/// <summary>
/// This method allows to fit the implied volatility using different models.
/// </summary>
/// <param name="Hdataset"></param>
/// <returns></returns>
IFunction FitImplVolModel(CallPriceMarketData Hdataset)
{
int model = 1;
switch (model)
{
case 0:
PFunction2D.PFunction2D pf = new PFunction2D.PFunction2D(Hdataset.Maturity, Hdataset.Strike, Hdataset.Volatility);
pf.Interpolation = DVPLUtils.EInterpolationType.LEAST_SQUARES;
pf.Extrapolation = DVPLUtils.ExtrapolationType.USEMODEL;
pf.Parse(null);
return(pf);
case 1:
//define a model for fitting the implied volatility
Fairmat.Statistics.LinearModel impVol = new Fairmat.Statistics.LinearModel(
new Fairmat.Statistics.Predictor[] {
delegate(Vector xx) { return(1); },
delegate(Vector xx) { return(xx[0]); },
delegate(Vector xx) { return(xx[1]); },
delegate(Vector xx) { return(System.Math.Pow(xx[0], 2)); },
delegate(Vector xx) { return(System.Math.Pow(xx[1], 2)); },
delegate(Vector xx) { return(xx[0] * xx[1]); },
});
// Unroll matrix and coordinate vectors in order to make it suitable
// for the Quadratic model implementation.
int n = Hdataset.Volatility.R * Hdataset.Volatility.C;
Matrix xy = new Matrix(n, 2);
Vector z = new Vector(n);
int count = 0;
for (int x = 0; x < Hdataset.Volatility.R; x++)
{
for (int y = 0; y < Hdataset.Volatility.C; y++)
{
if (Hdataset.Volatility[x, y] > 0.01)
{
xy[count, Range.All] = (new Vector()
{
Hdataset.Maturity[x], Hdataset.Strike[y]
}).T;
z[count] = Hdataset.Volatility[x, y];
count++;
}
}
}
xy.Resize(count, xy.C);
z.Resize(count);
impVol.Estimate(xy, z);
return(impVol);
}
return(null);
}
/// <summary>
/// Initializes a new instance of the HestonCallOptimizationProblem class using the
/// EquityCalibrationData data structure.
/// </summary>
/// <param name="equityCalData">
/// An EquityCalibrationData object containing market data for calibration.
/// </param>
/// <param name="matBound">
/// A vector containing the minimum and maximum values
/// for maturities to be used in calibration.
/// </param>
/// <param name="strikeBound">
/// A vector containing the minimum and maximum values
/// for strikes to be used in calibration.
/// </param>
public HestonCallOptimizationProblem(EquityCalibrationData equityCalData, Vector matBound, Vector strikeBound)
{
this.cpmd = equityCalData.Hdata;
this.matBound = matBound;
this.strikeBound = strikeBound;
SetVariables(equityCalData.Hdata.CallPrice, equityCalData.Hdata.Maturity,
equityCalData.Hdata.Strike, equityCalData.CallMatrixRiskFreeRate,
equityCalData.CallMatrixDividendYield, equityCalData.Hdata.S0);
displayObjInfo = false;
}
private EstimationResult FairmatEstimate(CurveMarketData discountingCurve, CallPriceMarketData Hdataset)
{
EquityCalibrationData HCalData = new EquityCalibrationData(Hdataset, discountingCurve);
//HCalData.Setup(Hdataset, discountingCurve);
bool hasArbitrage = HCalData.HasArbitrageOpportunity(10e-2);
if (hasArbitrage)
{
Console.WriteLine("Market data contains arbitrage opportunity");
}
this.r = new DVPLDOM.PFunction(discountingCurve.Durations, discountingCurve.Values);
this.q = HCalData.dyFunc as PFunction;
//this.q.Expr = (double[,])ArrayHelper.Concat(HCalData.MaturityDY.ToArray(), HCalData.DividendYield.ToArray());
this.r.Parse(null);
this.q.Parse(null);
Vector locVolMat, locVolStr;
//IFunction fittedSurface = FitImplVolModel(Hdataset);
//Matrix locVolMatrix = LocVolMatrixFromImpliedVol(Hdataset, fittedSurface, out locVolMat, out locVolStr);
CallPriceSurface fittedSurface = CallPriceSurface.NoArbitrageSurface(HCalData);
Matrix locVolMatrix = LocVolMatrixFromCallPrices(Hdataset, fittedSurface, out locVolMat, out locVolStr);
Console.WriteLine(locVolMatrix);
// Create dupire outputs.
