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);
}
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;
}
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);
}
public void Test()
{
Engine.MultiThread = true;
Document doc = new Document();
ProjectROV rov = new ProjectROV(doc);
doc.Part.Add(rov);
AFunction zerorate = new AFunction(rov);
zerorate.VarName = "zr";
zerorate.m_IndependentVariables = 1;
zerorate.m_Value = (RightValue)0.05;
rov.Symbols.Add(zerorate);
int n_sim = 4000;
double maturityOpt = 6.5;
// Simulation steps for a year. With stepPerYear = 150 the test will be passed.
// But notice that the price calculated through Monte Carlo is unstable when
// changing this value, even till 1000 steps per year.
int stepsPerYear = 150;
int n_steps = stepsPerYear * ((int)maturityOpt);
double strike = 0.01;
double tau = 0.5;
SquaredGaussianModel process = new SquaredGaussianModel();
process.a1 = (ModelParameter)0.1;
process.sigma1 = (ModelParameter)0.01;
process.zr = (ModelParameter)"@zr";
StochasticProcessExtendible s = new StochasticProcessExtendible(rov, process);
rov.Processes.AddProcess(s);
ModelParameter PT = new ModelParameter(maturityOpt, "TT");
PT.VarName = "TT";
rov.Symbols.Add(PT);
ModelParameter Ptau = new ModelParameter(tau, "tau");
Ptau.VarName = "tau";
rov.Symbols.Add(Ptau);
ModelParameter Pstrike = new ModelParameter(strike, "strike");
Pstrike.VarName = "strike";
rov.Symbols.Add(Pstrike);
// Set the discounting.
RiskFreeInfo rfi = rov.GetDiscountingModel() as RiskFreeInfo;
rfi.ActualizationType = EActualizationType.Stochastic;
rfi.m_deterministicRF = (ModelParameter)"@V1";
// Set the payoff.
OptionTree op = new OptionTree(rov);
op.PayoffInfo.PayoffExpression = "tau*max(rate(TT;tau;@v1) - strike; 0)";
op.PayoffInfo.Timing.EndingTime.m_Value = (RightValue)(maturityOpt + tau);
op.PayoffInfo.European = true;
rov.Map.Root = op;
rov.NMethods.Technology = ETechType.T_SIMULATION;
rov.NMethods.PathsNumber = n_sim;
rov.NMethods.SimulationSteps = n_steps;
ROVSolver solver = new ROVSolver();
solver.BindToProject(rov);
solver.DoValuation(-1);
if (rov.HasErrors)
{
rov.DisplayErrors();
}
Assert.IsFalse(rov.HasErrors);
ResultItem price = rov.m_ResultList[0] as ResultItem;
double mcPrice = price.value;
double mcDevST = price.stdDev / Math.Sqrt((double)n_sim);
Caplet cplt = new Caplet();
Vector Mat, fwd, Rk;
Vector capMatV;
double delta_k;
double capMat;
delta_k = 0.5;
capMat = maturityOpt + tau;
int nmat = 2 * ((int)capMat) + 1;
Mat = new Vector(nmat);
fwd = new Vector(nmat);
Mat[0] = 0;
fwd[0] = zerorate.Evaluate(0);
for (int k = 1; k < nmat; k++)
{
Mat[k] = tau * ((double)k);
fwd[k] = zerorate.Evaluate(Mat[k]) * Mat[k] - zerorate.Evaluate(Mat[k - 1]) * Mat[k - 1];
}
fwd = fwd / tau;
Rk = new Vector(1);
Rk[0] = strike;
capMatV = new Vector(2);
capMatV[0] = maturityOpt;
capMatV[1] = maturityOpt + tau;
Matrix caplet = cplt.PGSMCaplets(process, Mat, fwd, Rk, delta_k, capMatV);
double theoreticalPrice = caplet[1, 0] - caplet[0, 0];
Console.WriteLine("\nTheoretical Price = " + theoreticalPrice.ToString());
Console.WriteLine("Monte Carlo Price = " + mcPrice);
Console.WriteLine("Standard Deviation = " + mcDevST);
double tol = 4.0 * mcDevST;
Assert.Less(Math.Abs(theoreticalPrice - mcPrice), tol);
}
public void Test()
{
Engine.MultiThread = true;
Document doc = new Document();
ProjectROV rov = new ProjectROV(doc);
doc.Part.Add(rov);
AFunction zerorate = new AFunction(rov);
zerorate.VarName = "zr";
zerorate.m_IndependentVariables = 1;
zerorate.m_Value = (RightValue)0.05;
rov.Symbols.Add(zerorate);
int n_sim = 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 = 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);
}
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 = 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()
{
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()
{
// 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);
}
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 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 = 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);
}
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()
{
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 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);
}
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);
}