModel"/> set with the values.</returns>
internal static SquaredGaussianModel Assign(ProjectROV project, Vector x)
{
Engine.Parser.NewContext();
SquaredGaussianModel model = project.Processes[0].Plugin as SquaredGaussianModel;
// Assign the new values.
ModelParameter a1 = model.a1 as ModelParameter;
ModelParameter s1 = model.sigma1 as ModelParameter;
a1.m_Value = (RightValue)x[0];
s1.m_Value = (RightValue)x[1];
bool errors = model.Parse(null);
if (errors)
{
throw new Exception("Cannot Assing model");
}
return(model);
}
public void Test()
{
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 = 5000;
int n_steps = 900;
SquaredGaussianModel process = new SquaredGaussianModel();
process.a1 = (ModelParameter)0.0704877770928728;
process.sigma1 = (ModelParameter)0.116251516678772;
process.zr = (ModelParameter)"@zr";
StochasticProcessExtendible s = new StochasticProcessExtendible(rov, process);
rov.Processes.AddProcess(s);
OptionTree op = new OptionTree(rov);
op.PayoffInfo.PayoffExpression = "bond(t;10;@v1)";
// Set the simulation maturity.
op.PayoffInfo.Timing.EndingTime.m_Value = (RightValue)2.0;
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);
}
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 = 5000;
int n_steps = 900;
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);
// Set the discounting.
RiskFreeInfo rfi = rov.GetDiscountingModel() as RiskFreeInfo;
rfi.ActualizationType = EActualizationType.RiskFree;
rfi.m_deterministicRF = 0.0;
OptionTree op = new OptionTree(rov);
op.PayoffInfo.PayoffExpression = "bond(t;10;@v1)";
// Set the simulation maturity.
op.PayoffInfo.Timing.EndingTime.m_Value = (RightValue)2.0;
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;
Console.WriteLine("Bond Test Value = " + price.value.ToString());
Assert.LessOrEqual(Math.Abs(0.6702 - price.value), .01);
// Try to do some simple tests and check the results.
double b0_10 = process.Bond(DynamicParam(0, process), process.CacheDates, 0, 0, 10);
Console.WriteLine("Bond(0,10) = " + b0_10);
Assert.LessOrEqual(Math.Abs(b0_10 - 0.606513), .001);
double b7_10 = process.Bond(DynamicParam(0.00427631, process), process.CacheDates, 0, 7, 10);
Console.WriteLine("Bond(7,10) = " + b7_10);
Assert.LessOrEqual(Math.Abs(b7_10 - 0.856374), .001);
double b7_30 = process.Bond(DynamicParam(0.00427631, process), process.CacheDates, 0, 7, 30);
}
/// <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);
}
public void Test()
{
Engine.MultiThread = true;
Document doc = new Document();
ProjectROV rov = new ProjectROV(doc);
doc.Part.Add(rov);
doc.DefaultProject.NMethods.m_UseAntiteticPaths = true;
int n_sim = 10000;
int n_steps = 512;
double a = 0.2;
double DR = 0.02;
double r0 = 0.015;
double a1 = 1.0;
double sigma1 = 0.01;
double a2 = 0.1;
double sigma2 = 0.0165;
double correlation = 0.6;
double maturityOpt = 5.0;
double strike = 0.927;
double tau = 2.0;
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 Pa = new ModelParameter(a, "a");
Pa.VarName = "a";
rov.Symbols.Add(Pa);
ModelParameter PDR = new ModelParameter(DR, "PDR");
PDR.VarName = "DR";
rov.Symbols.Add(PDR);
ModelParameter Pr0 = new ModelParameter(r0, "r0");
Pr0.VarName = "r0";
rov.Symbols.Add(Pr0);
ModelParameter Pstrike = new ModelParameter(strike, "strike");
Pstrike.VarName = "strike";
rov.Symbols.Add(Pstrike);
AFunction zerorate = new AFunction(rov);
zerorate.VarName = "zr";
zerorate.m_IndependentVariables = 1;
zerorate.m_Value = (RightValue)("(1-exp(-a*x1))*DR + r0");
rov.Symbols.Add(zerorate);
HW2ProcessType pt = new HW2ProcessType();
// Set the short rate process.
pt = HW2ProcessType.ShortRate;
StocasticProcessHW2 process1 = new StocasticProcessHW2(rov, pt);
process1.zero_rate_curve = "@zr";
process1._a = (ModelParameter)a1;
process1._b = (ModelParameter)sigma1;
rov.Processes.AddProcess(process1);
// Set the mean reversion process.
pt = HW2ProcessType.Unobservable;
StocasticProcessHW2 process2 = new StocasticProcessHW2(rov, pt);
process2._a = (ModelParameter)a2;
process2._b = (ModelParameter)sigma2;
rov.Processes.AddProcess(process2);
// Set the correlation.
rov.Processes.r[0, 1] = (RightValue)correlation;
// Set the discounting.
RiskFreeInfo rfi = rov.GetDiscountingModel() as RiskFreeInfo;
rfi.ActualizationType = EActualizationType.Stochastic;
rfi.m_deterministicRF = (ModelParameter)"@v1";
OptionTree op = new OptionTree(rov);
op.PayoffInfo.PayoffExpression = "max(bond(TT;TT+tau;@v1)-strike;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 sampleMean = price.value;
double sampleDevSt = price.stdDev / Math.Sqrt((double)n_sim);
double theoreticalPrice = HW2BondCall(zerorate, maturityOpt, maturityOpt + tau, strike,
a1, sigma1, a2, sigma2, correlation);
Console.WriteLine("\nTheoretical Price = " + theoreticalPrice.ToString());
Console.WriteLine("Monte Carlo Price = " + sampleMean.ToString());
Console.WriteLine("Standard Deviation = " + sampleDevSt.ToString());
bool result;
double fact = 4.0;
result = (Math.Abs(sampleMean - theoreticalPrice) < fact * sampleDevSt);
Assert.IsTrue(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");
}
/// <summary>
/// Creates a representation of the Pelsser constraints.
/// </summary>
/// <remarks>
/// The method is static in order to be used by other classes.
/// </remarks>
/// <param name="project">The project where to evaluate the constraints.</param>
/// <param name="x">The vector of x values.</param>
/// <param name="maturity">The cap maturity to use to evaluate the constraints.</param>
/// <returns>
/// A vector with the representation of the Pelsser constraints.
/// </returns>
public static DVPLI.Vector PelsserConstraint(ProjectROV project, DVPLI.Vector x, double maturity)
{
// This is modeled as a one-dimensional bound.
SquaredGaussianModel model = Assign(project, x);
Vector res = new Vector(1);
double dt = 1.0 / (252);
for (double t = 0; t <= maturity; t += dt)
res[0] += Math.Max(0, -model.F2(t, dt)); // The square of F.
/*
dt = .1317;
for (double t = 0; t <= 2; t += dt)
res[0] +=Math.Max(0,-model.F2(t, dt)); // The square of F.
dt = .25;
for (double t = 0; t <= 2; t += dt)
res[0] +=Math.Max(0,-model.F2(t, dt)); // The square of F.
*/
return res;
}
public void Test()
{
double nu = 0.6;
double theta = -0.2;
double sigma = 0.2;
double rate = 0.02;
double dy = 0.01;
double s0 = 1;
double maturity = 2.0;
double strike = 1.2;
Vector mat = new Vector(1) + maturity;
Vector k = new Vector(1) + strike;
// Calculates the theoretical value of the call.
double theoreticalPrice = VarianceGammaOptionsCalibration.VGCall(theta, sigma, nu,
maturity, strike,
dy, s0, rate);
Engine.MultiThread = true;
Document doc = new Document();
ProjectROV rov = new ProjectROV(doc);
doc.Part.Add(rov);
doc.DefaultProject.NMethods.m_UseAntiteticPaths = true;
int n_sim = 50000;
int n_steps = 512;
ModelParameter paramStrike = new ModelParameter(strike, "strike");
paramStrike.VarName = "strike";
rov.Symbols.Add(paramStrike);
ModelParameter paramRate = new ModelParameter(rate, "rfrate");
paramRate.VarName = "rfrate";
rov.Symbols.Add(paramRate);
AFunction payoff = new AFunction(rov);
payoff.VarName = "payoff";
payoff.m_IndependentVariables = 1;
payoff.m_Value = (RightValue)("max(x1 - strike ; 0)");
rov.Symbols.Add(payoff);
VarianceGamma process = new VarianceGamma(s0, theta, sigma, nu, rate, dy);
StochasticProcessExtendible s = new StochasticProcessExtendible(rov, process);
rov.Processes.AddProcess(s);
// Set the discounting.
