/// <summary>
/// Constructor for the HW1 Calibration Problem based on caps matrices.
/// </summary>
/// <param name="hw1Caps">
/// A <see cref="HullAndWhiteOneFactor.CapHW1"/> object to use.
/// </param>
/// <param name="blackCaps">A Blacks caps matrix to use.</param>
/// <param name="capMaturity">Vector of cap maturities.</param>
/// <param name="capRate">Vector of cap strikes.</param>
/// <param name="deltaK">Interval between caplets expressed in year.</param>
internal CapsHW1OptimizationProblem(CapHW1 hw1Caps, Matrix blackCaps, Vector capMaturity, Vector capRate, double deltaK)
{
this.hw1Caps = hw1Caps;
this.blackCaps = blackCaps;
this.capMaturity = capMaturity;
this.capRate = capRate;
this.deltaK = deltaK;
}
public void Test()
{
double[,] values = { { .5, .015 },
{ 1, .0165 },
{ 2, .0168 },
{ 3, .0172 },
{ 5, .0182 },
{ 8, .0210 },
{ 10, .025 },
{ 15, .031 },
{ 20, .035 },
{ 30, .037 },
{ 40, .038 }, };
Function zeroratecurve = new PFunction(null);
zeroratecurve.Expr = values;
(zeroratecurve as PFunction).m_Function.iType = EInterpolationType.LINEAR;
// Execute the test.
CapHW1 hwc = new CapHW1(zeroratecurve);
// CAP and FLOOR Tests.
double[] results = new double[2];
results[0] = hwc.HWCap(0.14, 0.02, 0.02, 0.5, 1);
results[1] = hwc.HWCap(0.14, 0.02, 0.02, 0.5, 2);
Console.WriteLine("CAP 2 col 1 row:" + results[0]);
Console.WriteLine("CAP 2 col 2 row:" + results[1]);
// Check the results with previously manually calculated values.
double[] targets = { 0.00214717607719883, 0.0084939015243779 };
double eps = 10e-6;
for (int r = 0; r < results.Length; r++)
{
Assert.LessOrEqual(Math.Abs(targets[r] - results[r]), eps);
}
}
public void Test()
{
double[,] values = { { .5, .015 },
{ 1, .0165 },
{ 2, .0168 },
{ 3, .0172 },
{ 5, .0182 },
{ 8, .0210 },
{ 10, .025 },
{ 15, .031 },
{ 20, .035 },
{ 30, .037 },
{ 40, .038 },
};
Function zeroratecurve = new PFunction(null);
zeroratecurve.Expr = values;
(zeroratecurve as PFunction).m_Function.iType = EInterpolationType.LINEAR;
// Execute the test.
CapHW1 hwc = new CapHW1(zeroratecurve);
// CAP and FLOOR Tests.
double[] results = new double[2];
results[0] = hwc.HWCap(0.14, 0.02, 0.02, 0.5, 1);
results[1] = hwc.HWCap(0.14, 0.02, 0.02, 0.5, 2);
Console.WriteLine("CAP 2 col 1 row:" + results[0]);
Console.WriteLine("CAP 2 col 2 row:" + results[1]);
// Check the results with previously manually calculated values.
double[] targets = { 0.00214717607719883, 0.0084939015243779 };
double eps = 10e-6;
for (int r = 0; r < results.Length; r++)
{
Assert.LessOrEqual(Math.Abs(targets[r] - results[r]), eps);
}
}
/// <summary>
/// Attempts a calibration through <see cref="CapsHW1OptimizationProblem"/>
/// 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;
PFunction zr = new PFunction(null);
zr.VarName = "zr";
var preferences = settings as Fairmat.Calibration.CapVolatilityFiltering;
// Loads ZR
double[,] zrvalue = (double[,])ArrayHelper.Concat(dataset.ZRMarketDates.ToArray(), dataset.ZRMarket.ToArray());
zr.Expr = zrvalue;
BlackModel bm = new BlackModel(zr);
double deltak = dataset.CapTenor;
if (dataset.CapVolatility == null)
return new EstimationResult("Cap not available at requested date");
Matrix capVolatility = dataset.CapVolatility;
Vector capMaturity = dataset.CapMaturity;
Vector capRate = dataset.CapRate;
double a = 0.1;
double sigma = 0.1;
// Matrix calculated with Black.
