public override double[,] MakingOptionValueTree(double K, double r, double sigma, double T, int N, double div, double[,] StTree)
{
// Initial class Precalculate
PreCalculate precal = new PreCalculate();
precal.sigma = sigma;
precal.r = r;
precal.T = T;
precal.N = N;
precal.div = div;
// Get pu, pm, pd under discount
double disc_pu = precal.Get_disc_pu();
double disc_pm = precal.Get_disc_pm();
double disc_pd = precal.Get_disc_pd();
//Initiate St and outcome Vt.
double[,] St = new double[2 * N + 1, N + 1];
double[,] Vt = new double[2 * N + 1, N + 1];
// Copy old array that got from method to the new array.
for (int i = 0; i <= 2 * N; i++)
{
for (int j = 0; j <= N; j++)
{
St[i, j] = StTree[i, j];
}
}
// Calculate the option value of last step if it is a call option.
if (Iscall == true)
{
for (int j = (2 * N); j >= 0; j--)
{
Vt[j, N] = Math.Max(St[j, N] - K, 0);
}
}
// Calculate the option value of last step if it is a put option.
else
{
for (int j = (2 * N); j >= 0; j--)
{
Vt[j, N] = Math.Max(K - St[j, N], 0);
}
}
for (int i = N - 1; i >= 0; i--)
{
for (int j = 2 * i; j >= 0; j--)
{
// Every node, except that on the last step, equals expectation of nodes' on last step.
Vt[j, i] = disc_pu * Vt[j, i + 1] + disc_pm * Vt[j + 1, i + 1] + disc_pd * Vt[j + 2, i + 1];
}
}
return(Vt);
}
public double[,] MakeUnderlyingTree(double S, double sigma, double T, int N)
{
PreCalculate precal = new PreCalculate();
precal.sigma = sigma;
precal.T = T;
precal.N = N;
// Get St on every node.
// Get discount rate
double edx = precal.Get_edx();
// Get size of moving price dx
double dx = precal.Get_dx();
//Initiate the outcome St.
double[,] St = new double[2 * N + 1, N + 1];
// Calculate the underlying price if it always goes down in the whole period.
St[2 * N, N] = S * Math.Exp(-N * dx);
// Calculate all the possible underlying price at the last step.
for (int j = (2 * N - 1); j >= 0; j--)
{
St[j, N] = St[j + 1, N] * edx;
}
// Calculate all underlying prices St.
for (int i = N - 1; i >= 0; i--)
{
for (int j = 2 * i; j >= 0; j--)
{
// Every node, except that on the last step, has node on the next step which has the same price.
St[j, i] = St[j + 1, i + 1];
}
}
return(St);
}
public void Output_Calculation(double S, double K, double r, double T, double sigma, int N, double div)
{
// Get essential classes' instances.
PreCalculate precal = new PreCalculate();
TrinomialUnderlyingTree tree = new TrinomialUnderlyingTree();
Option opt = new Option();
EurOption Eur_option = new EurOption();
AmericanOption Amer_option = new AmericanOption();
Greek greeks = new Greek();
VegaRhoCalculation vega_cal = new VegaRhoCalculation();
// Initial array St and Vt
double[,] St = new double[2 * N + 1, N + 1];
double[,] Vt = new double[2 * N + 1, N + 1];
// Initial interval that used in Greeks
double diff_sigma = 0.001 * sigma;
double diff_r = 0.001 * r;
// Judge if this is an European Option
if (IsEuropean == true)
{
//Judge if this is a call option.
if (IsCall == true)
{
Console.WriteLine("The Underlying Prices Trinomial Tree:");
// Initial the parameters
Eur_option.Iscall = true;
vega_cal.IsEuropean = true;
vega_cal.Iscall = true;
// Ilerate underlying trinomial tree St.