RiskFreeInfo rfi = rov.GetDiscountingModel() as RiskFreeInfo;
rfi.ActualizationType = EActualizationType.RiskFree;
rfi.m_deterministicRF = rate;
OptionTree op = new OptionTree(rov);
op.PayoffInfo.PayoffExpression = "payoff(v1)";
op.PayoffInfo.Timing.EndingTime.m_Value = (RightValue)maturity;
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 samplePrice = price.value;
double sampleDevSt = price.stdDev / Math.Sqrt((double)n_sim);
Console.WriteLine("Theoretical Price = " + theoreticalPrice);
Console.WriteLine("Monte Carlo Price = " + samplePrice);
Console.WriteLine("Standard Deviation = " + sampleDevSt.ToString());
double tol = 4.0 * sampleDevSt;
Assert.Less(Math.Abs(theoreticalPrice - samplePrice), tol);
}
public void Test()
{
Engine.MultiThread = true;
Document doc = new Document();
ProjectROV rov = new ProjectROV(doc);
doc.Part.Add(rov);
doc.DefaultProject.NMethods.m_UseAntiteticPaths = true;
int n_sim = 20000;
int n_steps = 1024;
double a = 0.2;
double DR = 0.02;
double r0 = 0.015;
double a1 = 0.02;
double sigma1 = 0.01;
double maturityOpt = 5.0;
double strike = 0.005;
double tau = 0.5;
double strike2 = 1.0 / (1.0 + strike * tau);
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 Pa = new ModelParameter(a, "a");
Pa.VarName = "a";
rov.Symbols.Add(Pa);
ModelParameter PDR = new ModelParameter(DR, "PDR");
PDR.VarName = "DR";
rov.Symbols.Add(PDR);
ModelParameter Pr0 = new ModelParameter(r0, "r0");
Pr0.VarName = "r0";
rov.Symbols.Add(Pr0);
ModelParameter Pstrike = new ModelParameter(strike, "strike");
Pstrike.VarName = "strike";
rov.Symbols.Add(Pstrike);
AFunction zerorate = new AFunction(rov);
zerorate.VarName = "zr";
zerorate.m_IndependentVariables = 1;
zerorate.m_Value = (RightValue)("(1-exp(-a*x1))*DR + r0");
rov.Symbols.Add(zerorate);
HW1 process = new HW1(a1, sigma1, "@zr");
StochasticProcessExtendible s = new StochasticProcessExtendible(rov, process);
rov.Processes.AddProcess(s);
// Set the discounting.
RiskFreeInfo rfi = rov.GetDiscountingModel() as RiskFreeInfo;
rfi.ActualizationType = EActualizationType.Stochastic;
rfi.m_deterministicRF = (ModelParameter)"@V1";
OptionTree op = new OptionTree(rov);
// 1) RATE FUNCTION, with this the price is higher than the theoretical one
// op.PayoffInfo.PayoffExpression = "tau*max(rate(TT;tau;@v1) - strike; 0)";
// 2) OBTAIN RATE FROM bond = exp(-rate*t),
// with this the price is higher than the theoretical one but it's more near than 1)
// op.PayoffInfo.PayoffExpression = "tau*max(-ln(bond(TT;TT+tau;@v1))/tau - strike; 0)";
// 3) CONVERT RATE from discrete to continuous through (1+r_d) = exp(r_c)
// In this way the price is the same as the theoretical one.
op.PayoffInfo.PayoffExpression = "tau*max(ln(1+rate(TT;tau;@v1)) - strike; 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 samplePrice = price.value;
double sampleDevSt = price.stdDev / Math.Sqrt(2.0 * (double)n_sim);
// Calculation of the theoretical value of the caplet.
CapHW1 cap = new CapHW1(zerorate);
double theoreticalPrice = cap.HWCaplet(a1, sigma1, maturityOpt,
maturityOpt + tau, strike2);
Console.WriteLine("Theoretical Price = " + theoreticalPrice.ToString());
Console.WriteLine("Monte Carlo Price = " + samplePrice);
Console.WriteLine("Standard Deviation = " + sampleDevSt.ToString());
double tol = 4.0 * sampleDevSt;
Assert.Less(Math.Abs(theoreticalPrice - samplePrice), tol);
}
/// <summary>
/// Attempts to solve the Heston optimization problem using
/// <see cref="Heston.HestonOptimizationProblem"/>.
/// </summary>
/// <param name="marketData">Data to be used in order to perform the optimization.</param>
/// <param name="settings">The parameter is not used.</param>
/// <param name="controller">IController.</param>
/// <returns>The results of the optimization.</returns>
public EstimationResult Estimate(List<object> marketData, IEstimationSettings settings = null, IController controller = null, Dictionary<string, object> properties = null)
{
DateTime t0 = DateTime.Now;
var interestDataSet = (CurveMarketData)marketData[0];
CallPriceMarketData callDataSet = (CallPriceMarketData)marketData[1];
EquityCalibrationData equityCalData = new EquityCalibrationData(callDataSet, interestDataSet);
var spotPrice = (DVPLI.MarketDataTypes.Scalar)marketData[2];
Setup(equityCalData, settings);
var calSettings = settings as HestonCalibrationSettings;
// Creates the context.
Document doc = new Document();
ProjectROV prj = new ProjectROV(doc);
doc.Part.Add(prj);
// Optimization problem instance.
Vector matBound = new Vector(2);
Vector strikeBound = new Vector(2);
if (calSettings != null)
{
matBound[0] = calSettings.MinMaturity;
matBound[1] = calSettings.MaxMaturity;
strikeBound[0] = calSettings.MinStrike;
strikeBound[1] = calSettings.MaxStrike;
}
else
{
//use defaults
matBound[0] = 1.0 / 12;// .25;
matBound[1] = 6;// 10; //Up to 6Y maturities
strikeBound[0] = 0.4;
strikeBound[1] = 1.6;
}
Console.WriteLine(callDataSet);
/*
//CBA TEST
matBound[0] = 1;// .25;
matBound[1] = 3.5;// 10; //Up to 6Y maturities
strikeBound[0] = 0.5;// 0.5;
strikeBound[1] = 2;//1.5;
*/
HestonCallOptimizationProblem problem = NewOptimizationProblem(equityCalData, matBound, strikeBound);
int totalOpts = problem.numCall + problem.numPut;
Console.WriteLine("Calibration based on "+totalOpts+ " options. (" + problem.numCall + " call options and "+problem.numPut+" put options).");
IOptimizationAlgorithm solver = new QADE();
//IOptimizationAlgorithm solver = new MultiLevelSingleLinkage();
IOptimizationAlgorithm solver2 = new SteepestDescent();
DESettings o = new DESettings();
o.controller = controller;
// If true the optimization algorithm will operate in parallel.
