public void modifyLattice(double U)
{ // Forward induction; building the tree
double down = str.downValue();
double up = str.upValue();
int si = lattice.MinIndex;
lattice[si, si] = U;
// Loop from the min index to the end index
for (int n = lattice.MinIndex + 1; n <= lattice.MaxIndex; n++)
{
for (int i = 0; i < lattice.NumberColumns(n) - 1; i++)
{
lattice[n, i] = down * lattice[n - 1, i];
lattice[n, i + 1] = up * lattice[n - 1, i];
}
}
// Postcondition: we now have the complete lattice for the underlying asset
}
/* public static double EarlyImpl(double P, double S)
* {
*
* double K = 10.0;
*
* if (P > K - S)
* {
* return P;
* }
* return K - S;
* }*/
// This could be made into a member function of Option
public static void Main()
{
// Phase I: Create and initialise the option
IOptionFactory fac = getFactory();
int N = 200;
Console.Write("Number of time steps: ");
N = Convert.ToInt32(Console.ReadLine());
double S;
Console.Write("Underlying price: ");
S = Convert.ToDouble(Console.ReadLine());
Option opt = fac.create();
double k = opt.T / N;
// Create basic lattice
double discounting = Math.Exp(-opt.r * k);
// Phase II: Create the binomial method and forward induction
BinomialLatticeStrategy binParams = getStrategy(opt.sig, opt.r, k, S, opt.K, N); // Factory
BinomialMethod bn = new BinomialMethod(discounting, binParams, N);
bn.modifyLattice(S);
// Phase III: Backward Induction and compute option price
Vector <double> RHS = new Vector <double>(bn.BasePyramidVector());
if (binParams.bType == BinomialType.Additive)
{
RHS[RHS.MinIndex] = S * Math.Exp(N * binParams.downValue());
for (int j = RHS.MinIndex + 1; j <= RHS.MaxIndex; j++)
{
RHS[j] = RHS[j - 1] * Math.Exp(binParams.upValue() - binParams.downValue());
}
}
Vector <double> Pay = opt.PayoffVector(RHS);
double pr = bn.getPrice(Pay);
Console.WriteLine("European {0}", pr);
// Binomial method with early exercise
BinomialMethod bnEarly = new BinomialMethod(discounting, binParams, N, opt.EarlyImpl);
bnEarly.modifyLattice(S);
Vector <double> RHS2 = new Vector <double>(bnEarly.BasePyramidVector());
Vector <double> Pay2 = opt.PayoffVector(RHS2);
double pr2 = bnEarly.getPrice(Pay2);
Console.WriteLine("American {0}", pr2);
// Display in Excel; first create array of asset mesh points
int startIndex = 0;
Vector <double> xarr = new Vector <double>(N + 1, startIndex);
xarr[xarr.MinIndex] = 0.0;
for (int j = xarr.MinIndex + 1; j <= xarr.MaxIndex; j++)
{
xarr[j] = xarr[j - 1] + k;
}
// Display lattice in Excel
ExcelMechanisms exl = new ExcelMechanisms();
try
{
// public void printLatticeInExcel(Lattice<double> lattice, Vector<double> xarr, string SheetName)
string sheetName = "Lattice";
exl.printLatticeInExcel(bnEarly.getLattice(), xarr, sheetName);
}
catch (Exception e)
{
Console.WriteLine(e);
}
}