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] = fittedSurface;
//Console.WriteLine("r = " + HCalData.Rate.ToString());
//Console.WriteLine("q = " + HCalData.DividendYield.ToString());
return(result);
}
private Matrix LocVolMatrixFromImpliedVol(CallPriceMarketData Hdataset, IFunction impVol, out Vector locVolMat, out Vector locVolStr)
{
int nmat = calibrationSettings.LocalVolatilityMaturities;
int nstrike = calibrationSettings.LocalVolatilityStrikes;
double lastMat = Hdataset.Maturity[Range.End];
double lastStr = Hdataset.Strike[Range.End];
locVolMat = Vector.Linspace(Hdataset.Maturity[0], lastMat, nmat);
locVolStr = Vector.Linspace(Hdataset.Strike[0], lastStr, nstrike);
Matrix locVolMatrix = new Matrix(nmat, nstrike);
Integrate integrate = new Integrate(this);
double sigma, dSigmadk, num, y, den, avgGrowthRate;
Vector x = new Vector(2);
for (int i = 0; i < nmat; i++)
{
avgGrowthRate = integrate.AdaptLobatto(0.0, locVolMat[i]);
int j = 0;
x[0] = locVolMat[i];
x[1] = locVolStr[j];
sigma = impVol.Evaluate(x);
dSigmadk = impVol.Partial(x, 1);
num = Math.Pow(sigma, 2) + 2.0 * sigma * x[0] * impVol.Partial(x, 0);
den = 1.0;
locVolMatrix[i, j] = Math.Sqrt(num / den);
// The rest of the cycle.
for (j = 1; j < nstrike; j++)
{
x[1] = locVolStr[j];
sigma = impVol.Evaluate(x);
dSigmadk = impVol.Partial(x, 1);
num = Math.Pow(sigma, 2) + 2.0 * sigma * x[0] *
(impVol.Partial(x, 0) + avgGrowthRate * x[1] * dSigmadk);
y = Math.Log(locVolStr[j] / Hdataset.S0) + avgGrowthRate;
den = System.Math.Pow(1.0 - x[1] * y * dSigmadk / sigma, 2) + x[1] * sigma * x[0] *
(dSigmadk - 0.25 * x[1] * sigma * x[0] * dSigmadk * dSigmadk + x[1] * impVol.Partial2(x, 1));
locVolMatrix[i, j] = Math.Sqrt(num / den);
}
}
return(locVolMatrix);
}
/// <summary>
/// Attempts to solve the Variance Gamma Optimization problem using
/// <see cref="Heston.VarianceGammaOptimizationProblem"/>.
/// </summary>
/// <param name="data">
/// The data to be used in order to perform the optimization.
/// </param>
/// <param name="settings">The parameter is not used.</param>
/// <returns>The results of the optimization.</returns>
public EstimationResult Estimate(List <object> data, IEstimationSettings settings = null, IController controller = null, Dictionary <string, object> properties = null)
{
EquitySpotMarketData espmd = data[0] as EquitySpotMarketData;
CallPriceMarketData cpmd = data[1] as CallPriceMarketData;
DiscountingCurveMarketData dcmd = data[2] as DiscountingCurveMarketData;
EquityCalibrationData ecd = new EquityCalibrationData(cpmd, dcmd);
this.s0 = espmd.Price;
this.r = espmd.RiskFreeRate;
this.q = espmd.DividendYield;
this.k = ecd.Hdata.Strike;
this.m = ecd.Hdata.Maturity;
this.cp = ecd.Hdata.CallPrice;
Vector x0 = (Vector) new double[] { -0.1, 0.2, 0.1 };
IOptimizationAlgorithm algorithm = new QADE();
OptimizationSettings optimizationSettings = new DESettings();
// Maximum number of iteration allowed.