o.Parallel = Engine.MultiThread;
o.h = 10e-8;
o.epsilon = 10e-8;
SolutionInfo solution = null;
double minObj=double.MaxValue;
Vector minX= null;
int Z = 1;
//if (problem.GetType() == typeof(Heston.HestonCallSimulationOptimizationProblem))
// Z = 2;
for(int z=0;z<Z;z++)
{
if (solver.GetType() == typeof(MultiLevelSingleLinkage))
{
o.NP = 50;
o.MaxIter = 25;
o.MaxGamma = 6;
}
else
{
o.NP = 60;
o.MaxIter = 35;
}
o.Verbosity = 1;
Vector x0 = null;// new Vector(new double[] { 0.5, 0.5, 0.8, -0.5, 0.05 });
// GA
solution = solver.Minimize(problem, o, x0);
if (solution.errors)
return null;
o.options = "qn";
o.MaxIter = 500;// 1000;
if (solution != null)
solution = solver2.Minimize(problem, o, solution.x);
else
{
solution = solver2.Minimize(problem, o, x0);
}
if (solution.errors)
return null;
if (solution.obj < minObj)
{
minObj = solution.obj;
minX = solution.x.Clone();
}
}
solution.obj = minObj;
solution.x = minX;
//Displays pricing error structure
HestonCallOptimizationProblem.displayObjInfo = true;
problem.Obj(solution.x);
HestonCallOptimizationProblem.displayObjInfo = false;
Console.WriteLine("Calibration Time (s)\t" + (DateTime.Now - t0).TotalSeconds);
return BuildEstimate(spotPrice,interestDataSet, callDataSet, equityCalData, solution);
}
private EstimationResult QuantLibEstimate(CurveMarketData discoutingCurve, CallPriceMarketData Hdataset)
{
EquityCalibrationData HCalData = new EquityCalibrationData(Hdataset, discoutingCurve);
bool hasArbitrage = HCalData.HasArbitrageOpportunity(10e-2);
if (hasArbitrage)
Console.WriteLine("Market data contains arbitrage opportunity");
this.r = new DVPLDOM.PFunction(discoutingCurve.Durations,discoutingCurve.Values);
this.q = HCalData.dyFunc as PFunction;
//this.r.Parse(null);
//this.q.Parse(null);
Hdataset.Volatility = new Matrix(Hdataset.CallPrice.R, Hdataset.CallPrice.C);
for (int i = 0; i < Hdataset.Volatility.R; i++)
{
double m=Hdataset.Maturity[i];
for (int j = 0; j < Hdataset.Volatility.C; j++)
{
if (Hdataset.CallPrice[i, j] > 0)
{
var bs = new Fairmat.Finance.BlackScholes(r.Evaluate(m), Hdataset.S0, Hdataset.Strike[j], 0, m, q.Evaluate(m));
//Hdataset.Volatility[i, j] = Hdataset.Volatility[i, j] * Hdataset.Volatility[i, j] * Hdataset.Maturity[i];
//Hdataset.Volatility[i, j] = bs.ImpliedCallVolatility(Hdataset.CallPrice[i, j]);
}
}
}
Console.WriteLine(Hdataset.Volatility);
IFunction impVol = FitImplVolModel(Hdataset);
Document doc = new Document();
ProjectROV prj = new ProjectROV(doc);
doc.Part.Add(prj);
prj.Symbols.Add(impVol);
// doc.WriteToXMLFile("impVol.fair");
int nmat = calibrationSettings.LocalVolatilityMaturities;
int nstrike = calibrationSettings.LocalVolatilityStrikes;
double lastMat = Hdataset.Maturity[SymbolicIntervalExtremes.End];
double lastStr = Hdataset.Strike[SymbolicIntervalExtremes.End];
Vector locVolMat = Vector.Linspace(Hdataset.Maturity[0], lastMat, nmat);
Vector locVolStr = Vector.Linspace(Hdataset.Strike[0], lastStr, nstrike);
Matrix locVolMatrix = new Matrix(nmat, nstrike);
double t, dt, forwardValue, y, dy, strike, strikep, strikem, w, wp, wm, dwdy;
double d2wdy2, den1, den2, den3, strikept, strikemt, wpt, wmt, dwdt;
Integrate integrate = new Integrate(this);
for (int i = 0; i < nmat; i++)
{
t = locVolMat[i];
forwardValue = Hdataset.S0 * Math.Exp(integrate.AdaptLobatto(0.0, t));
for (int j = 0; j < nstrike; j++)
{
strike = locVolStr[j];
y = Math.Log(strike / forwardValue);
dy = ((Math.Abs(y) > 0.001) ? y * 0.0001 : 0.000001);
// strike derivative
strikep = strike * Math.Exp(dy);
strikem = strike / Math.Exp(dy);
w = impVol.Evaluate(t, strike);
wp = impVol.Evaluate(t, strikep);
wm = impVol.Evaluate(t, strikem);
dwdy = (wp - wm) / (2.0 * dy);
d2wdy2 = (wp - 2.0 * w + wm) / (dy * dy);
// time derivative
if (t == 0.0)
{
dt = 0.0001;
strikept = strike * Math.Exp(integrate.AdaptLobatto(0.0, t + dt));
wpt = impVol.Evaluate(t + dt, strikept);
// if (wpt < w)
// Console.WriteLine("Decreasing variance at strike {0} between time {1} and time {2}", strike, t, t + dt);
dwdt = (wpt - w) / dt;
}
else
{
dt = Math.Min(0.0001, t / 2.0);
strikept = strike * Math.Exp(integrate.AdaptLobatto(t, t + dt));
strikemt = strike * Math.Exp(-integrate.AdaptLobatto(t - dt, t));
wpt = impVol.Evaluate(t + dt, strikept);
wmt = impVol.Evaluate(t + dt, strikemt);
//if (wpt < w)
// Console.WriteLine("Decreasing variance at strike {0} between time {1} and time {2}", strike, t, t + dt);
//if (w < wmt)
// Console.WriteLine("Decreasing variance at strike {0} between time {1} and time {2}", strike, t-dt, t);
dwdt = (wpt - wmt) / (2.0 * dt);
}
if (dwdy == 0.0 && d2wdy2 == 0.0)
locVolMatrix[i, j] = Math.Sqrt(dwdt);
else
{
den1 = 1.0 - y / w * dwdy;
den2 = 0.25 * (-0.25 - 1.0 / w + y * y / w / w) * dwdy * dwdy;
den3 = 0.5 * d2wdy2;
locVolMatrix[i, j] = dwdt / (den1 + den2 + den3);
//if (locVolMatrix[i,j] < 0.0)
// Console.WriteLine("Negative local vol^2 at strike {0} and time {1}; " +
// "Black vol surface is not smooth enought.", strike, t);
}
}
}
// Create dupire outputs.
Console.WriteLine(locVolMat);
PFunction2D.PFunction2D localVol = new PFunction2D.PFunction2D(locVolMat, locVolStr, locVolMatrix);
localVol.Parse(null);
string[] names = new string[] { "S0" };
Vector param = new Vector(1);
param[0] = Hdataset.S0;
EstimationResult result = new EstimationResult(names, param);
//result.Objects = new object[3];
result.Objects = new object[4];
result.Objects[0] = this.r;
result.Objects[1] = this.q;
result.Objects[2] = localVol;
result.Objects[3] = impVol;
//Console.WriteLine("r = " + HCalData.Rate.ToString());
//Console.WriteLine("q = " + HCalData.DividendYield.ToString());
return result;
}
/// <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;
}
/// <summary>
/// Attempts a calibration through <see cref="CapsCIROptimizationProblem"/>
/// 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">A controller used for the optimization 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;
// Creates the context.
Document doc = new Document();
ProjectROV prj = new ProjectROV(doc);
doc.Part.Add(prj);
CapCIROptimizationProblem problem = new CapCIROptimizationProblem(dataset);
IOptimizationAlgorithm solver = new QADE();
IOptimizationAlgorithm solver2 = new SteepestDescent();
DESettings o = new DESettings();
o.NP = 50;
o.MaxIter = 50;
o.Verbosity = 1;
o.Parallel = false;
o.controller = controller;
SolutionInfo solution = null;
Vector x0 = new Vector(new double[] { 1, 0.01, 0.05 });
solution = solver.Minimize(problem, o, x0);
if (solution.errors)
return new EstimationResult(solution.message);
o.epsilon = 10e-10;
o.h = 10e-10;
o.MaxIter = 1000;
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:");
Console.WriteLine(solution);
string[] names = CIR.parameterNames;
Vector values = new Vector(4);
values[Range.New(0, 2)] = solution.x;
values[3] = problem.r0;
EstimationResult result = new EstimationResult(names, values);
return result;
}
/// <summary>
/// Attempts a calibration through <see cref="CapsCIROptimizationProblem"/>
/// 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">A controller used for the optimization 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;
// Creates the context.
Document doc = new Document();
ProjectROV prj = new ProjectROV(doc);
doc.Part.Add(prj);
CapCIROptimizationProblem problem = new CapCIROptimizationProblem(dataset);
IOptimizationAlgorithm solver = new QADE();
IOptimizationAlgorithm solver2 = new SteepestDescent();
DESettings o = new DESettings();
o.NP = 50;
o.MaxIter = 50;
o.Verbosity = 1;
o.Parallel = false;
o.controller = controller;
SolutionInfo solution = null;
Vector x0 = new Vector(new double[] { 1, 0.01, 0.05 });
solution = solver.Minimize(problem, o, x0);
if (solution.errors)
{
return(new EstimationResult(solution.message));
}
o.epsilon = 10e-10;
o.h = 10e-10;
o.MaxIter = 1000;
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:");
Console.WriteLine(solution);
string[] names = CIR.parameterNames;
Vector values = new Vector(4);
values[Range.New(0, 2)] = solution.x;
values[3] = problem.r0;
EstimationResult result = new EstimationResult(names, values);
return(result);
}
public void Test()
{
// Tests HW1 dynamics comparing the price of a call option on a bond
// calculated through simulation and the theoretical one.
Engine.MultiThread = true;
Document doc = new Document();
ProjectROV rov = new ProjectROV(doc);
doc.Part.Add(rov);
doc.DefaultProject.NMethods.m_UseAntiteticPaths = true;
int n_sim = 20000;
int n_steps = 1024;
double a = 0.2;
double DR = 0.02;
double r0 = 0.015;
double a1 = 0.02;
double sigma1 = 0.01;
double maturityOpt = 5.0;
double strike = 0.98192;
double tau = 1.0;
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 Pa = new ModelParameter(a, "a");
Pa.VarName = "a";
rov.Symbols.Add(Pa);
ModelParameter PDR = new ModelParameter(DR, "PDR");
PDR.VarName = "DR";
rov.Symbols.Add(PDR);
ModelParameter Pr0 = new ModelParameter(r0, "r0");
Pr0.VarName = "r0";
rov.Symbols.Add(Pr0);
ModelParameter Pstrike = new ModelParameter(strike, "strike");
Pstrike.VarName = "strike";
rov.Symbols.Add(Pstrike);
AFunction zerorate = new AFunction(rov);
zerorate.VarName = "zr";
zerorate.m_IndependentVariables = 1;
zerorate.m_Value = (RightValue)("(1-exp(-a*x1))*DR + r0");
rov.Symbols.Add(zerorate);
HW1 process = new HW1(a1, sigma1, "@zr");
StochasticProcessExtendible s = new StochasticProcessExtendible(rov, process);
rov.Processes.AddProcess(s);
// Set the discounting.
