// Bisection Algorithm for Black Scholes Implied Volatility
public double BisecBSIV(string PutCall, double S, double K, double rf, double q, double T, double a, double b, double MktPrice, double Tol, int MaxIter)
{
BlackScholesPrice BS = new BlackScholesPrice();
double lowCdif = MktPrice - BS.BlackScholes(S, K, T, rf, q, a, PutCall);
double highCdif = MktPrice - BS.BlackScholes(S, K, T, rf, q, b, PutCall);
double BSIV = 0.0;
double midP;
if (lowCdif * highCdif > 0.0)
{
BSIV = -1.0;
}
else
{
for (int x = 0; x <= MaxIter; x++)
{
midP = (a + b) / 2.0;
double midCdif = MktPrice - BS.BlackScholes(S, K, T, rf, q, midP, PutCall);
if (Math.Abs(midCdif) < Tol)
{
break;
}
else
{
if (midCdif > 0.0)
{
a = midP;
}
else
{
b = midP;
}
}
BSIV = midP;
}
}
return(BSIV);
}
static void Main(string[] args)
{
// Classes
BlackScholesPrice BS = new BlackScholesPrice();
BisectionAlgo BA = new BisectionAlgo();
NelderMeadAlgo NM = new NelderMeadAlgo();
ObjectiveFunction OF = new ObjectiveFunction();
HestonPriceTD HPTD = new HestonPriceTD();
// 32-point Gauss-Laguerre Abscissas and weights
double[] X = new Double[32];
double[] W = new Double[32];
using (TextReader reader = File.OpenText("../../GaussLaguerre32.txt"))
for (int k = 0; k <= 31; k++)
{
string text = reader.ReadLine();
string[] bits = text.Split(' ');
X[k] = double.Parse(bits[0]);
W[k] = double.Parse(bits[1]);
}
int NT = 4;
int NK = 13;
double[,] PutIV = new double[13, 4] {
{ 0.1962, 0.1947, 0.2019, 0.2115 }, { 0.1910, 0.1905, 0.1980, 0.2082 },
{ 0.1860, 0.1861, 0.1943, 0.2057 }, { 0.1810, 0.1812, 0.1907, 0.2021 },
{ 0.1761, 0.1774, 0.1871, 0.2000 }, { 0.1718, 0.1743, 0.1842, 0.1974 },
{ 0.1671, 0.1706, 0.1813, 0.1950 }, { 0.1644, 0.1671, 0.1783, 0.1927 },
{ 0.1645, 0.1641, 0.1760, 0.1899 }, { 0.1661, 0.1625, 0.1743, 0.1884 },
{ 0.1701, 0.1602, 0.1726, 0.1862 }, { 0.1755, 0.1610, 0.1716, 0.1846 },
{ 0.1796, 0.1657, 0.1724, 0.1842 }
};
double[] K = new double[13] {
124.0, 125.0, 126.0, 127.0, 128.0, 129.0, 130.0, 131.0, 132.0, 133.0, 134.0, 135.0, 136.0,
};
double[] T = new double[4] {
0.1014, 0.1973, 0.3699, 0.6192
};
string[,] PutCall = new string[13, 4];
double[,] MktPrice = new double[13, 4];
double Spot = 129.14;
double r = 0.0010;
double q = 0.0068;
int trap = 1;
int LossFunction = 2;
for (int t = 0; t <= NT - 1; t++)
{
for (int k = 0; k <= NK - 1; k++)
{
PutCall[k, t] = "P";
MktPrice[k, t] = BS.BlackScholes(Spot, K[k], T[t], r, q, PutIV[k, t], PutCall[k, t]);
}
}
// Create the maturity increments
double[] tau = new double[4];
tau[0] = T[0];
for (int t = 1; t <= NT - 1; t++)
{
tau[t] = T[t] - T[t - 1];
}
// Starting values and upper bounds
double e = 1e-5;
double[] lb = new double[5] {
e, e, e, e, -0.999
}; // Lower bound on the estimates
double[] ub = new double[5] {
20.0, 2.0, 2.0, 3.0, 0.999
}; // Upper bound on the estimates
// Starting values (vertices) in vector form. Add random increment about each starting value
int N = 5;
double kappaS = 4.0;
double thetaS = 0.1;