Matrix blackCaps = new Matrix(capMaturity.Length, capRate.Length);
Matrix logic = new Matrix(capMaturity.Length, capRate.Length);
for (int m = 0; m < capMaturity.Length; m++)
{
for (int s = 0; s < capRate.Length; s++)
{
blackCaps[m, s] = bm.Cap(capRate[s], capVolatility[m, s], deltak, capMaturity[m]);
if (double.IsNaN(blackCaps[m, s]))
{
bm.Cap(capRate[s], capVolatility[m, s], deltak, capMaturity[m]);
throw new Exception("Malformed black caps");
}
if (blackCaps[m, s] == 0.0)
{
logic[m, s] = 0.0;
}
else
{
logic[m, s] = 1.0;
}
//filter
if (preferences != null)
{
if (capRate[s] < preferences.MinCapRate || capRate[s] > preferences.MaxCapRate ||
capMaturity[m]<preferences.MinCapMaturity|| capMaturity[m]>preferences.MaxCapMaturity)
{logic[m, s] = 0; blackCaps[m, s] = 0;}
}
}
}
DateTime t0 = DateTime.Now;
CapHW1 hw1Caps = new CapHW1(zr);
Matrix caps = hw1Caps.HWMatrixCaps(capMaturity, capRate, a, sigma, deltak);
for (int m = 0; m < capMaturity.Length; m++)
{
for (int s = 0; s < capRate.Length; s++)
{
caps[m, s] = logic[m, s] * caps[m, s];
}
}
CapsHW1OptimizationProblem problem = new CapsHW1OptimizationProblem(hw1Caps, blackCaps, capMaturity, capRate, deltak);
Vector provaparam = new Vector(2);
var solver = new QADE();
IOptimizationAlgorithm solver2 = new SteepestDescent();
DESettings o = new DESettings();
o.NP = 20;
o.MaxIter = 10;
o.Verbosity = 1;
o.Parallel = false;
SolutionInfo solution = null;
Vector x0 = new Vector(new double[] { 0.05, 0.01 });
o.controller = controller;
solution = solver.Minimize(problem, o, x0);
o.epsilon = 10e-8;
o.h = 10e-8;
o.MaxIter = 100;
solution = solver2.Minimize(problem, o, solution.x);
if (solution.errors)
return new EstimationResult(solution.message);
Console.WriteLine("Solution:");
Console.WriteLine(solution);
string[] names = new string[] { "Alpha", "Sigma" };
//solution.x[0] *= 3;
EstimationResult result = new EstimationResult(names, solution.x);
result.ZRX = (double[])dataset.ZRMarketDates.ToArray();
result.ZRY = (double[])dataset.ZRMarket.ToArray();
return result;
}
/// <summary>
/// Attempts a calibration through <see cref="CapsHW1OptimizationProblem"/>
/// 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;
PFunction zr = new PFunction(null);
zr.VarName = "zr";
var preferences = settings as Fairmat.Calibration.CapVolatilityFiltering;
// Loads ZR
double[,] zrvalue = (double[, ])ArrayHelper.Concat(dataset.ZRMarketDates.ToArray(), dataset.ZRMarket.ToArray());
zr.Expr = zrvalue;
BlackModel bm = new BlackModel(zr);
double deltak = dataset.CapTenor;
if (dataset.CapVolatility == null)
{
return(new EstimationResult("Cap not available at requested date"));
}
Matrix capVolatility = dataset.CapVolatility;
Vector capMaturity = dataset.CapMaturity;
Vector capRate = dataset.CapRate;
double a = 0.1;
double sigma = 0.1;
// Matrix calculated with Black.
Matrix blackCaps = new Matrix(capMaturity.Length, capRate.Length);
Matrix logic = new Matrix(capMaturity.Length, capRate.Length);
for (int m = 0; m < capMaturity.Length; m++)
{
for (int s = 0; s < capRate.Length; s++)
{
blackCaps[m, s] = bm.Cap(capRate[s], capVolatility[m, s], deltak, capMaturity[m]);
if (double.IsNaN(blackCaps[m, s]))
{
bm.Cap(capRate[s], capVolatility[m, s], deltak, capMaturity[m]);
throw new Exception("Malformed black caps");
}
if (blackCaps[m, s] == 0.0)
{
logic[m, s] = 0.0;
}
else
{
logic[m, s] = 1.0;
}
//filter
if (preferences != null)
{
if (capRate[s] < preferences.MinCapRate || capRate[s] > preferences.MaxCapRate ||
capMaturity[m] < preferences.MinCapMaturity || capMaturity[m] > preferences.MaxCapMaturity)
{
logic[m, s] = 0; blackCaps[m, s] = 0;
}
}
}
}
DateTime t0 = DateTime.Now;
CapHW1 hw1Caps = new CapHW1(zr);
Matrix caps = hw1Caps.HWMatrixCaps(capMaturity, capRate, a, sigma, deltak);
for (int m = 0; m < capMaturity.Length; m++)
{
for (int s = 0; s < capRate.Length; s++)
{
caps[m, s] = logic[m, s] * caps[m, s];
}
}
CapsHW1OptimizationProblem problem = new CapsHW1OptimizationProblem(hw1Caps, blackCaps, capMaturity, capRate, deltak);
Vector provaparam = new Vector(2);
var solver = new QADE();
IOptimizationAlgorithm solver2 = new SteepestDescent();
DESettings o = new DESettings();
o.NP = 20;
o.MaxIter = 10;
o.Verbosity = 1;
o.Parallel = false;
SolutionInfo solution = null;
Vector x0 = new Vector(new double[] { 0.05, 0.01 });
o.controller = controller;
solution = solver.Minimize(problem, o, x0);
o.epsilon = 10e-8;
o.h = 10e-8;
o.MaxIter = 100;
solution = solver2.Minimize(problem, o, solution.x);
if (solution.errors)
{
return(new EstimationResult(solution.message));
}
Console.WriteLine("Solution:");
Console.WriteLine(solution);
string[] names = new string[] { "Alpha", "Sigma" };
//solution.x[0] *= 3;
EstimationResult result = new EstimationResult(names, solution.x);
result.ZRX = (double[])dataset.ZRMarketDates.ToArray();
result.ZRY = (double[])dataset.ZRMarket.ToArray();
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 = 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 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>
/// Constructor for the HW1 Calibration Problem based on caps matrices.
/// </summary>
/// <param name="hw1Caps">
/// A <see cref="HullAndWhiteOneFactor.CapHW1"/> object to use.
/// </param>
/// <param name="blackCaps">A Blacks caps matrix to use.</param>
/// <param name="capMaturity">Vector of cap maturities.</param>
/// <param name="capRate">Vector of cap strikes.</param>
/// <param name="deltaK">Interval between caplets expressed in year.</param>
internal CapsHW1OptimizationProblem(CapHW1 hw1Caps, Matrix blackCaps, Vector capMaturity, Vector capRate, double deltaK)
{
this.hw1Caps = hw1Caps;
this.blackCaps = blackCaps;
this.capMaturity = capMaturity;
this.capRate = capRate;
this.deltaK = deltaK;
}
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);
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);
}