RiskFreeInfo rfi = rov.GetDiscountingModel() as RiskFreeInfo;
rfi.ActualizationType = EActualizationType.Stochastic;
rfi.m_deterministicRF = (ModelParameter)"@V1";
OptionTree op = new OptionTree(rov);
op.PayoffInfo.PayoffExpression = "Max(bond(TT;TT+tau;@v1)-strike;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 samplePrice = price.value;
double sampleDevSt = price.stdDev / Math.Sqrt((double)n_sim);
// Calculation of the theoretical value of the call.
CapHW1 cap = new CapHW1(zerorate);
double d1 = cap.D1(a1, sigma1, maturityOpt, maturityOpt + tau, strike);
double d2 = cap.D2(a1, sigma1, maturityOpt, maturityOpt + tau, strike);
double theoreticalPrice = ZCB(zerorate, maturityOpt + tau) * SpecialFunctions.NormCdf(d1) - strike * ZCB(zerorate, maturityOpt) * SpecialFunctions.NormCdf(d2);
Console.WriteLine("Theoretical Price = " + theoreticalPrice.ToString());
Console.WriteLine("Monte Carlo Price = " + samplePrice);
Console.WriteLine("Standard Deviation = " + sampleDevSt.ToString());
double tol = 4.0 * sampleDevSt;
Assert.Less(Math.Abs(theoreticalPrice - samplePrice), 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 = 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()
{
// Tests HW1 dynamics comparing the price of a call option on a bond
// calculated through simulation and the theoretical one.
Engine.MultiThread = true;
Document doc = new Document();
ProjectROV rov = new ProjectROV(doc);
doc.Part.Add(rov);
doc.DefaultProject.NMethods.m_UseAntiteticPaths = true;
int n_sim = 20000;
int n_steps = 1024;
double a = 0.2;
double DR = 0.02;
double r0 = 0.015;
double a1 = 0.02;
double sigma1 = 0.01;
double maturityOpt = 5.0;
double strike = 0.98192;
double tau = 1.0;
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 Pa = new ModelParameter(a, "a");
Pa.VarName = "a";
rov.Symbols.Add(Pa);
ModelParameter PDR = new ModelParameter(DR, "PDR");
PDR.VarName = "DR";
rov.Symbols.Add(PDR);
ModelParameter Pr0 = new ModelParameter(r0, "r0");
Pr0.VarName = "r0";
rov.Symbols.Add(Pr0);
ModelParameter Pstrike = new ModelParameter(strike, "strike");
Pstrike.VarName = "strike";
rov.Symbols.Add(Pstrike);
AFunction zerorate = new AFunction(rov);
zerorate.VarName = "zr";
zerorate.m_IndependentVariables = 1;
zerorate.m_Value = (RightValue)("(1-exp(-a*x1))*DR + r0");
rov.Symbols.Add(zerorate);
HW1 process = new HW1(a1, sigma1, "@zr");
StochasticProcessExtendible s = new StochasticProcessExtendible(rov, process);
rov.Processes.AddProcess(s);
// Set the discounting.
RiskFreeInfo rfi = rov.GetDiscountingModel() as RiskFreeInfo;
rfi.ActualizationType = EActualizationType.Stochastic;
rfi.m_deterministicRF = (ModelParameter)"@V1";
OptionTree op = new OptionTree(rov);
op.PayoffInfo.PayoffExpression = "Max(bond(TT;TT+tau;@v1)-strike;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 samplePrice = price.value;
double sampleDevSt = price.stdDev / Math.Sqrt((double)n_sim);
// Calculation of the theoretical value of the call.
CapHW1 cap = new CapHW1(zerorate);
double d1 = cap.D1(a1, sigma1, maturityOpt, maturityOpt + tau, strike);
double d2 = cap.D2(a1, sigma1, maturityOpt, maturityOpt + tau, strike);
double theoreticalPrice = ZCB(zerorate, maturityOpt + tau) * SpecialFunctions.NormCdf(d1) - strike * ZCB(zerorate, maturityOpt) * SpecialFunctions.NormCdf(d2);
Console.WriteLine("Theoretical Price = " + theoreticalPrice.ToString());
Console.WriteLine("Monte Carlo Price = " + samplePrice);
Console.WriteLine("Standard Deviation = " + sampleDevSt.ToString());
double tol = 4.0 * sampleDevSt;
Assert.Less(Math.Abs(theoreticalPrice - samplePrice), tol);
}
/// <summary>
///
/// </summary>
/// <param name="p_VarCov">input Covariance Matrix</param>
/// <param name="p_kappa"> input mean reverting coefficient</param>
/// <param name="p_mean_series">Historical Mean vector</param>
/// <param name="p_log">true if the component is a log mean reverting</param>
/// <param name="p_deltat">vector of deltaT</param>
/// <param name="p_ProbTreshold">p in the report</param>
/// <param name="p_AUM">let to false</param>
/// <param name="p_MCR">number of children when montecarlo (Z in the Report)</param>
/// <param name="p_seed"></param>
public MultivariateTree(ProjectROV project)
{
this.prj = project;
}
public void Test()
{
Engine.MultiThread = true;
Document doc = new Document();
ProjectROV rov = new ProjectROV(doc);
doc.Part.Add(rov);
doc.DefaultProject.NMethods.m_UseAntiteticPaths = true;
int n_sim = 10000;
int n_steps = 512;
double a = 0.2;
double DR = 0.02;
double r0 = 0.015;
double a1 = 1.0;
double sigma1 = 0.01;
double a2 = 0.1;
double sigma2 = 0.0165;
double correlation = 0.6;
double maturityOpt = 5.0;
double strike = 0.927;
double tau = 2.0;
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 Pa = new ModelParameter(a, "a");
Pa.VarName = "a";
rov.Symbols.Add(Pa);
ModelParameter PDR = new ModelParameter(DR, "PDR");
PDR.VarName = "DR";
rov.Symbols.Add(PDR);
ModelParameter Pr0 = new ModelParameter(r0, "r0");
Pr0.VarName = "r0";
rov.Symbols.Add(Pr0);
ModelParameter Pstrike = new ModelParameter(strike, "strike");
Pstrike.VarName = "strike";
rov.Symbols.Add(Pstrike);
AFunction zerorate = new AFunction(rov);
zerorate.VarName = "zr";
zerorate.m_IndependentVariables = 1;
zerorate.m_Value = (RightValue)("(1-exp(-a*x1))*DR + r0");
rov.Symbols.Add(zerorate);
HW2ProcessType pt = new HW2ProcessType();
// Set the short rate process.
pt = HW2ProcessType.ShortRate;
StocasticProcessHW2 process1 = new StocasticProcessHW2(rov, pt);
process1.zero_rate_curve = "@zr";
process1._a = (ModelParameter)a1;
process1._b = (ModelParameter)sigma1;
rov.Processes.AddProcess(process1);
// Set the mean reversion process.
pt = HW2ProcessType.Unobservable;
StocasticProcessHW2 process2 = new StocasticProcessHW2(rov, pt);
process2._a = (ModelParameter)a2;
process2._b = (ModelParameter)sigma2;
rov.Processes.AddProcess(process2);
// Set the correlation.
rov.Processes.r[0, 1] = (RightValue)correlation;
// Set the discounting.