// Positive integer values print debug info.
optimizationSettings.Verbosity = 1;
// Tolerance.
optimizationSettings.epsilon = 10e-5;
var solution = algorithm.Minimize(new VarianceGammaOptimizationProblem(this.q, this.s0, this.k,
this.r, this.cp, this.m),
optimizationSettings, x0);
if (solution.errors)
{
return(new EstimationResult(solution.message));
}
var er = new EstimationResult();
er.Names = new string[] { "S0", "theta", "sigma", "nu", "rate", "dividend" };
er.Values = new double[] { this.s0, solution.x[0], solution.x[1], solution.x[2], this.r, this.q };
return(er);
}
public EstimationResult Estimate(System.Collections.Generic.List <object> marketData, IEstimationSettings settings = null, IController controller = null, System.Collections.Generic.Dictionary <string, object> properties = null)
{
CurveMarketData discountingCurve = (CurveMarketData)marketData[0];
CallPriceMarketData Hdataset = (CallPriceMarketData)marketData[1];
//gets the settings
calibrationSettings = settings as DupireCalibrationSettings;
//return this.FairmatEstimate(discountingCurve, Hdataset);
// Removed quantlib estimate, it does not work correctly
switch (calibrationSettings.LocalVolatilityCalculation)
{
case LocalVolatilityCalculation.Method1:
return(this.FairmatEstimate(discountingCurve, Hdataset));
case LocalVolatilityCalculation.QuantLib:
return(QuantLibEstimate(discountingCurve, Hdataset));
default:
throw new NotImplementedException("Method not implemented");
}
}
private EstimationResult FairmatEstimate(CurveMarketData discountingCurve, CallPriceMarketData Hdataset)
{
EquityCalibrationData HCalData = new EquityCalibrationData(Hdataset, discountingCurve);
//HCalData.Setup(Hdataset, discountingCurve);
bool hasArbitrage = HCalData.HasArbitrageOpportunity(10e-2);
if (hasArbitrage)
Console.WriteLine("Market data contains arbitrage opportunity");
this.r = new DVPLDOM.PFunction(discountingCurve.Durations,discountingCurve.Values);
this.q = HCalData.dyFunc as PFunction;
//this.q.Expr = (double[,])ArrayHelper.Concat(HCalData.MaturityDY.ToArray(), HCalData.DividendYield.ToArray());
this.r.Parse(null);
this.q.Parse(null);
Vector locVolMat, locVolStr;
//IFunction fittedSurface = FitImplVolModel(Hdataset);
//Matrix locVolMatrix = LocVolMatrixFromImpliedVol(Hdataset, fittedSurface, out locVolMat, out locVolStr);
CallPriceSurface fittedSurface = CallPriceSurface.NoArbitrageSurface(HCalData);
Matrix locVolMatrix = LocVolMatrixFromCallPrices(Hdataset, fittedSurface, out locVolMat, out locVolStr);
Console.WriteLine(locVolMatrix);
// Create dupire outputs.
