// Objective function ===========================================================================
public double DHObjFunSVC(double[] param, OpSet settings, MktData data, double[] X, double[] W, int objectivefun, double[] lb, double[] ub)
{
HestonPriceDH HPDH = new HestonPriceDH();
BisectionAlgo BA = new BisectionAlgo();
double S = settings.S;
double r = settings.r;
double q = settings.q;
int trap = settings.trap;
double[,] MktIV = data.MktIV;
double[,] MktPrice = data.MktPrice;
string[,] PutCall = data.PutCall;
double[] K = data.K;
double[] T = data.T;
int NK = PutCall.GetLength(0);
int NT = PutCall.GetLength(1);
int NX = X.Length;
DHParam param2 = new DHParam();
param2.kappa1 = param[0];
param2.theta1 = param[1];
param2.sigma1 = param[2];
param2.v01 = param[3];
param2.rho1 = param[4];
param2.kappa2 = param[5];
param2.theta2 = param[6];
param2.sigma2 = param[7];
param2.v02 = param[8];
param2.rho2 = param[9];
// Settings for the Bisection algorithm
double a = 0.001;
double b = 3.0;
double Tol = 1e5;
int BSIVMaxIter = 10000;
// Initialize the model price and model implied vol vectors, and the objective function value
double[,] ModelPrice = new double[NK, NT];
double[,] ModelIV = new double[NK, NT];
double BSVega = 0.0;
double Error = 0.0;
double pi = Math.PI;
double kappaLB = lb[0]; double kappaUB = ub[0];
double thetaLB = lb[1]; double thetaUB = ub[1];
double sigmaLB = lb[2]; double sigmaUB = ub[2];
double v0LB = lb[3]; double v0UB = ub[3];
double rhoLB = lb[4]; double rhoUB = ub[4];
double phi, P1, P2, CallPrice;
Complex Integrand1, Integrand2;
Complex i = Complex.ImaginaryOne;
Complex[] f2 = new Complex[NX];
Complex[] f1 = new Complex[NX];
double[] int1 = new double[NX];
double[] int2 = new double[NX];
if ((param2.kappa1 <= kappaLB) || (param2.theta1 <= thetaLB) || (param2.sigma1 <= sigmaLB) || (param2.v01 <= v0LB) || (param2.rho1 <= rhoLB) ||
(param2.kappa1 >= kappaUB) || (param2.theta1 >= thetaUB) || (param2.sigma1 >= sigmaUB) || (param2.v01 >= v0UB) || (param2.rho1 >= rhoUB) ||
(param2.kappa2 <= kappaLB) || (param2.theta2 <= thetaLB) || (param2.sigma2 <= sigmaLB) || (param2.v02 <= v0LB) || (param2.rho2 <= rhoLB) ||
(param2.kappa2 >= kappaUB) || (param2.theta2 >= thetaUB) || (param2.sigma2 >= sigmaUB) || (param2.v02 >= v0UB) || (param2.rho2 >= rhoUB))
{
Error = 1e50;
}
else
{
for (int t = 0; t < NT; t++)
{
for (int j = 0; j < NX; j++)
{
settings.T = T[t];
phi = X[j];
f2[j] = HPDH.HestonDoubleCF(phi, param2, settings);
f1[j] = HPDH.HestonDoubleCF(phi - i, param2, settings);
}
for (int k = 0; k < NK; k++)
{
for (int j = 0; j < NX; j++)
{
phi = X[j];
Integrand2 = Complex.Exp(-i * phi * Complex.Log(K[k])) * f2[j] / i / phi;
int2[j] = W[j] * Integrand2.Real;
Integrand1 = Complex.Exp(-i * phi * Complex.Log(K[k])) * f1[j] / i / phi / S / Complex.Exp((r - q) * T[t]);
int1[j] = W[j] * Integrand1.Real;
}
P1 = 0.5 + 1.0 / pi * int1.Sum();
P2 = 0.5 + 1.0 / pi * int2.Sum();
// The call price
CallPrice = S * Math.Exp(-q * T[t]) * P1 - K[k] * Math.Exp(-r * T[t]) * P2;
if (PutCall[k, t] == "C")
{
ModelPrice[k, t] = CallPrice;
}
else
{
ModelPrice[k, t] = CallPrice - S * Math.Exp(-q * T[t]) + Math.Exp(-r * T[t]) * K[k];
}
switch (objectivefun)
{
case 1:
// MSE Loss Function
Error += Math.Pow(ModelPrice[k, t] - MktPrice[k, t], 2.0);
break;
case 2:
// RMSE Loss Function
Error += Math.Pow(ModelPrice[k, t] - MktPrice[k, t], 2.0) / MktPrice[k, t];
break;
case 3:
// IVMSE Loss Function
ModelIV[k, t] = BA.BisecBSIV(PutCall[k, t], S, K[k], r, q, T[t], a, b, ModelPrice[k, t], Tol, BSIVMaxIter);
