private double ZCB(AFunction zr, double time)
{
return(Math.Exp(-zr.Evaluate(time) * time));
}
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);
}
private double ZCB(AFunction zr, double t)
{
return Math.Exp(-zr.Evaluate(t) * t);
}
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);
}