double sigmaS = 1.5;
double v0S = 0.04;
double rhoS = -0.30;
double[,] s = new double[N, N + 1];
for (int j = 0; j <= N; j++)
{
s[0, j] = kappaS + BA.RandomNum(-0.01, 0.01);
s[1, j] = thetaS + BA.RandomNum(-0.01, 0.01);
s[2, j] = sigmaS + BA.RandomNum(-0.01, 0.01);
s[3, j] = v0S + BA.RandomNum(-0.01, 0.01);
s[4, j] = rhoS + BA.RandomNum(-0.01, 0.01);
}
// Arrays for old maturities and parameters, and current parameters (old parameters, but stacked)
ArrayList OldTau = new ArrayList();
double[,] param0 = new double[NT - 1, 5];
double[,] paramTD = new double[NT, 5];
// Nelder Mead settings
int MaxIters = 1000;
double Tolerance = 1e-5;
// Market data
MktData data = new MktData();
double[] MKIV = new double[NK];
double[] MKPR = new double[NK];
string[] PC = new string[NK];
// Step-by-step parameter estimates
double[] B = new double[6];
double[] ObjectiveFun = new double[NT];
double[] NumIteration = new double[NT];
// First maturity parameter estimates ===================================================================
double[] tau0 = { 0.0 };
for (int k = 0; k <= NK - 1; k++)
{
MKIV[k] = PutIV[k, 0];
MKPR[k] = MktPrice[k, 0];
PC[k] = PutCall[k, 0];
}
data.MktIV = MKIV;
data.PutCall = PC;
data.MktPrice = MKPR;
B = NM.NelderMead(OF.f, N, MaxIters, Tolerance, s, tau[0], tau0, param0, data, Spot, K, r, q, trap, X, W, LossFunction, lb, ub);
Console.WriteLine("Finished parameter estimate set 1");
for (int k = 0; k <= 4; k++)
{
paramTD[0, k] = B[k];
}
ObjectiveFun[0] = B[5];
NumIteration[0] = B[6];
// Remaining Maturity estimates and updated starting values ==================================================
for (int mat = 1; mat <= NT - 1; mat++)
{
OldTau.Add(tau[mat - 1]);
for (int k = 0; k <= 4; k++)
{
param0[mat - 1, k] = B[k];
}
for (int k = 0; k <= NK - 1; k++)
{
MKIV[k] = PutIV[k, mat];
MKPR[k] = MktPrice[k, mat];
PC[k] = PutCall[k, mat];
}
data.MktIV = MKIV;
data.PutCall = PC;
data.MktPrice = MKPR;
for (int j = 0; j <= N; j++)
{
s[0, j] = B[0] + BA.RandomNum(-0.01, 0.01);
s[1, j] = B[1] + BA.RandomNum(-0.01, 0.01);
s[2, j] = B[2] + BA.RandomNum(-0.01, 0.01);
s[3, j] = B[3] + BA.RandomNum(-0.01, 0.01);
s[4, j] = B[4] + BA.RandomNum(-0.01, 0.01);
}
B = NM.NelderMead(OF.f, N, MaxIters, Tolerance, s, tau[mat], tau0, param0, data, Spot, K, r, q, trap, X, W, LossFunction, lb, ub);
Console.WriteLine("Finished parameter estimate set {0}", mat + 1);
for (int k = 0; k <= 4; k++)
{
paramTD[mat, k] = B[k];
}
ObjectiveFun[mat] = B[5];
NumIteration[mat] = B[6];
}
// Fit the prices and implied volatilities ====================================================================
// Bisection algorithm settings
double a = 0.001;
double b = 5.0;
double Tol = 1e-5;
int MaxIter = 5000;
ArrayList OldTau00 = new ArrayList();
double[] tau00 = { 0.0 };
double[,] ModelPrice = new double[NK, NT];
double[,] ModelIV = new double[NK, NT];
Array.Clear(param0, 0, 15);
// First maturity
HParam param = new HParam();
param.kappa = paramTD[0, 0];
param.theta = paramTD[0, 1];
