// 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 void ValueTest()
{
BilinearInterpolator target = new BilinearInterpolator();
IPoint point = new Point2D(4, 2, 0);
List <IPoint> bounds = new List <IPoint>();
bounds.Add(new Point2D(2, 1, 9));
bounds.Add(new Point2D(6, 1, 13));
bounds.Add(new Point2D(2, 3, 7));
bounds.Add(new Point2D(6, 3, 11));
double expected = 10;
double actual = target.Value(point, bounds);
Assert.AreEqual(expected, actual);
bounds = new List <IPoint>();
bounds.Add(new Point2D(2, 1, 3));
bounds.Add(new Point2D(6, 1, 7));
bounds.Add(new Point2D(2, 3, 5));
bounds.Add(new Point2D(6, 3, 9));
expected = 6;
actual = target.Value(point, bounds);
Assert.AreEqual(expected, actual);
}
// 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 void ValueTest1()
{
BilinearInterpolator target = new BilinearInterpolator();
// Create the point to interpolate at
IPoint point = new Point2D(4, 2, 0);
// Create the bounding points
List <IPoint> bounds = new List <IPoint>();
bounds.Add(new Point2D(3, 1, 3));
bounds.Add(new Point2D(5, 1, 9));
bounds.Add(new Point2D(3, 3, 7));
bounds.Add(new Point2D(5, 3, 13));
// Set the expected value
double expected = 8;
// Interpolate at the point and test result
double actual = target.Value(point, bounds);
Assert.AreEqual(expected, actual);
// Create the point to interpolate at
point = new Point2D(4, 3, 0);
// Create the bounding points
bounds = new List <IPoint>();
bounds.Add(new Point2D(2, 2, 2));
bounds.Add(new Point2D(5, 2, 11));
bounds.Add(new Point2D(2, 4, 6));
bounds.Add(new Point2D(5, 4, 15));
// Set the expected value
expected = 10;
// Interpolate at the point and test result
actual = target.Value(point, bounds);
Assert.AreEqual(expected, actual);
// Test the boundary condition xy > x1y1
// Create the point to interpolate at
point = new Point2D(5, 5, 0);
// Create the bounding points
bounds = new List <IPoint>();
bounds.Add(new Point2D(4, 3, 10));
bounds.Add(new Point2D(5, 3, 13));
bounds.Add(new Point2D(4, 4, 12));
bounds.Add(new Point2D(5, 4, 15));
// Set the expected value
expected = 15.0d;
// Interpolate at the point and test result
actual = target.Value(point, bounds);
Assert.AreEqual(expected, actual);
}
private void Ini(double[] T, double[] df, double[] fwd, double[] yf, double[] Tquoted, List <double[]> VolSilos, double[] strike)
{
// data member
Exp = T; Strike = strike;
// Caplet are telescopic, max number of caplets. Fill data in CapletVolMatrix.
CapletVolMatrix = new List <double[]>();
for (int i = 0; i < strike.Length; i++)
{
monoStrikeCapletVolBuilder b = new monoStrikeCapletVolBuilder();
b.LateIni(T, df, fwd, yf, Tquoted, VolSilos[i], strike[i]);
CapletVolMatrix.Add(b.GetCapletVol());
}
// Inizialize the Bilinear Interpolator
BI = new BilinearInterpolator(T, strike, CapletVolMatrix);
}
protected void drawQuad(DrawContext dc, Matrix geoToCartesian, int slices, int stacks)
{
Vec4 ll = this.transformToQuadCoordinates(geoToCartesian, this.corners.get(0));
Vec4 lr = this.transformToQuadCoordinates(geoToCartesian, this.corners.get(1));
Vec4 ur = this.transformToQuadCoordinates(geoToCartesian, this.corners.get(2));
Vec4 ul = this.transformToQuadCoordinates(geoToCartesian, this.corners.get(3));
BilinearInterpolator interp = new BilinearInterpolator(ll, lr, ur, ul);
GL2 gl = dc.getGL().getGL2(); // GL initialization checks for GL2 compatibility.