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] = fittedSurface;
//Console.WriteLine("r = " + HCalData.Rate.ToString());
//Console.WriteLine("q = " + HCalData.DividendYield.ToString());
return result;
}
public static void Main(string[] args)
{
int Caso = 1;
if (Caso == 0)
{
InterestRateMarketData MData = InterestRateMarketData.FromFile("../../../TestData/InterestRatesModels/05052009-EU.xml");
CallPriceMarketData test = CallPriceMarketData.FromFile("../../../TestData/Heston/05052009-SX5E-HestonData.xml");
EquityCalibrationData CalData = new EquityCalibrationData(test, MData);
Matrix CallMarketPrice = (Matrix)test.CallPrice;
Vector Maturity = (Vector)test.Maturity;
Vector Strike = (Vector)test.Strike;
Vector DividendYield = (Vector)test.DividendYield;
Vector Drift = CalData.Rate - CalData.DividendYield;
Vector Rate = CalData.Rate;
double u, kappa, theta, sigma, rho, v0, s0, r, q, T, K, val;
u = 1.0;
kappa = 19.4;
theta = 0.235;
sigma = 0.00500999;
rho = -0.96;
v0 = 0.664;
s0 = 3872.15;
r = -0.0867303549580581;
q = 0;
T = 0.50;
K = 6000;
Vector MatBound = new Vector(2);
Vector StrikeBound = new Vector(2);
MatBound[0] = 0.0;
MatBound[1] = 2.0;
StrikeBound[0] = 0.7;
StrikeBound[1] = 1.3;
Matrix Volatility = new Matrix(test.CallPrice.R, test.CallPrice.C);
HestonCallOptimizationProblem HP = new HestonCallOptimizationProblem(CallMarketPrice, Maturity, Strike, Rate, DividendYield, test.S0, MatBound, StrikeBound, Volatility);
Complex Cval, Cu;
Cu = u - Complex.I;
HestonCall hc = new HestonCall(HP);
Cval = hc.phi(u, kappa, theta, sigma, rho, s0, v0, r, T);
Console.WriteLine("phi1 = {0}", Cval);
Cval = hc.phi(Cu, kappa, theta, sigma, rho, s0, v0, r, T);
Console.WriteLine("phi2 = {0}", Cval);
val = hc.IntegrandFunc(u, kappa, theta, sigma, rho, s0, v0, r, q, T, K);
Console.WriteLine("IntFunc = {0}", val);
Vector x = new Vector(5);
x[0] = kappa;
x[1] = theta;
x[2] = sigma;
x[3] = rho;
x[4] = v0;
DateTime T1, T2;
TimeSpan ElapsedTime;
double Time, Time2, Time3;
T1 = DateTime.Now;
val = hc.HestonCallPrice(x, s0, T, K, r, q);
T2 = DateTime.Now;
ElapsedTime = T2 - T1;
Time = (double)ElapsedTime.Milliseconds;
Time2 = (double)ElapsedTime.Seconds;
Console.WriteLine("Price = {0}", val);
Console.WriteLine("Elapsed Time = {0}", Time2 + Time / 1000);
int NProve = 10;
int NPassi = 1000;
double val2;
Random CasNum = new Random();
for (int i = 0; i < NProve; i++)
{
for (int j = 0; j < 5; j++)
{
val2 = ((double)CasNum.Next(0, NPassi)) / ((double)NPassi);
x[j] = HP.Bounds.Lb[j] + (HP.Bounds.Ub[j] - HP.Bounds.Lb[j]) * val2;
}
Console.Write("Trial {0} x = " + x.ToString(), i + 1);
T1 = DateTime.Now;
val = HP.Obj(x);
T2 = DateTime.Now;
ElapsedTime = T2 - T1;
Time = (double)ElapsedTime.Milliseconds;
Time2 = (double)ElapsedTime.Seconds;
Time3 = (double)ElapsedTime.Minutes;
Console.WriteLine(" Time = {0}' {1}'' Val = {2}", Time3, Time2 + Time / 1000, val);
}
}
if (Caso == 1)
{
TestHestonCallEstimation NewTest = new TestHestonCallEstimation();
bool Result = NewTest.Run();
}
}
protected virtual EstimationResult BuildEstimate(Scalar spotPrice, CurveMarketData interestDataSet, CallPriceMarketData callDataSet, EquityCalibrationData equityCalData, SolutionInfo solution)
{
string[] names = new string[] { "S0", "kappa", "theta", "sigma", "rho", "V0" };
Vector param = new Vector(6);
param[0] = spotPrice.Value;
param[Range.New(1, 5)] = solution.x;
var result = new EstimationResult(names, param);
// In the following the two function describing the ZR and dividend yields are created
//Matrix zerorate = new Matrix(interestDataSet.Durations.Length, 2);
