/// <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 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 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;
}
/// <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 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 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);
}