for (int i = 0; i <= 2 * N; i++)
{
for (int j = 0; j <= N; j++)
{
St[i, j] = Math.Round(tree.MakeUnderlyingTree(S, sigma, T, N)[i, j], 2);
Console.Write(St[i, j].ToString() + "\t");
}
Console.WriteLine();
}
Console.WriteLine();
Console.WriteLine("The Option Value Trinomial Tree:");
// Ilerate option value trinomial tree Vt
for (int i = 0; i <= 2 * N; i++)
{
for (int j = 0; j <= N; j++)
{
Vt[i, j] = Math.Round(Eur_option.MakingOptionValueTree(K, r, sigma, T, N, div, St)[i, j], 2);
Console.Write(Vt[i, j].ToString() + "\t");
}
Console.WriteLine();
}
// Output the option price
Console.WriteLine("European Call Option Price is" + " " + Vt[0, 0].ToString());
Console.WriteLine();
// Output Greeks
Console.WriteLine("Greeks of this option ");
greeks.St = St;
greeks.Vt = Vt;
double delta = greeks.Delta();
Console.WriteLine("Delta =" + " " + delta.ToString());
double gamma = greeks.Gamma();
Console.WriteLine("Gamma =" + " " + gamma.ToString());
double theta = greeks.Theta(T, N);
Console.WriteLine("Theta =" + " " + theta.ToString());
double vega = vega_cal.GetVegaRho(diff_sigma, diff_r, S, K, r, sigma, T, N, div)[0, 0];
double rho = vega_cal.GetVegaRho(diff_sigma, diff_r, S, K, r, sigma, T, N, div)[0, 1];
Console.WriteLine("Vega =" + " " + vega.ToString());
Console.WriteLine("Rho =" + " " + rho.ToString());
Console.ReadLine();
}
// If this is a put option.
else
{
Console.WriteLine("The Underlying Prices Trinomial Tree:");
// Initial the parameters
Eur_option.Iscall = false;
vega_cal.IsEuropean = true;
vega_cal.Iscall = false;
// Ilerate underlying trinomial tree St.
for (int i = 0; i <= 2 * N; i++)
{
for (int j = 0; j <= N; j++)
{
St[i, j] = Math.Round(tree.MakeUnderlyingTree(S, sigma, T, N)[i, j], 2);
Console.Write(St[i, j].ToString() + "\t");
}
Console.WriteLine();
}
Console.WriteLine();
Console.WriteLine("The Option Value Trinomial Tree:");
// Ilerate option value trinomial tree Vt
for (int i = 0; i <= 2 * N; i++)
{
for (int j = 0; j <= N; j++)
{
Vt[i, j] = Math.Round(Eur_option.MakingOptionValueTree(K, r, sigma, T, N, div, St)[i, j], 2);
Console.Write(Vt[i, j].ToString() + "\t");
}
Console.WriteLine();
}
// Output option price.
Console.WriteLine("European Put Option Price is" + " " + Vt[0, 0].ToString());
Console.WriteLine();
// Output Greeks
Console.WriteLine("Greeks of this option :");
greeks.St = St;
greeks.Vt = Vt;
double delta = greeks.Delta();
Console.WriteLine("Delta =" + " " + delta.ToString());
double gamma = greeks.Gamma();
Console.WriteLine("Gamma =" + " " + gamma.ToString());
double theta = greeks.Theta(T, N);
Console.WriteLine("Theta =" + " " + theta.ToString());
double vega = vega_cal.GetVegaRho(diff_sigma, diff_r, S, K, r, sigma, T, N, div)[0, 0];
double rho = vega_cal.GetVegaRho(diff_sigma, diff_r, S, K, r, sigma, T, N, div)[0, 1];
Console.WriteLine("Vega =" + " " + vega.ToString());
Console.WriteLine("Rho =" + " " + rho.ToString());
Console.ReadLine();
}
}
// If this is an American Option
else
{
//Judge if this is a call option.
if (IsCall == true)
{
Console.WriteLine("The Underlying Prices Trinomial Tree:");
// Initial the parameters
Amer_option.Iscall = true;
vega_cal.IsEuropean = false;
vega_cal.Iscall = true;
// Ilerate underlying trinomial tree St.