RiskFreeInfo rfi = rov.GetDiscountingModel() as RiskFreeInfo;
rfi.ActualizationType = EActualizationType.Stochastic;
rfi.m_deterministicRF = (ModelParameter)"@v1";
OptionTree op = new OptionTree(rov);
op.PayoffInfo.PayoffExpression = "max(bond(TT;TT+tau;@v1)-strike;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 sampleMean = price.value;
double sampleDevSt = price.stdDev / Math.Sqrt((double)n_sim);
double theoreticalPrice = HW2BondCall(zerorate, maturityOpt, maturityOpt + tau, strike,
a1, sigma1, a2, sigma2, correlation);
Console.WriteLine("\nTheoretical Price = " + theoreticalPrice.ToString());
Console.WriteLine("Monte Carlo Price = " + sampleMean.ToString());
Console.WriteLine("Standard Deviation = " + sampleDevSt.ToString());
bool result;
double fact = 4.0;
result = (Math.Abs(sampleMean - theoreticalPrice) < fact * sampleDevSt);
Assert.IsTrue(result);
}
public void TestSimulation()
{
Engine.MultiThread = true;
Document doc = new Document();
ProjectROV rov = new ProjectROV(doc);
doc.Part.Add(rov);
doc.DefaultProject.NMethods.m_UseAntiteticPaths = true;
int n_sim = 10000;
int n_steps = 512;
double strike = 90.0;
double maturity = 2.0;
double rate = 0.1;
double dy = 0.05;
double volatility = 0.2;
double S0 = 100;
ModelParameter Pstrike = new ModelParameter(strike, string.Empty, "strike");
rov.Symbols.Add(Pstrike);
ModelParameter PS0 = new ModelParameter(S0, string.Empty, "S0");
rov.Symbols.Add(PS0);
AFunction payoff = new AFunction(rov);
payoff.VarName = "payoff";
payoff.m_IndependentVariables = 1;
payoff.m_Value = (RightValue)("max(x1 - strike ; 0)");
rov.Symbols.Add(payoff);
AFunction rfunc = new AFunction(rov);
rfunc.VarName = "r";
rfunc.m_IndependentVariables = 1;
rfunc.m_Value = (RightValue)rate;
rov.Symbols.Add(rfunc);
AFunction qfunc = new AFunction(rov);
qfunc.VarName = "q";
qfunc.m_IndependentVariables = 1;
qfunc.m_Value = (RightValue)dy;
rov.Symbols.Add(qfunc);
AFunction volfunc = new AFunction(rov);
volfunc.VarName = "localvol";
volfunc.m_IndependentVariables = 2;
volfunc.m_Value = (RightValue)volatility;
rov.Symbols.Add(volfunc);
DupireProcess process = new DupireProcess();
process.s0 = (ModelParameter)"S0";
process.r = (ModelParameter)"@r";
process.q = (ModelParameter)"@q";
process.localVol = (ModelParameter)"@localvol";
StochasticProcessExtendible s = new StochasticProcessExtendible(rov, process);
rov.Processes.AddProcess(s);
// Set the discounting.
RiskFreeInfo rfi = rov.GetDiscountingModel() as RiskFreeInfo;
rfi.ActualizationType = EActualizationType.RiskFree;
rfi.m_deterministicRF = rate;
OptionTree op = new OptionTree(rov);
op.PayoffInfo.PayoffExpression = "payoff(v1)";
op.PayoffInfo.Timing.EndingTime.m_Value = (RightValue)maturity;
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 samplePrice = price.value;
double sampleDevSt = price.stdDev / Math.Sqrt((double)n_sim);
// Calculation of the theoretical value of the call.
double theoreticalPrice = BlackScholes.Call(rate, S0, strike, volatility, maturity, dy);
Console.WriteLine("Theoretical Price = " + theoreticalPrice.ToString());
Console.WriteLine("Monte Carlo Price = " + samplePrice);
Console.WriteLine("Standard Deviation = " + sampleDevSt.ToString());
double tol = 4.0 * sampleDevSt;
Assert.LessOrEqual(Math.Abs(theoreticalPrice - samplePrice), tol);
}
/// <summary>
/// Attempts to solve the Heston optimization problem using
/// <see cref="Heston.HestonOptimizationProblem"/>.
/// </summary>
/// <param name="marketData">Data to be used in order to perform the optimization.</param>
/// <param name="settings">The parameter is not used.</param>
/// <param name="controller">IController.</param>
/// <returns>The results of the optimization.</returns>
public EstimationResult Estimate(List <object> marketData, IEstimationSettings settings = null, IController controller = null, Dictionary <string, object> properties = null)
{
DateTime t0 = DateTime.Now;
var interestDataSet = (CurveMarketData)marketData[0];
CallPriceMarketData callDataSet = (CallPriceMarketData)marketData[1];
EquityCalibrationData equityCalData = new EquityCalibrationData(callDataSet, interestDataSet);
var spotPrice = (DVPLI.MarketDataTypes.Scalar)marketData[2];
Setup(equityCalData, settings);
var calSettings = settings as HestonCalibrationSettings;
// Creates the context.
Document doc = new Document();
ProjectROV prj = new ProjectROV(doc);
doc.Part.Add(prj);
// Optimization problem instance.
Vector matBound = new Vector(2);
Vector strikeBound = new Vector(2);
if (calSettings != null)
{
matBound[0] = calSettings.MinMaturity;
matBound[1] = calSettings.MaxMaturity;
strikeBound[0] = calSettings.MinStrike;
strikeBound[1] = calSettings.MaxStrike;
}
else
{
//use defaults
matBound[0] = 1.0 / 12; // .25;
matBound[1] = 6; // 10; //Up to 6Y maturities
strikeBound[0] = 0.4;
strikeBound[1] = 1.6;
}
Console.WriteLine(callDataSet);
/*
* //CBA TEST
* matBound[0] = 1;// .25;
* matBound[1] = 3.5;// 10; //Up to 6Y maturities
* strikeBound[0] = 0.5;// 0.5;
* strikeBound[1] = 2;//1.5;
*/
HestonCallOptimizationProblem problem = NewOptimizationProblem(equityCalData, matBound, strikeBound);
int totalOpts = problem.numCall + problem.numPut;
Console.WriteLine("Calibration based on " + totalOpts + " options. (" + problem.numCall + " call options and " + problem.numPut + " put options).");
IOptimizationAlgorithm solver = new QADE();
//IOptimizationAlgorithm solver = new MultiLevelSingleLinkage();
IOptimizationAlgorithm solver2 = new SteepestDescent();
DESettings o = new DESettings();
o.controller = controller;
// If true the optimization algorithm will operate in parallel.
o.Parallel = Engine.MultiThread;
o.h = 10e-8;
o.epsilon = 10e-8;
SolutionInfo solution = null;
double minObj = double.MaxValue;
Vector minX = null;
int Z = 1;
//if (problem.GetType() == typeof(Heston.HestonCallSimulationOptimizationProblem))
// Z = 2;
for (int z = 0; z < Z; z++)
{
if (solver.GetType() == typeof(MultiLevelSingleLinkage))
{
o.NP = 50;
o.MaxIter = 25;
o.MaxGamma = 6;
}
else
{
o.NP = 60;
o.MaxIter = 35;
}
o.Verbosity = 1;
Vector x0 = null;// new Vector(new double[] { 0.5, 0.5, 0.8, -0.5, 0.05 });
// GA
solution = solver.Minimize(problem, o, x0);
if (solution.errors)
{
return(null);
}
o.options = "qn";
o.MaxIter = 500;// 1000;
if (solution != null)
{
solution = solver2.Minimize(problem, o, solution.x);
}
else
{
solution = solver2.Minimize(problem, o, x0);
}
if (solution.errors)
{
return(null);
}
if (solution.obj < minObj)
{
minObj = solution.obj;
minX = solution.x.Clone();
}
}
solution.obj = minObj;
solution.x = minX;
//Displays pricing error structure
HestonCallOptimizationProblem.displayObjInfo = true;
problem.Obj(solution.x);
HestonCallOptimizationProblem.displayObjInfo = false;
Console.WriteLine("Calibration Time (s)\t" + (DateTime.Now - t0).TotalSeconds);
return(BuildEstimate(spotPrice, interestDataSet, callDataSet, equityCalData, solution));
}
public void Test()
{
Engine.MultiThread = true;
Document doc = new Document();
ProjectROV rov = new ProjectROV(doc);
doc.Part.Add(rov);
doc.DefaultProject.NMethods.m_UseAntiteticPaths = true;
int n_sim = 50000;
int n_steps = 512;
double strike = 100.0;
double tau = 5.0;
double rate = 0.1;
double dy = 0.07;
ModelParameter pStrike = new ModelParameter(strike, "strike");
pStrike.VarName = "strike";
rov.Symbols.Add(pStrike);
ModelParameter pRate = new ModelParameter(rate, "rfrate");
pRate.VarName = "rfrate";
rov.Symbols.Add(pRate);
AFunction payoff = new AFunction(rov);
payoff.VarName = "payoff";
payoff.m_IndependentVariables = 1;
payoff.m_Value = (RightValue)("max(x1 - strike ; 0)");
rov.Symbols.Add(payoff);
HestonProcess process = new HestonProcess();
process.r = (ModelParameter)rate;
process.q = (ModelParameter)dy;
process.k = (ModelParameter)2.5;
process.theta = (ModelParameter)0.4;
process.sigma = (ModelParameter)0.2;
process.S0 = (ModelParameter)100.0;
process.V0 = (ModelParameter)0.3;
StochasticProcessExtendible s = new StochasticProcessExtendible(rov, process);
rov.Processes.AddProcess(s);
// Set the discounting.
RiskFreeInfo rfi = rov.GetDiscountingModel() as RiskFreeInfo;
rfi.ActualizationType = EActualizationType.RiskFree;
rfi.m_deterministicRF = rate;
OptionTree op = new OptionTree(rov);
op.PayoffInfo.PayoffExpression = "payoff(v1a)";
op.PayoffInfo.Timing.EndingTime.m_Value = (RightValue)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)
{
Console.WriteLine(rov.m_RuntimeErrorList[0]);
}
Assert.IsFalse(rov.HasErrors);
ResultItem price = rov.m_ResultList[0] as ResultItem;
double samplePrice = price.value;
double sampleDevSt = price.stdDev / Math.Sqrt((double)n_sim);
// Calculates the theoretical value of the call.