//zerorate[Range.All, 0] = interestDataSet.Durations;
//zerorate[Range.All, 1] = interestDataSet.Values;
//Matrix dividendYield = new Matrix(equityCalData.MaturityDY.Length, 2);
//dividendYield[Range.All, 0] = equityCalData.MaturityDY;
//dividendYield[Range.All, 1] = equityCalData.DividendYield;
Matrix zerorate = new Matrix((equityCalData.zrFunc as PFunction).Expr);
//Matrix dividendYield = new Matrix((equityCalData.dyFunc as PFunction).Expr);
Matrix dividendYield = ToMatrix(IstantaneousDividendYield(equityCalData));
result.Objects = new object[2];
result.Objects[0] = zerorate;
result.Objects[1] = dividendYield;
result.Fit = solution.obj;
Console.WriteLine(result);
return result;
}
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;
}
private Matrix LocVolMatrixFromImpliedVol(CallPriceMarketData Hdataset, IFunction impVol, out Vector locVolMat, out Vector locVolStr)
{
int nmat = calibrationSettings.LocalVolatilityMaturities;
int nstrike = calibrationSettings.LocalVolatilityStrikes;
double lastMat = Hdataset.Maturity[Range.End];
double lastStr = Hdataset.Strike[Range.End];
locVolMat = Vector.Linspace(Hdataset.Maturity[0], lastMat, nmat);
locVolStr = Vector.Linspace(Hdataset.Strike[0], lastStr, nstrike);
Matrix locVolMatrix = new Matrix(nmat, nstrike);
Integrate integrate = new Integrate(this);
double sigma, dSigmadk, num, y, den, avgGrowthRate;
Vector x = new Vector(2);
for (int i = 0; i < nmat; i++)
{
avgGrowthRate = integrate.AdaptLobatto(0.0, locVolMat[i]);
int j = 0;
x[0] = locVolMat[i];
x[1] = locVolStr[j];
sigma = impVol.Evaluate(x);
dSigmadk = impVol.Partial(x, 1);
num = Math.Pow(sigma, 2) + 2.0 * sigma * x[0] * impVol.Partial(x, 0);
den = 1.0;
locVolMatrix[i, j] = Math.Sqrt(num / den);
// The rest of the cycle.
for (j = 1; j < nstrike; j++)
{
x[1] = locVolStr[j];
sigma = impVol.Evaluate(x);
dSigmadk = impVol.Partial(x, 1);
num = Math.Pow(sigma, 2) + 2.0 * sigma * x[0] *
(impVol.Partial(x, 0) + avgGrowthRate * x[1] * dSigmadk);
y = Math.Log(locVolStr[j] / Hdataset.S0) + avgGrowthRate;
den = System.Math.Pow(1.0 - x[1] * y * dSigmadk / sigma, 2) + x[1] * sigma * x[0] *
(dSigmadk - 0.25 * x[1] * sigma * x[0] * dSigmadk * dSigmadk + x[1] * impVol.Partial2(x, 1));
locVolMatrix[i, j] = Math.Sqrt(num / den);
}
}
return locVolMatrix;
}
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;
}
protected override EstimationResult BuildEstimate(Scalar spotPrice, CurveMarketData interestDataSet, CallPriceMarketData callDataSet, EquityCalibrationData equityCalData, SolutionInfo solution)
{
string[] names = new string[] { "S0", "kappa", "theta", "sigma",
"rho", "V0", "r", "q" };
Vector param = new Vector(8);
param[0] = spotPrice.Value;
param[Range.New(1, 5)] = solution.x[Range.New(0, 4)];
param[6] = equityCalData.zrFunc.Evaluate(TheoreticalModelsSettings.ConstantDYRFMaturity);
if (impliedDividends)
param[7] = solution.x[Range.End];// equityCalData.dyFunc.Evaluate(TheoreticalModelsSettings.ConstantDYRFMaturity);
else
param[7] = DY(equityCalData);
var result = new EstimationResult(names, param);
result.Fit = HestonCallOptimizationProblem.avgPricingError;
Console.WriteLine(result);
return result;
}
/// <summary>
/// Initializes a new instance of the HestonCallOptimizationProblem class using the
/// EquityCalibrationData data structure.
/// </summary>
/// <param name="equityCalData">
/// An EquityCalibrationData object containing market data for calibration.
/// </param>
/// <param name="matBound">
/// A vector containing the minimum and maximum values
/// for maturities to be used in calibration.
