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 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;
}
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);
}