Vector param = new Vector(5);
param[0] = process.k.V();
param[1] = process.theta.V();
param[2] = process.sigma.V();
param[3] = 0.0;
param[4] = process.V0.V();
HestonCall hestonCall = new HestonCall();
double thPrice = hestonCall.HestonCallPrice(param, process.S0.V(),
tau, strike, rate, dy);
Console.WriteLine("Theoretical Price = " + thPrice.ToString());
Console.WriteLine("Monte Carlo Price = " + samplePrice);
Console.WriteLine("Standard Deviation = " + sampleDevSt.ToString());
double tol = 4.0 * sampleDevSt;
Assert.Less(Math.Abs(thPrice - samplePrice), tol);
}
/// <summary>
/// Assigns new trial values for x in order to use it
/// for the evaluation of the constraints and the objective function.
/// </summary>
/// <param name="project">The project where to evaluate.</param>
/// <param name="x">The vector of x values.</param>
/// <returns>A <see cref="SquaredGaussianModel"/> set with the values.</returns>
internal static SquaredGaussianModel Assign(ProjectROV project, Vector x)
{
Engine.Parser.NewContext();
SquaredGaussianModel model = project.Processes[0].Plugin as SquaredGaussianModel;
// Assign the new values.
ModelParameter a1 = model.a1 as ModelParameter;
ModelParameter s1 = model.sigma1 as ModelParameter;
a1.m_Value = (RightValue)x[0];
s1.m_Value = (RightValue)x[1];
bool errors=model.Parse(null);
if (errors)
throw new Exception("Cannot Assing model");
return model;
}
public static void Calculate(double t1, double t2, double simEnd, int numSim, int numSteps, out double val, out double stDev)
{
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);
// To be changed to 350000.
int n_sim = numSim;
int n_steps = numSteps;
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);
// Set the discounting.
RiskFreeInfo rfi = rov.GetDiscountingModel() as RiskFreeInfo;
rfi.ActualizationType = EActualizationType.RiskFree;
rfi.m_deterministicRF = 0.0;
OptionTree op = new OptionTree(rov);
op.PayoffInfo.PayoffExpression = "bond(" + t1.ToString() + ";" + t2.ToString() + ";@v1)";
// Here we put the simulation maturity.
op.PayoffInfo.Timing.EndingTime.m_Value = (RightValue)simEnd;
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]);
}
ResultItem price = rov.m_ResultList[0] as ResultItem;
val = price.value;
stDev = price.stdDev / Math.Sqrt((double)numSim);
}
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 = 5000;
int n_steps = 900;
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);
// Set the discounting.
RiskFreeInfo rfi = rov.GetDiscountingModel() as RiskFreeInfo;
rfi.ActualizationType = EActualizationType.RiskFree;
rfi.m_deterministicRF = 0.0;
OptionTree op = new OptionTree(rov);
op.PayoffInfo.PayoffExpression = "bond(t;10;@v1)";
// Set the simulation maturity.
op.PayoffInfo.Timing.EndingTime.m_Value = (RightValue)2.0;
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;
Console.WriteLine("Bond Test Value = " + price.value.ToString());
Assert.LessOrEqual(Math.Abs(0.6702 - price.value), .01);
// Try to do some simple tests and check the results.
double b0_10 = process.Bond(DynamicParam(0, process), process.CacheDates, 0, 0, 10);
Console.WriteLine("Bond(0,10) = " + b0_10);
Assert.LessOrEqual(Math.Abs(b0_10 - 0.606513), .001);
double b7_10 = process.Bond(DynamicParam(0.00427631, process), process.CacheDates, 0, 7, 10);
Console.WriteLine("Bond(7,10) = " + b7_10);
Assert.LessOrEqual(Math.Abs(b7_10 - 0.856374), .001);
double b7_30 = process.Bond(DynamicParam(0.00427631, process), process.CacheDates, 0, 7, 30);
}
public void Test()
{
Engine.MultiThread = true;
Document doc = new Document();
ProjectROV rov = new ProjectROV(doc);
doc.Part.Add(rov);
doc.DefaultProject.NMethods.m_UseAntiteticPaths = true;
int n_sim = 20000;
int n_steps = 1024;
double a = 0.2;
double DR = 0.02;
double r0 = 0.015;
double a1 = 0.02;
double sigma1 = 0.01;
double maturityOpt = 5.0;
double strike = 0.005;
double tau = 0.5;
double strike2 = 1.0 / (1.0 + strike * tau);
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 Pa = new ModelParameter(a, "a");
Pa.VarName = "a";
rov.Symbols.Add(Pa);
ModelParameter PDR = new ModelParameter(DR, "PDR");
PDR.VarName = "DR";
rov.Symbols.Add(PDR);
ModelParameter Pr0 = new ModelParameter(r0, "r0");
Pr0.VarName = "r0";
rov.Symbols.Add(Pr0);
ModelParameter Pstrike = new ModelParameter(strike, "strike");
Pstrike.VarName = "strike";
rov.Symbols.Add(Pstrike);
AFunction zerorate = new AFunction(rov);
zerorate.VarName = "zr";
zerorate.m_IndependentVariables = 1;
zerorate.m_Value = (RightValue)("(1-exp(-a*x1))*DR + r0");
rov.Symbols.Add(zerorate);
HW1 process = new HW1(a1, sigma1, "@zr");
StochasticProcessExtendible s = new StochasticProcessExtendible(rov, process);
rov.Processes.AddProcess(s);
// Set the discounting.
RiskFreeInfo rfi = rov.GetDiscountingModel() as RiskFreeInfo;
rfi.ActualizationType = EActualizationType.Stochastic;
rfi.m_deterministicRF = (ModelParameter)"@V1";
OptionTree op = new OptionTree(rov);
// 1) RATE FUNCTION, with this the price is higher than the theoretical one
// op.PayoffInfo.PayoffExpression = "tau*max(rate(TT;tau;@v1) - strike; 0)";
// 2) OBTAIN RATE FROM bond = exp(-rate*t),
// with this the price is higher than the theoretical one but it's more near than 1)
// op.PayoffInfo.PayoffExpression = "tau*max(-ln(bond(TT;TT+tau;@v1))/tau - strike; 0)";
// 3) CONVERT RATE from discrete to continuous through (1+r_d) = exp(r_c)
// In this way the price is the same as the theoretical one.
op.PayoffInfo.PayoffExpression = "tau*max(ln(1+rate(TT;tau;@v1)) - strike; 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 samplePrice = price.value;
double sampleDevSt = price.stdDev / Math.Sqrt(2.0 * (double)n_sim);
// Calculation of the theoretical value of the caplet.
CapHW1 cap = new CapHW1(zerorate);
double theoreticalPrice = cap.HWCaplet(a1, sigma1, maturityOpt,
maturityOpt + tau, strike2);
Console.WriteLine("Theoretical Price = " + theoreticalPrice.ToString());
Console.WriteLine("Monte Carlo Price = " + samplePrice);
Console.WriteLine("Standard Deviation = " + sampleDevSt.ToString());
double tol = 4.0 * sampleDevSt;
Assert.Less(Math.Abs(theoreticalPrice - samplePrice), tol);
}
public void TestSimulation()
{
Engine.MultiThread = true;
Document doc = new Document();
ProjectROV rov = new ProjectROV(doc);
doc.Part.Add(rov);
doc.DefaultProject.NMethods.m_UseAntiteticPaths = true;
int n_sim = 10000;
int n_steps = 512;
double strike = 90.0;
double maturity = 2.0;
double rate = 0.1;
double dy = 0.05;
double volatility = 0.2;
double S0 = 100;
ModelParameter Pstrike = new ModelParameter(strike, string.Empty, "strike");
rov.Symbols.Add(Pstrike);
ModelParameter PS0 = new ModelParameter(S0, string.Empty, "S0");
rov.Symbols.Add(PS0);
AFunction payoff = new AFunction(rov);
payoff.VarName = "payoff";
payoff.m_IndependentVariables = 1;
payoff.m_Value = (RightValue)("max(x1 - strike ; 0)");
rov.Symbols.Add(payoff);
AFunction rfunc = new AFunction(rov);
rfunc.VarName = "r";
rfunc.m_IndependentVariables = 1;
rfunc.m_Value = (RightValue)rate;
rov.Symbols.Add(rfunc);
AFunction qfunc = new AFunction(rov);
qfunc.VarName = "q";
qfunc.m_IndependentVariables = 1;
qfunc.m_Value = (RightValue)dy;
rov.Symbols.Add(qfunc);
AFunction volfunc = new AFunction(rov);
volfunc.VarName = "localvol";
volfunc.m_IndependentVariables = 2;
volfunc.m_Value = (RightValue)volatility;
rov.Symbols.Add(volfunc);
DupireProcess process = new DupireProcess();
process.s0 = (ModelParameter)"S0";
process.r = (ModelParameter)"@r";
process.q = (ModelParameter)"@q";
process.localVol = (ModelParameter)"@localvol";
StochasticProcessExtendible s = new StochasticProcessExtendible(rov, process);
rov.Processes.AddProcess(s);
// Set the discounting.