/// </param>
/// <param name="strikeBound">
/// A vector containing the minimum and maximum values
/// for strikes to be used in calibration.
/// </param>
public HestonCallOptimizationProblem(EquityCalibrationData equityCalData, Vector matBound, Vector strikeBound)
{
this.cpmd = equityCalData.Hdata;
this.matBound = matBound;
this.strikeBound = strikeBound;
SetVariables(equityCalData.Hdata.CallPrice, equityCalData.Hdata.Maturity,
equityCalData.Hdata.Strike, equityCalData.CallMatrixRiskFreeRate,
equityCalData.CallMatrixDividendYield, equityCalData.Hdata.S0);
displayObjInfo = false;
}
protected virtual EstimationResult BuildEstimate(Scalar spotPrice, CurveMarketData interestDataSet, CallPriceMarketData callDataSet, EquityCalibrationData equityCalData, SolutionInfo solution)
{
string[] names = new string[] { "S0", "kappa", "theta", "sigma", "rho", "V0" };
Vector param = new Vector(6);
param[0] = spotPrice.Value;
param[Range.New(1, 5)] = solution.x;
var result = new EstimationResult(names, param);
// In the following the two function describing the ZR and dividend yields are created
//Matrix zerorate = new Matrix(interestDataSet.Durations.Length, 2);
//zerorate[Range.All, 0] = interestDataSet.Durations;
//zerorate[Range.All, 1] = interestDataSet.Values;
//Matrix dividendYield = new Matrix(equityCalData.MaturityDY.Length, 2);
//dividendYield[Range.All, 0] = equityCalData.MaturityDY;
//dividendYield[Range.All, 1] = equityCalData.DividendYield;
Matrix zerorate = new Matrix((equityCalData.zrFunc as PFunction).Expr);
//Matrix dividendYield = new Matrix((equityCalData.dyFunc as PFunction).Expr);
Matrix dividendYield = ToMatrix(IstantaneousDividendYield(equityCalData));
result.Objects = new object[2];
result.Objects[0] = zerorate;
result.Objects[1] = dividendYield;
result.Fit = solution.obj;
Console.WriteLine(result);
return(result);
}
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);
}
private Matrix LocVolMatrixFromCallPrices(CallPriceMarketData Hdataset, CallPriceSurface CallPrice, out Vector locVolMat, out Vector locVolStr)
{
Integrate integrate = new Integrate(this);
int nmat = calibrationSettings.LocalVolatilityMaturities;
int nstrike = calibrationSettings.LocalVolatilityStrikes;
double firstMat = CallPrice.MinMaturity;
double lastMat = CallPrice.MaxMaturity;
double firstStr = CallPrice.MinStrike;
double lastStr = CallPrice.MaxStrike;
double delta = (lastStr - firstStr) / nstrike;
locVolMat = Vector.Linspace(firstMat, lastMat, nmat);
locVolStr = Vector.Linspace(firstStr + delta, lastStr - delta, nstrike);
Matrix locVolMatrix = new Matrix(nmat, nstrike);
// this next matrix is created only for debugging pourpose
Matrix squaredLocVolMatrix = new Matrix(nmat, nstrike);
double num, den, call, dCdt, dCdk, d2Cdk2;
Vector x = new Vector(2);
