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 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 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);
}
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);
}