RiskFreeInfo rfi = rov.GetDiscountingModel() as RiskFreeInfo;
rfi.ActualizationType = EActualizationType.RiskFree;
rfi.m_deterministicRF = rate;
OptionTree op = new OptionTree(rov);
op.PayoffInfo.PayoffExpression = "payoff(v1)";
op.PayoffInfo.Timing.EndingTime.m_Value = (RightValue)maturity;
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 samplePrice = price.value;
double sampleDevSt = price.stdDev / Math.Sqrt((double)n_sim);
// Calculation of the theoretical value of the call.
double theoreticalPrice = BlackScholes.Call(rate, S0, strike, volatility, maturity, dy);
Console.WriteLine("Theoretical Price = " + theoreticalPrice.ToString());
Console.WriteLine("Monte Carlo Price = " + samplePrice);
Console.WriteLine("Standard Deviation = " + sampleDevSt.ToString());
double tol = 4.0 * sampleDevSt;
Assert.LessOrEqual(Math.Abs(theoreticalPrice - samplePrice), 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);
}
public void Test()
{
Engine.MultiThread = true;
Document doc = new Document();
ProjectROV rov = new ProjectROV(doc);
doc.Part.Add(rov);
doc.DefaultProject.NMethods.m_UseAntiteticPaths = true;
int n_sim = 100000;
int n_steps = 256;
double strike = 90.0;
double tau = 2.0;
double rate = 0.1;
double dy = 0.07;
ModelParameter pStrike = new ModelParameter(strike, "strike");
pStrike.VarName = "strike";
rov.Symbols.Add(pStrike);
AFunction payoff = new AFunction(rov);
payoff.VarName = "payoff";
payoff.m_IndependentVariables = 1;
payoff.m_Value = (RightValue)("max(x1 - strike ; 0)");
rov.Symbols.Add(payoff);
AFunction zrfunc = new AFunction(rov);
zrfunc.VarName = "zr";
zrfunc.m_IndependentVariables = 1;
zrfunc.m_Value = (RightValue)rate;
rov.Symbols.Add(zrfunc);
AFunction dyfunc = new AFunction(rov);
dyfunc.VarName = "dy";
dyfunc.m_IndependentVariables = 1;
dyfunc.m_Value = (RightValue)dy;
rov.Symbols.Add(dyfunc);
HestonExtendedProcess process = new HestonExtendedProcess();
process.k = (ModelParameter)2.5;
process.theta = (ModelParameter)0.4;
process.sigma = (ModelParameter)0.2;
process.S0 = (ModelParameter)100.0;
process.V0 = (ModelParameter)0.3;
process.zrReference = (ModelParameter)"@zr";
process.dyReference = (ModelParameter)"@dy";
double discount = Math.Exp(-rate * tau);
StochasticProcessExtendible s = new StochasticProcessExtendible(rov, process);
rov.Processes.AddProcess(s);
// Set the discounting.
RiskFreeInfo rfi = rov.GetDiscountingModel() as RiskFreeInfo;
rfi.ActualizationType = EActualizationType.RiskFree;
rfi.m_deterministicRF = 0.0;
OptionTree op = new OptionTree(rov);
op.PayoffInfo.PayoffExpression = "payoff(v1a)";
op.PayoffInfo.Timing.EndingTime.m_Value = (RightValue)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)
{
Console.WriteLine(rov.m_RuntimeErrorList[0]);
}
Assert.IsFalse(rov.HasErrors);
ResultItem price = rov.m_ResultList[0] as ResultItem;
double samplePrice = discount * price.value;
double sampleDevSt = price.stdDev / Math.Sqrt((double)n_sim);
// Calculates the theoretical value of the call.
Vector param = new Vector(5);
param[0] = process.k.V();
param[1] = process.theta.V();
param[2] = process.sigma.V();
param[3] = 0.0;
param[4] = process.V0.V();
HestonCall hestonCall = new HestonCall();
double theoreticalPrice = hestonCall.HestonCallPrice(param, process.S0.V(),
tau, strike, rate, dy);
Console.WriteLine("Theoretical Price = " + theoreticalPrice.ToString());
Console.WriteLine("Monte Carlo Price = " + samplePrice);
Console.WriteLine("Standard Deviation = " + sampleDevSt.ToString());
double tol = 4.0 * sampleDevSt;
Assert.Less(Math.Abs(theoreticalPrice - samplePrice), tol);
}
public void Test()
{
double nu = 0.6;
double theta = -0.2;
double sigma = 0.2;
double rate = 0.02;
double dy = 0.01;
double s0 = 1;
double maturity = 2.0;
double strike = 1.2;
Vector mat = new Vector(1) + maturity;
Vector k = new Vector(1) + strike;
// Calculates the theoretical value of the call.
double theoreticalPrice = VarianceGammaOptionsCalibration.VGCall(theta, sigma, nu,
maturity, strike,
dy, s0, rate);
Engine.MultiThread = true;
Document doc = new Document();
ProjectROV rov = new ProjectROV(doc);
doc.Part.Add(rov);
doc.DefaultProject.NMethods.m_UseAntiteticPaths = true;
int n_sim = 50000;
int n_steps = 512;
ModelParameter paramStrike = new ModelParameter(strike, "strike");
paramStrike.VarName = "strike";
rov.Symbols.Add(paramStrike);
ModelParameter paramRate = new ModelParameter(rate, "rfrate");
paramRate.VarName = "rfrate";
rov.Symbols.Add(paramRate);
AFunction payoff = new AFunction(rov);
payoff.VarName = "payoff";
payoff.m_IndependentVariables = 1;
payoff.m_Value = (RightValue)("max(x1 - strike ; 0)");
rov.Symbols.Add(payoff);
VarianceGamma process = new VarianceGamma(s0, theta, sigma, nu, rate, dy);
StochasticProcessExtendible s = new StochasticProcessExtendible(rov, process);
rov.Processes.AddProcess(s);
// Set the discounting.
RiskFreeInfo rfi = rov.GetDiscountingModel() as RiskFreeInfo;
rfi.ActualizationType = EActualizationType.RiskFree;
rfi.m_deterministicRF = rate;
OptionTree op = new OptionTree(rov);
op.PayoffInfo.PayoffExpression = "payoff(v1)";
op.PayoffInfo.Timing.EndingTime.m_Value = (RightValue)maturity;
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 samplePrice = price.value;
double sampleDevSt = price.stdDev / Math.Sqrt((double)n_sim);
Console.WriteLine("Theoretical Price = " + theoreticalPrice);
Console.WriteLine("Monte Carlo Price = " + samplePrice);
Console.WriteLine("Standard Deviation = " + sampleDevSt.ToString());
double tol = 4.0 * sampleDevSt;
Assert.Less(Math.Abs(theoreticalPrice - samplePrice), tol);
}
public void TestCalibration()
{
InterestRateMarketData IData = InterestRateMarketData.FromFile("../../TestData/IRMD-sample.xml");
CallPriceMarketData HData = CallPriceMarketData.FromFile("../../TestData/CallData-sample.xml");
//InterestRateMarketData IData = InterestRateMarketData.FromFile("../../../EquityModels.Tests/TestData/IRMD-EU-30102012-close.xml");
//CallPriceMarketData HData = CallPriceMarketData.FromFile("../../../EquityModels.Tests/TestData/30102012-SX5E_Index-HestonData.xml");
//CallPriceMarketData HData = ObjectSerialization.ReadFromXMLFile("../../../EquityModels.Tests/TestData/FTSE.xml") as CallPriceMarketData;
List <object> l = new List <object>();
l.Add(IData.DiscountingCurve);
l.Add(HData);
DupireEstimator DE = new DupireEstimator();
DupireCalibrationSettings settings = new DupireCalibrationSettings();
settings.LocalVolatilityCalculation = LocalVolatilityCalculation.Method1;
//settings.LocalVolatilityCalculation = LocalVolatilityCalculation.QuantLib;
EstimationResult res = DE.Estimate(l, settings);
//int nmat = HData.Maturity.Length;
//int nstrike = HData.Strike.Length;
int i = 5; // Maturity.
int j = 4; // Strike.