double h0 = 0.02 * Hdataset.S0; //increment for numerical derivatives (stock)
double ht = 0.02; // 0.25 * (lastMat - firstMat) / nmat;//increment for numerical derivatives (maturities)
double hs = h0;
double d2Threshold = 10e-5;
for (int i = 0; i < nmat; i++)
{
double growthRate = integrate.AdaptLobatto(0.0, locVolMat[i]);
x[0] = locVolMat[i];
for (int j = 0; j < nstrike; j++)
{
x[1] = locVolStr[j];
var support = CallPrice.SupportY(x[0]);
//if (x[1] > support[1] && j > 1)
if (x[1] < support[0] || x[1] > support[1])
{
//skip...fill later
//squaredLocVolMatrix[i, j] = squaredLocVolMatrix[i, j - 1];
//locVolMatrix[i, j] = locVolMatrix[i, j-1];
}
else
{
bool fail = false;
call = CallPrice.Evaluate(x);
dCdt = CallPrice.Partial(x, 0, ht);
//do
// {
dCdk = CallPrice.Partial(x, 1, hs);
d2Cdk2 = CallPrice.Partial2(x, 1, hs);
//if (Math.Abs(d2Cdk2) > d2Threshold || hs > 0.1 * Hdataset.S0)
if (Math.Abs(d2Cdk2) < d2Threshold)
{
fail = true;
//break;
}
// hs *= 2;
//} while (true);
if (!fail)
{
double qq = this.q.Evaluate(x[0]);
num = dCdt + growthRate * x[1] * dCdk + qq * call;
den = x[1] * x[1] * d2Cdk2;
squaredLocVolMatrix[i, j] = 2.0 * num / den;
locVolMatrix[i, j] = Math.Sqrt(Math.Abs(2.0 * num / den));
}
}
}
}
//Fill missing vol
for (int i = 0; i < nmat; i++)
{
double lastVol = 0;
for (int j = 0; j < nstrike; j++)
{
if (locVolMatrix[i, j] != 0)
{
lastVol = locVolMatrix[i, j];
}
else
{
locVolMatrix[i, j] = lastVol;
}
}
lastVol = 0;
for (int j = nstrike - 1; j >= 0; j--)
{
if (locVolMatrix[i, j] != 0)
{
lastVol = locVolMatrix[i, j];
}
else
{
locVolMatrix[i, j] = lastVol;
}
}
//
}
return(locVolMatrix);
}
/// <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));
}
/// <summary>
/// This method allows to fit the implied volatility using different models.
/// </summary>
/// <param name="Hdataset"></param>
/// <returns></returns>
IFunction FitImplVolModel(CallPriceMarketData Hdataset)
{
int model = 1;
switch (model)
{
case 0:
PFunction2D.PFunction2D pf = new PFunction2D.PFunction2D(Hdataset.Maturity, Hdataset.Strike, Hdataset.Volatility);
pf.Interpolation = DVPLUtils.EInterpolationType.LEAST_SQUARES;
pf.Extrapolation = DVPLUtils.ExtrapolationType.USEMODEL;
pf.Parse(null);
return pf;
case 1:
//define a model for fitting the implied volatility
Fairmat.Statistics.LinearModel impVol = new Fairmat.Statistics.LinearModel(
new Fairmat.Statistics.Predictor[] {
delegate(Vector xx) { return 1; },
delegate(Vector xx) { return xx[0]; },
delegate(Vector xx) { return xx[1]; },
delegate(Vector xx) { return System.Math.Pow(xx[0], 2); },
delegate(Vector xx) { return System.Math.Pow(xx[1], 2); },
delegate(Vector xx) { return xx[0] * xx[1]; }, });
// Unroll matrix and coordinate vectors in order to make it suitable
// for the Quadratic model implementation.