param.sigma = paramTD[0, 2];
param.v0 = paramTD[0, 3];
param.rho = paramTD[0, 4];
for (int k = 0; k <= NK - 1; k++)
{
ModelPrice[k, 0] = HPTD.MNPriceGaussLaguerre(param, param0, tau[0], tau00, Spot, K[k], r, q, PutCall[k, 0], trap, X, W);
ModelIV[k, 0] = BA.BisecBSIV(PutCall[k, 0], Spot, K[k], r, q, T[0], a, b, ModelPrice[k, 0], Tol, MaxIter);
}
// Remaining maturity
for (int t = 1; t <= NT - 1; t++)
{
OldTau00.Add(tau[t - 1]);
param.kappa = paramTD[t, 0];
param.theta = paramTD[t, 1];
param.sigma = paramTD[t, 2];
param.v0 = paramTD[t, 3];
param.rho = paramTD[t, 4];
for (int j = 0; j <= 4; j++)
{
param0[t - 1, j] = paramTD[t - 1, j];
}
for (int k = 0; k <= NK - 1; k++)
{
ModelPrice[k, t] = HPTD.MNPriceGaussLaguerre(param, param0, tau[t], tau00, Spot, K[k], r, q, PutCall[k, t], trap, X, W);
ModelIV[k, t] = BA.BisecBSIV(PutCall[k, t], Spot, K[k], r, q, T[t], a, b, ModelPrice[k, t], Tol, MaxIter);
}
}
// Mean Square Implied Volatility Error
double Error = 0.0;
for (int t = 0; t <= NT - 1; t++)
{
for (int k = 0; k <= NK - 1; k++)
{
Error += Math.Pow(ModelIV[k, t] - PutIV[k, t], 2);
}
}
Error /= (Convert.ToDouble(NT) * Convert.ToDouble(NK));
// Output the estimation result
Console.WriteLine("-----------------------------------------------------------------------------");
Console.WriteLine("Market/Model implied volatilities");
Console.WriteLine(" Mat1 Mat2 Mat3 Mat4");
for (int k = 0; k <= NK - 1; k++)
{
Console.WriteLine("--------------------------------------------- Strike {0} Market/Model", K[k]);
Console.WriteLine("{0,10:F4} {1,10:F4} {2,10:F4} {3,10:F4}", PutIV[k, 0], PutIV[k, 1], PutIV[k, 2], PutIV[k, 3]);
Console.WriteLine("{0,10:F4} {1,10:F4} {2,10:F4} {3,10:F4}", ModelIV[k, 0], ModelIV[k, 1], ModelIV[k, 2], ModelIV[k, 3]);
}
Console.WriteLine("-----------------------------------------------------------------------------");
Console.WriteLine("Model Price ");
for (int k = 0; k <= NK - 1; k++)
{
Console.WriteLine("{0,10:0} {1,10:F4} {2,10:F4} {3,10:F4} {4,10:F4}", K[k], ModelPrice[k, 0], ModelPrice[k, 1], ModelPrice[k, 2], ModelPrice[k, 3]);
}
Console.WriteLine("-----------------------------------------------------------------------------");
Console.WriteLine("Results of time dependent parameter estimation");
Console.WriteLine(" ");
Console.WriteLine("Maturity kappa theta sigma v0 rho ObjecFun NumIterations");
Console.WriteLine("-----------------------------------------------------------------------------");
for (int t = 0; t <= NT - 1; t++)
{
Console.WriteLine("{0} {1,10:F4} {2,7:F4} {3,7:F4} {4,7:F4} {5,8:F4} {6,8:F4} {7,7:0}",
T[t], paramTD[t, 0], paramTD[t, 1], paramTD[t, 2], paramTD[t, 3], paramTD[t, 4], ObjectiveFun[t], NumIteration[t]);
}
Console.WriteLine("-----------------------------------------------------------------------------");
Console.WriteLine("IVMSE from time dependent estimates {0,10:E5}", Error);
Console.WriteLine("-----------------------------------------------------------------------------");
}