/// <summary>
/// Returns the root mean square error between market and model call prices
/// </summary>
/// <param name="x">Parameter vector</param>
/// <param name="q">Dividend yield</param>
/// <param name="s0">Index starting value</param>
/// <param name="k">Call strike vector</param>
/// <param name="r">Short rate</param>
/// <param name="cp">Call price matrix</param>
/// <param name="m">Call maturity vector</param>
/// <returns>Call price root mean square error</returns>
public static double VGDiff(Vector x, double q, double s0, Vector k, double r, Matrix cp, Vector m)
{
double y = 0;
double residual;
for (int i = 0; i < m.Length; i++)
{
for (int j = 0; j < k.Length; j++)
{
double par = m[i] / x[2];
double rest = par - Math.Floor(par);
if (rest != 0.5 && rest != 0.0 && cp[i, j] != 0.0)
{
residual = Math.Pow(cp[i, j] - VarianceGammaOptionsCalibration.VGCall(x[0], x[1], x[2], m[i], k[j], q, s0, r), 2);
if (residual > Math.Pow(10, 10) || double.IsNaN(residual))
{
y = y + 1000 * Math.Sqrt(x[0] * x[0] + x[1] * x[1] + x[2] * x[2]);
}
else
{
y = y + residual;
}
}
}
}
return(Math.Sqrt(y / (m.Length * k.Length)));
}
private static Vector Test(int nm, int nk, double q, double s0, double r, double t, double theta, double sigma, double nu)
{
// Simulate synthetic data.
Vector m = new Vector(nm);
Vector k = new Vector(nk);
Matrix cp = new Matrix(nm, nk);
Random rand = new Random();
for (int i = 0; i < nm; i++)
{
m[i] = 0.01 + rand.NextDouble() * 0.99;
}
for (int i = 0; i < nk; i++)
{
k[i] = 60 + rand.NextDouble() * 90;
}
for (int i = 0; i < nm; i++)
{
for (int j = 0; j < nk; j++)
{
cp[i, j] = VarianceGammaOptionsCalibration.VGCall(theta, sigma, nu, m[i], k[j], q, s0, r);
}
}
Console.WriteLine("Benchmark value");
Console.WriteLine(new Vector()
{
theta, sigma, nu
});
Console.WriteLine("Call prices");
Console.WriteLine(cp);
// VGDiff at optimum.
double fopt = VarianceGammaOptimizationProblem.VGDiff(new Vector()
{
theta, sigma, nu
}, q, s0, k, r, cp, m);
Console.WriteLine("fopt");
Console.WriteLine(fopt);
VarianceGammaOptionsCalibration c = new VarianceGammaOptionsCalibration();
List <object> marketData = new List <object>();
var espmd = new EquitySpotMarketData();
espmd.Price = s0;
espmd.RiskFreeRate = r;
espmd.DividendYield = q;
var cpmd = new CallPriceMarketData();
cpmd.Strike = k;
cpmd.Maturity = m;
cpmd.CallPrice = cp;
var dc = new DiscountingCurveMarketData();
dc.Durations = new Vector()
{
0
};
dc.Values = new Vector()
{
r
};
marketData.Add(espmd);
marketData.Add(cpmd);
marketData.Add(dc);
EstimationResult res = c.Estimate(marketData, null);
return((Vector)res.Values);
}
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);
}
private static Vector Test(int nm, int nk, double q, double s0, double r, double t, double theta, double sigma, double nu)
{
// Simulate synthetic data.
Vector m = new Vector(nm);
Vector k = new Vector(nk);
Matrix cp = new Matrix(nm, nk);
Random rand = new Random();
for (int i = 0; i < nm; i++)
{
m[i] = 0.01 + rand.NextDouble() * 0.99;
}
for (int i = 0; i < nk; i++)
{
k[i] = 60 + rand.NextDouble() * 90;
}
for (int i = 0; i < nm; i++)
{
for (int j = 0; j < nk; j++)
{
cp[i, j] = VarianceGammaOptionsCalibration.VGCall(theta, sigma, nu, m[i], k[j], q, s0, r);
}
}
Console.WriteLine("Benchmark value");
Console.WriteLine(new Vector() { theta, sigma, nu });
Console.WriteLine("Call prices");
Console.WriteLine(cp);
// VGDiff at optimum.
double fopt = VarianceGammaOptimizationProblem.VGDiff(new Vector() { theta, sigma, nu }, q, s0, k, r, cp, m);
Console.WriteLine("fopt");
Console.WriteLine(fopt);
VarianceGammaOptionsCalibration c = new VarianceGammaOptionsCalibration();
List<object> marketData = new List<object>();
EquitySpotMarketData espmd = new EquitySpotMarketData();
CallPriceMarketData cpmd = new CallPriceMarketData();
espmd.Price = s0;
espmd.RiskFreeRate = r;
espmd.DividendYield = q;
cpmd.Strike = k;
cpmd.Maturity = m;
cpmd.CallPrice = cp;
marketData.Add(espmd);
marketData.Add(cpmd);
EstimationResult res = c.Estimate(marketData, null);
return (Vector)res.Values;
}
