// 13.12.4 Bilinear Interpolation
public static void BilinearInterpolation1()
{
Console.WriteLine("Vectors initialised: ");
// Create mesh arrays
int startIndex = 0;
int N = 1;
Vector <double> x1arr = new Vector <double>(N + 1, startIndex, 0.0);
x1arr[0] = 20.0; x1arr[1] = 21.0;
Vector <double> x2arr = new Vector <double>(x1arr);
x2arr[0] = 14.0; x2arr[1] = 15.0;
Console.WriteLine(x1arr);
Console.WriteLine(x2arr);
// Control values;
NumericMatrix <double> Control
= new NumericMatrix <double>(N + 1, N + 1, startIndex, startIndex);
Control[0, 0] = 91.0; Control[1, 1] = 95.0;
Control[0, 1] = 210.0; Control[1, 0] = 162.0;
BilinearInterpolator myInterpolator
= new BilinearInterpolator(x1arr, x2arr, Control);
double x = 20.2; double y = 14.5; // 146.1
double value = myInterpolator.Solve(x, y);
Console.WriteLine("Interpolated value: {0}", value);
}
public static double CapBlack(string Tenor, double strike, double N, IRateCurve curve, BilinearInterpolator VolCapletMatrix)
{
Date refDate = curve.RefDate();
SwapStyle y = (SwapStyle) new BuildingBlockFactory().CreateBuildingBlock(refDate, 0, Tenor, curve.GetSwapStyle().buildingBlockType);
double[] yf = y.scheduleLeg2.GetYFVect(Dc._Act_360);
int toRemove = yf.Length - 1;
yf = yf.Where((val, inx) => inx != toRemove).ToArray();
List <Date> ToDate = y.scheduleLeg2.toDates.ToList();
ToDate.RemoveAt(ToDate.Count - 1); // remove last element
double[] T = (from c in ToDate
select refDate.YF_365(c)).ToArray();
// df- getting relevant dates
Date[] dfDate = y.scheduleLeg2.payDates;
int Ncaplet = yf.Length; // number of caplets
double[] df = new double[Ncaplet];
// fwd rate
double[] fwd = new double[Ncaplet];
Date[] fwdDate = y.scheduleLeg2.fromDates;
for (int i = 0; i < Ncaplet; i++) // Note the loop start from 1
{ // first discount factor is on first payment date of caplet (first caplet skipped)
df[i] = curve.Df(dfDate[i + 1]);
fwd[i] = curve.Fwd(fwdDate[i + 1]);
}
double[] sigma = (from t in T
select VolCapletMatrix.Solve(t, strike)).ToArray();
return(CapBlack(T, yf, N, strike, sigma, df, fwd));
}
// Cap Price using VolCapletMatrix as argument
public static double CapBlack(double[] T, double[] yf, double N, double K, BilinearInterpolator VolCapletMatrix, double[] df, double[] fwd)
{
// LINQ: getting interpolated vol
double[] sigma = (from t in T
select VolCapletMatrix.Solve(t, K)).ToArray();
return(CapBlack(T, yf, N, K, sigma, df, fwd));
}
public static double Swaption(double N, double K, string Start, string SwapTenor, bool isPayer, BilinearInterpolator VolMatrix, IRateCurve Curve)
{
Date refDate = Curve.RefDate(); // curve ref date
// false/true with fwd swap matrix
Date startDate = refDate.add_period(Start, false); // swap start 2 business days after the expiry
Date expDate = startDate.add_workdays(-2); // expiry of swaption
Date today = refDate.add_workdays(-2);
double T = today.YF_365(expDate);
Period p = new Period(SwapTenor); // should be in year 1Y, 2Y (not 3m,...)
double sigma = VolMatrix.Solve(T, p.tenor);
return(Swaption(N, K, Start, SwapTenor, isPayer, sigma, Curve));
}
public static void BilinearInterpolation2()
{
// Create mesh arrays
int startIndex = 0;
// Number of subdivisions N,M in the x and y directions
int N = 4;
int M = 3;
Vector <double> x1arr = new Vector <double>(N + 1, startIndex, 0.0);
double a = 0.0; double b = 1.0;
double h1 = (b - a) / (double)N;
x1arr[x1arr.MinIndex] = a;
for (int j = x1arr.MinIndex + 1; j <= x1arr.MaxIndex; j++)
{
x1arr[j] = x1arr[j - 1] + h1;
}
Vector <double> x2arr = new Vector <double>(M + 1, startIndex, 0.0);
double h2 = (b - a) / (double)M;
x1arr[x1arr.MinIndex] = a;
for (int j = x2arr.MinIndex + 1; j <= x2arr.MaxIndex; j++)
{
x2arr[j] = x2arr[j - 1] + h2;
}
Console.WriteLine(x1arr);
Console.WriteLine(x2arr);
// Control values;
NumericMatrix <double> Control
= new NumericMatrix <double>(N + 1, M + 1,
startIndex, startIndex);
Func <double, double, double> func = (double x1, double x2) => x1 + x2;
for (int i = Control.MinRowIndex; i <= Control.MaxRowIndex; i++)
{
for (int j = Control.MinColumnIndex; j <= Control.MaxColumnIndex; j++)
{
Control[i, j] = func(x1arr[i], x2arr[j]);
}
}
BilinearInterpolator myInterpolator
= new BilinearInterpolator(x1arr, x2arr, Control);
double x = 0.1; double y = 0.7;
double value = myInterpolator.Solve(x, y);
Console.WriteLine("Interpolated value: {0}", value);
// Take center point (xm, ym) of each element and interpolate on it
NumericMatrix <double> InterpolatedMatrix
= new NumericMatrix <double>(N, M, startIndex, startIndex);
// Abscissa points of new interpolated matrix
Vector <double> Xarr
= new Vector <double>(InterpolatedMatrix.Rows, startIndex, 0.0);
Vector <double> Yarr
= new Vector <double>(InterpolatedMatrix.Columns, startIndex, 0.0);
for (int i = InterpolatedMatrix.MinRowIndex;
i <= InterpolatedMatrix.MaxRowIndex; i++)
{
for (int j = InterpolatedMatrix.MinColumnIndex;
j <= InterpolatedMatrix.MaxColumnIndex; j++)
{
Xarr[i] = 0.5 * (x1arr[i] + x1arr[i + 1]); // xm
Yarr[j] = 0.5 * (x2arr[j] + x2arr[j + 1]); // ym
InterpolatedMatrix[i, j]
= myInterpolator.Solve(Xarr[i], Yarr[j]);
}
}
// Present the interpolated matrix in Excel
ExcelMechanisms driver = new ExcelMechanisms();
string title = "Interpolated matrix";
driver.printMatrixInExcel <double>(InterpolatedMatrix,
Xarr, Yarr, title);
}