for (int i = 0; i <= 2 * N; i++)
{
for (int j = 0; j <= N; j++)
{
St[i, j] = Math.Round(tree.MakeUnderlyingTree(S, sigma, T, N)[i, j], 2);
Console.Write(St[i, j].ToString() + "\t");
}
Console.WriteLine();
}
Console.WriteLine();
Console.WriteLine("The Option Value Trinomial Tree:");
// Ilerate option value trinomial tree Vt
for (int i = 0; i <= 2 * N; i++)
{
for (int j = 0; j <= N; j++)
{
Vt[i, j] = Math.Round(Amer_option.MakingOptionValueTree(K, r, sigma, T, N, div, St)[i, j], 2);
Console.Write(Vt[i, j].ToString() + "\t");
}
Console.WriteLine();
}
// Output American call option price
Console.WriteLine("American Call Option Price is" + " " + Vt[0, 0].ToString());
Console.WriteLine();
// Output Greeks
Console.WriteLine("Greeks of this option:");
greeks.St = St;
greeks.Vt = Vt;
double delta = greeks.Delta();
Console.WriteLine("Delta =" + " " + delta.ToString());
double gamma = greeks.Gamma();
Console.WriteLine("Gamma =" + " " + gamma.ToString());
double theta = greeks.Theta(T, N);
Console.WriteLine("Theta =" + " " + theta.ToString());
double vega = vega_cal.GetVegaRho(diff_sigma, diff_r, S, K, r, sigma, T, N, div)[0, 0];
double rho = vega_cal.GetVegaRho(diff_sigma, diff_r, S, K, r, sigma, T, N, div)[0, 1];
Console.WriteLine("Vega =" + " " + vega.ToString());
Console.WriteLine("Rho =" + " " + rho.ToString());
Console.ReadLine();
}
//If this is a put option.
else
{
Console.WriteLine("The Underlying Prices Trinomial Tree:");
// Initial the parameters
Amer_option.Iscall = false;
vega_cal.IsEuropean = false;
vega_cal.Iscall = false;
// Ilerate underlying trinomial tree St.
for (int i = 0; i <= 2 * N; i++)
{
for (int j = 0; j <= N; j++)
{
St[i, j] = Math.Round(tree.MakeUnderlyingTree(S, sigma, T, N)[i, j], 2);
Console.Write(St[i, j].ToString() + "\t");
}
Console.WriteLine();
}
Console.WriteLine();
Console.WriteLine("The Option Value Trinomial Tree:");
// Ilerate option value trinomial tree Vt
for (int i = 0; i <= 2 * N; i++)
{
for (int j = 0; j <= N; j++)
{
Vt[i, j] = Math.Round(Amer_option.MakingOptionValueTree(K, r, sigma, T, N, div, St)[i, j], 2);
Console.Write(Vt[i, j].ToString() + "\t");
}
Console.WriteLine();
}
// Output American call option price
Console.WriteLine("American Put Option Price is" + " " + Vt[0, 0].ToString());
Console.WriteLine();
// Output Greeks
Console.WriteLine("Greeks of this option:");
greeks.St = St;
greeks.Vt = Vt;
double delta = greeks.Delta();
Console.WriteLine("Delta =" + " " + delta.ToString());
double gamma = greeks.Gamma();
Console.WriteLine("Gamma =" + " " + gamma.ToString());
double theta = greeks.Theta(T, N);
Console.WriteLine("Theta =" + " " + theta.ToString());
double vega = vega_cal.GetVegaRho(diff_sigma, diff_r, S, K, r, sigma, T, N, div)[0, 0];
double rho = vega_cal.GetVegaRho(diff_sigma, diff_r, S, K, r, sigma, T, N, div)[0, 1];
Console.WriteLine("Vega =" + " " + vega.ToString());
Console.WriteLine("Rho =" + " " + rho.ToString());
Console.ReadLine();
}
}
}