int n = Hdataset.Volatility.R * Hdataset.Volatility.C;
Matrix xy = new Matrix(n, 2);
Vector z = new Vector(n);
int count = 0;
for (int x = 0; x < Hdataset.Volatility.R; x++)
{
for (int y = 0; y < Hdataset.Volatility.C; y++)
{
if (Hdataset.Volatility[x, y] > 0.01)
{
xy[count, Range.All] = (new Vector() { Hdataset.Maturity[x],Hdataset.Strike[y] }).T;
z[count] = Hdataset.Volatility[x, y];
count++;
}
}
}
xy.Resize(count, xy.C);
z.Resize(count);
impVol.Estimate(xy, z);
return impVol;
}
return null;
}
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);
}
private Matrix LocVolMatrixFromCallPrices(CallPriceMarketData Hdataset, CallPriceSurface CallPrice, out Vector locVolMat, out Vector locVolStr)
{
Integrate integrate = new Integrate(this);
int nmat = calibrationSettings.LocalVolatilityMaturities;
int nstrike = calibrationSettings.LocalVolatilityStrikes;
double firstMat = CallPrice.MinMaturity;
double lastMat = CallPrice.MaxMaturity;
double firstStr = CallPrice.MinStrike;
double lastStr = CallPrice.MaxStrike;
double delta = (lastStr - firstStr) / nstrike;
locVolMat = Vector.Linspace(firstMat, lastMat, nmat);
locVolStr = Vector.Linspace(firstStr + delta, lastStr - delta, nstrike);
Matrix locVolMatrix = new Matrix(nmat, nstrike);
// this next matrix is created only for debugging pourpose
Matrix squaredLocVolMatrix = new Matrix(nmat, nstrike);
double num, den, call, dCdt, dCdk, d2Cdk2;
Vector x = new Vector(2);
double h0 = 0.02*Hdataset.S0;//increment for numerical derivatives (stock)
double ht = 0.02;// 0.25 * (lastMat - firstMat) / nmat;//increment for numerical derivatives (maturities)
double hs = h0;
double d2Threshold=10e-5;
for (int i = 0; i < nmat; i++)
{
double growthRate = integrate.AdaptLobatto(0.0, locVolMat[i]);
x[0] = locVolMat[i];
for (int j = 0; j < nstrike; j++)
{
x[1] = locVolStr[j];
var support=CallPrice.SupportY(x[0]);
//if (x[1] > support[1] && j > 1)
if(x[1]<support[0]||x[1]>support[1])
{
//skip...fill later
//squaredLocVolMatrix[i, j] = squaredLocVolMatrix[i, j - 1];
//locVolMatrix[i, j] = locVolMatrix[i, j-1];
}
else
{
bool fail = false;
call = CallPrice.Evaluate(x);
dCdt = CallPrice.Partial(x, 0, ht);
//do
// {
dCdk = CallPrice.Partial(x, 1, hs);
d2Cdk2 = CallPrice.Partial2(x, 1, hs);
//if (Math.Abs(d2Cdk2) > d2Threshold || hs > 0.1 * Hdataset.S0)
if (Math.Abs(d2Cdk2) < d2Threshold)
{
fail = true;
//break;
}
// hs *= 2;
//} while (true);
if (!fail)
{
double qq = this.q.Evaluate(x[0]);
num = dCdt + growthRate * x[1] * dCdk + qq * call;
den = x[1] * x[1] * d2Cdk2;
squaredLocVolMatrix[i, j] = 2.0 * num / den;
locVolMatrix[i, j] = Math.Sqrt(Math.Abs(2.0 * num / den));
}
}
}
}
//Fill missing vol
for (int i = 0; i < nmat; i++)
{
double lastVol=0;
for (int j = 0; j < nstrike; j++)
{
if (locVolMatrix[i, j] != 0)
lastVol = locVolMatrix[i, j];
else
locVolMatrix[i, j] = lastVol;
}
lastVol = 0;
for (int j = nstrike-1; j >=0; j--)
{
if (locVolMatrix[i, j] != 0)
lastVol = locVolMatrix[i, j];
else
locVolMatrix[i, j] = lastVol;
}
//
}
return locVolMatrix;
}
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);
}
protected override EstimationResult BuildEstimate(Scalar spotPrice, CurveMarketData interestDataSet, CallPriceMarketData callDataSet, EquityCalibrationData equityCalData, SolutionInfo solution)
{
string[] names = new string[] { "S0", "kappa", "theta", "sigma",
"rho", "V0", "r", "q" };
Vector param = new Vector(8);
param[0] = spotPrice.Value;
param[Range.New(1, 5)] = solution.x[Range.New(0, 4)];
param[6] = equityCalData.zrFunc.Evaluate(TheoreticalModelsSettings.ConstantDYRFMaturity);
if (impliedDividends)
{
param[7] = solution.x[Range.End];// equityCalData.dyFunc.Evaluate(TheoreticalModelsSettings.ConstantDYRFMaturity);
}
else
{
param[7] = DY(equityCalData);
}
var result = new EstimationResult(names, param);
result.Fit = HestonCallOptimizationProblem.avgPricingError;
Console.WriteLine(result);
return(result);
}