Engine.MultiThread = true;
Document doc = new Document();
ProjectROV rov = new ProjectROV(doc);
doc.Part.Add(rov);
doc.DefaultProject.NMethods.m_UseAntiteticPaths = true;
int n_sim = 10000;
int n_steps = 500;
double strike = HData.Strike[j];
//double volatility = HData.Volatility[i, j];
/*
* PFunction2D.PFunction2D impvolfunc = new PFunction2D.PFunction2D(rov);
* impvolfunc = res.Objects[3] as PFunction2D.PFunction2D;
* impvolfunc.VarName = "impvol";
* rov.Symbols.Add(impvolfunc);
* double volatility = impvolfunc.Evaluate(HData.Maturity[i], HData.Strike[j]);
*/
double volatility = 0.2;
double maturity = HData.Maturity[i];
ModelParameter Pstrike = new ModelParameter(strike, string.Empty, "strike");
rov.Symbols.Add(Pstrike);
AFunction payoff = new AFunction(rov);
payoff.VarName = "payoff";
payoff.m_IndependentVariables = 1;
payoff.m_Value = (RightValue)("max(x1 - strike ; 0)");
rov.Symbols.Add(payoff);
bool found;
double S0 = PopulateHelper.GetValue("S0", res.Names, res.Values, out found);
ModelParameter PS0 = new ModelParameter(S0, string.Empty, "S0");
rov.Symbols.Add(PS0);
PFunction rfunc = new PFunction(rov);
rfunc = res.Objects[0] as PFunction;
rfunc.VarName = "r";
rov.Symbols.Add(rfunc);
PFunction qfunc = new PFunction(rov);
qfunc = res.Objects[1] as PFunction;
qfunc.VarName = "q";
rov.Symbols.Add(qfunc);
PFunction2D.PFunction2D volfunc = new PFunction2D.PFunction2D(rov);
volfunc = res.Objects[2] as PFunction2D.PFunction2D;
volfunc.VarName = "localvol";
rov.Symbols.Add(volfunc);
DupireProcess process = new DupireProcess();
process.s0 = (ModelParameter)"S0";
process.r = (ModelParameter)"@r";
process.q = (ModelParameter)"@q";
process.localVol = (ModelParameter)"@localvol";
double rate = rfunc.Evaluate(maturity);
double dy = qfunc.Evaluate(maturity);
StochasticProcessExtendible s = new StochasticProcessExtendible(rov, process);
rov.Processes.AddProcess(s);
// Set the discounting.
RiskFreeInfo rfi = rov.GetDiscountingModel() as RiskFreeInfo;
rfi.ActualizationType = EActualizationType.RiskFree;
rfi.m_deterministicRF = rate;
OptionTree op = new OptionTree(rov);
op.PayoffInfo.PayoffExpression = "payoff(v1)";
op.PayoffInfo.Timing.EndingTime.m_Value = (RightValue)maturity;
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 samplePrice = price.value;
double sampleDevSt = price.stdDev / Math.Sqrt((double)n_sim);
Console.WriteLine("Surf = " + volfunc.Expr);
// Calculation of the theoretical value of the call.
double theoreticalPrice = BlackScholes.Call(rate, S0, strike, volatility, maturity, dy);
Console.WriteLine("Theoretical Price = " + theoreticalPrice.ToString());
Console.WriteLine("Monte Carlo Price = " + samplePrice);
Console.WriteLine("Standard Deviation = " + sampleDevSt.ToString());
double tol = 4.0 * sampleDevSt;
doc.WriteToXMLFile("Dupire.fair");
Assert.LessOrEqual(Math.Abs(theoreticalPrice - samplePrice), tol);
}
private EstimationResult QuantLibEstimate(CurveMarketData discoutingCurve, CallPriceMarketData Hdataset)
{
EquityCalibrationData HCalData = new EquityCalibrationData(Hdataset, discoutingCurve);
bool hasArbitrage = HCalData.HasArbitrageOpportunity(10e-2);
if (hasArbitrage)
{
Console.WriteLine("Market data contains arbitrage opportunity");
}
this.r = new DVPLDOM.PFunction(discoutingCurve.Durations, discoutingCurve.Values);
this.q = HCalData.dyFunc as PFunction;
//this.r.Parse(null);
//this.q.Parse(null);
Hdataset.Volatility = new Matrix(Hdataset.CallPrice.R, Hdataset.CallPrice.C);
for (int i = 0; i < Hdataset.Volatility.R; i++)
{
double m = Hdataset.Maturity[i];
for (int j = 0; j < Hdataset.Volatility.C; j++)
{
if (Hdataset.CallPrice[i, j] > 0)
{
var bs = new Fairmat.Finance.BlackScholes(r.Evaluate(m), Hdataset.S0, Hdataset.Strike[j], 0, m, q.Evaluate(m));
//Hdataset.Volatility[i, j] = Hdataset.Volatility[i, j] * Hdataset.Volatility[i, j] * Hdataset.Maturity[i];
//Hdataset.Volatility[i, j] = bs.ImpliedCallVolatility(Hdataset.CallPrice[i, j]);
}
}
}
Console.WriteLine(Hdataset.Volatility);
IFunction impVol = FitImplVolModel(Hdataset);
Document doc = new Document();
ProjectROV prj = new ProjectROV(doc);
doc.Part.Add(prj);
prj.Symbols.Add(impVol);
// doc.WriteToXMLFile("impVol.fair");
int nmat = calibrationSettings.LocalVolatilityMaturities;
int nstrike = calibrationSettings.LocalVolatilityStrikes;
double lastMat = Hdataset.Maturity[SymbolicIntervalExtremes.End];
double lastStr = Hdataset.Strike[SymbolicIntervalExtremes.End];
Vector locVolMat = Vector.Linspace(Hdataset.Maturity[0], lastMat, nmat);
Vector locVolStr = Vector.Linspace(Hdataset.Strike[0], lastStr, nstrike);
Matrix locVolMatrix = new Matrix(nmat, nstrike);
double t, dt, forwardValue, y, dy, strike, strikep, strikem, w, wp, wm, dwdy;
double d2wdy2, den1, den2, den3, strikept, strikemt, wpt, wmt, dwdt;
Integrate integrate = new Integrate(this);
for (int i = 0; i < nmat; i++)
{
t = locVolMat[i];
forwardValue = Hdataset.S0 * Math.Exp(integrate.AdaptLobatto(0.0, t));
for (int j = 0; j < nstrike; j++)
{
strike = locVolStr[j];
y = Math.Log(strike / forwardValue);
dy = ((Math.Abs(y) > 0.001) ? y * 0.0001 : 0.000001);
// strike derivative
strikep = strike * Math.Exp(dy);
strikem = strike / Math.Exp(dy);
w = impVol.Evaluate(t, strike);
wp = impVol.Evaluate(t, strikep);
wm = impVol.Evaluate(t, strikem);
dwdy = (wp - wm) / (2.0 * dy);
d2wdy2 = (wp - 2.0 * w + wm) / (dy * dy);
// time derivative
if (t == 0.0)
{
dt = 0.0001;
strikept = strike * Math.Exp(integrate.AdaptLobatto(0.0, t + dt));
wpt = impVol.Evaluate(t + dt, strikept);
// if (wpt < w)
// Console.WriteLine("Decreasing variance at strike {0} between time {1} and time {2}", strike, t, t + dt);
dwdt = (wpt - w) / dt;
}
else
{
dt = Math.Min(0.0001, t / 2.0);
strikept = strike * Math.Exp(integrate.AdaptLobatto(t, t + dt));
strikemt = strike * Math.Exp(-integrate.AdaptLobatto(t - dt, t));
wpt = impVol.Evaluate(t + dt, strikept);
wmt = impVol.Evaluate(t + dt, strikemt);
//if (wpt < w)
// Console.WriteLine("Decreasing variance at strike {0} between time {1} and time {2}", strike, t, t + dt);
//if (w < wmt)
// Console.WriteLine("Decreasing variance at strike {0} between time {1} and time {2}", strike, t-dt, t);
dwdt = (wpt - wmt) / (2.0 * dt);
}
if (dwdy == 0.0 && d2wdy2 == 0.0)
{
locVolMatrix[i, j] = Math.Sqrt(dwdt);
}
else
{
den1 = 1.0 - y / w * dwdy;
den2 = 0.25 * (-0.25 - 1.0 / w + y * y / w / w) * dwdy * dwdy;
den3 = 0.5 * d2wdy2;
locVolMatrix[i, j] = dwdt / (den1 + den2 + den3);
//if (locVolMatrix[i,j] < 0.0)
// Console.WriteLine("Negative local vol^2 at strike {0} and time {1}; " +
// "Black vol surface is not smooth enought.", strike, t);
}
}
}
// Create dupire outputs.
Console.WriteLine(locVolMat);
PFunction2D.PFunction2D localVol = new PFunction2D.PFunction2D(locVolMat, locVolStr, locVolMatrix);
localVol.Parse(null);
string[] names = new string[] { "S0" };
Vector param = new Vector(1);
param[0] = Hdataset.S0;
EstimationResult result = new EstimationResult(names, param);
//result.Objects = new object[3];
result.Objects = new object[4];
result.Objects[0] = this.r;
result.Objects[1] = this.q;
result.Objects[2] = localVol;
result.Objects[3] = impVol;
//Console.WriteLine("r = " + HCalData.Rate.ToString());
//Console.WriteLine("q = " + HCalData.DividendYield.ToString());
return(result);
}