Error += Math.Pow(ModelIV[k, t] - MktIV[k, t], 2);
break;
case 4:
// IVRMSE Christoffersen, Heston, Jacobs proxy
double d = (Math.Log(S / K[k]) + (r - q + MktIV[k, t] * MktIV[k, t] / 2.0) * T[t]) / MktIV[k, t] / Math.Sqrt(T[t]);
double NormPDF = Math.Exp(-0.5 * d * d) / Math.Sqrt(2.0 * pi);
BSVega = S * NormPDF * Math.Sqrt(T[t]);
Error += Math.Pow(ModelPrice[k, t] - MktPrice[k, t], 2.0) / (BSVega * BSVega);
break;
}
}
}
}
return(Error);
}
// Objective function ===========================================================================
public double DHObjFun(double[] param, OpSet settings, MktData data, double[] X, double[] W, int objectivefun, double[] lb, double[] ub)
{
HestonPriceDH HPDH = new HestonPriceDH();
BisectionAlgo BA = new BisectionAlgo();
double S = settings.S;
double r = settings.r;
double q = settings.q;
int trap = settings.trap;
double[,] MktIV = data.MktIV;
double[,] MktPrice = data.MktPrice;
string[,] PutCall = data.PutCall;
double[] K = data.K;
double[] T = data.T;
int NK = PutCall.GetLength(0);
int NT = PutCall.GetLength(1);
DHParam param2 = new DHParam();
param2.kappa1 = param[0];
param2.theta1 = param[1];
param2.sigma1 = param[2];
param2.v01 = param[3];
param2.rho1 = param[4];
param2.kappa2 = param[5];
param2.theta2 = param[6];
param2.sigma2 = param[7];
param2.v02 = param[8];
param2.rho2 = param[9];
// Settings for the Bisection algorithm
double a = 0.001;
double b = 3.0;
double Tol = 1e5;
int MaxIter = 10000;
// Initialize the model price and model implied vol vectors, and the objective function value
double[,] ModelPrice = new double[NK, NT];
double[,] ModelIV = new double[NK, NT];
double BSVega = 0.0;
double Error = 0.0;
double pi = Math.PI;
double kappaLB = lb[0]; double kappaUB = ub[0];
double thetaLB = lb[1]; double thetaUB = ub[1];
double sigmaLB = lb[2]; double sigmaUB = ub[2];
double v0LB = lb[3]; double v0UB = ub[3];
double rhoLB = lb[4]; double rhoUB = ub[4];
if ((param2.kappa1 <= kappaLB) || (param2.theta1 <= thetaLB) || (param2.sigma1 <= sigmaLB) || (param2.v01 <= v0LB) || (param2.rho1 <= rhoLB) ||
(param2.kappa1 >= kappaUB) || (param2.theta1 >= thetaUB) || (param2.sigma1 >= sigmaUB) || (param2.v01 >= v0UB) || (param2.rho1 >= rhoUB) ||
(param2.kappa2 <= kappaLB) || (param2.theta2 <= thetaLB) || (param2.sigma2 <= sigmaLB) || (param2.v02 <= v0LB) || (param2.rho2 <= rhoLB) ||
(param2.kappa2 >= kappaUB) || (param2.theta2 >= thetaUB) || (param2.sigma2 >= sigmaUB) || (param2.v02 >= v0UB) || (param2.rho2 >= rhoUB))
{
Error = 1e50;
}
else
{
for (int k = 0; k < NK; k++)
{
for (int t = 0; t < NT; t++)
{
settings.K = K[k];
settings.T = T[t];
ModelPrice[k, t] = HPDH.DoubleHestonPriceGaussLaguerre(param2, settings, X, W);
switch (objectivefun)
{
case 1:
// MSE Loss Function
Error += Math.Pow(ModelPrice[k, t] - MktPrice[k, t], 2.0);
break;
case 2:
// RMSE Loss Function
Error += Math.Pow(ModelPrice[k, t] - MktPrice[k, t], 2.0) / MktPrice[k, t];
break;
case 3:
// IVMSE Loss Function
ModelIV[k, t] = BA.BisecBSIV(PutCall[k, t], S, K[k], r, q, T[t], a, b, ModelPrice[k, t], Tol, MaxIter);
Error += Math.Pow(ModelIV[k, t] - MktIV[k, t], 2.0);
break;
case 4:
// IVRMSE Christoffersen, Heston, Jacobs proxy
double d = (Math.Log(S / K[k]) + (r - q + MktIV[k, t] * MktIV[k, t] / 2.0) * T[t]) / MktIV[k, t] / Math.Sqrt(T[t]);
double NormPDF = Math.Exp(-0.5 * d * d) / Math.Sqrt(2.0 * pi);
BSVega = S * NormPDF * Math.Sqrt(T[t]);
Error += Math.Pow(ModelPrice[k, t] - MktPrice[k, t], 2.0) / (BSVega * BSVega);
break;
}
}
}
}
return(Error);
}