gl.glBegin(GL2.GL_TRIANGLE_STRIP);
try
{
this.drawQuad(dc, interp, slices, stacks);
}
finally
{
gl.glEnd();
}
}
// used in constructor
private void Ini(string tenor, IRateCurve curve, BilinearInterpolator capletVolMatrix, double nominal)
{
stringTenor = tenor;
rateCurve = curve;
volMatrix = capletVolMatrix;
N = nominal;
// yf of longer cap
SwapStyle y = (SwapStyle) new BuildingBlockFactory().CreateBuildingBlock(curve.RefDate(), 0, tenor, curve.GetSwapStyle().buildingBlockType);
yf = y.scheduleLeg2.GetYFVect(Dc._Act_360);
capSchedule = y.scheduleLeg2;
int toRemove = yf.Length - 1;
yf = yf.Where((val, inx) => inx != toRemove).ToArray();
// T all tenor needed. They are more than input
Date refDate = curve.RefDate();
List <Date> ToDate = y.scheduleLeg2.toDates.ToList();
ToDate.RemoveAt(ToDate.Count - 1); // remove last element
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
df = new double[Ncaplet];
// fwd rate
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]);
}
}
protected void drawQuad(DrawContext dc, BilinearInterpolator interp, int slices, int stacks)
{
double[] compArray = new double[4];
double du = 1.0f / (float)slices;
double dv = 1.0f / (float)stacks;
GL2 gl = dc.getGL().getGL2(); // GL initialization checks for GL2 compatibility.
for (int vi = 0; vi < stacks; vi++)
{
double v = vi * dv;
double vn = (vi + 1) * dv;
if (vi != 0)
{
interp.interpolate(slices * du, v, compArray);
gl.glTexCoord2d(slices * du, v);
gl.glVertex3dv(compArray, 0);
interp.interpolate(0, v, compArray);
gl.glTexCoord2d(0, v);
gl.glVertex3dv(compArray, 0);
}
for (int ui = 0; ui <= slices; ui++)
{
double u = ui * du;
interp.interpolate(u, v, compArray);
gl.glTexCoord2d(u, v);
gl.glVertex3dv(compArray, 0);
interp.interpolate(u, vn, compArray);
gl.glTexCoord2d(u, vn);
gl.glVertex3dv(compArray, 0);
}
}
}
public override double Price(BilinearInterpolator CapletVolMatrix, double strike)
{
return(Formula.CapBlack(T, yf, N, strike, CapletVolMatrix, df, fwd));
}
public void BilinearInterpolatorConstructorTest()
{
BilinearInterpolator target = new BilinearInterpolator();
Assert.IsNotNull(target);
}
void TestEdges(string dataSetName, double lat, double lon
, string rasterSouthWestName, string rasterSouthEastName
, string rasterNorthWestName, string rasterNorthEastName)
{
DEMDataSet dataSet = DEMDataSet.RegisteredDatasets.FirstOrDefault(d => d.Name == dataSetName);
Assert.NotNull(dataSet);
DEMFileType fileType = dataSet.FileFormat.Type;
int rasterSize = dataSet.PointsPerDegree;
double amountx = (1d / rasterSize) / 4d;
double amounty = (1d / rasterSize) / 4d;
// Regenerates all metadata
//_rasterService.GenerateDirectoryMetadata(dataSet
// , force: true
// , deleteOnError: false
// , maxDegreeOfParallelism: 1);
_elevationService.DownloadMissingFiles(dataSet, lat, lon);
var tiles = _rasterService.GenerateReportForLocation(dataSet, lat, lon);
Assert.True(tiles.Count == 4);
Assert.Single(tiles, t => string.Equals(Path.GetFileName(t.LocalName), rasterSouthWestName, StringComparison.OrdinalIgnoreCase));
Assert.Single(tiles, t => string.Equals(Path.GetFileName(t.LocalName), rasterSouthEastName, StringComparison.OrdinalIgnoreCase));
Assert.Single(tiles, t => string.Equals(Path.GetFileName(t.LocalName), rasterNorthWestName, StringComparison.OrdinalIgnoreCase));
Assert.Single(tiles, t => string.Equals(Path.GetFileName(t.LocalName), rasterNorthEastName, StringComparison.OrdinalIgnoreCase));
if (dataSet.FileFormat.Registration == DEMFileRegistrationMode.Cell)
{
using (var rasterNW = _rasterService.OpenFile(tiles.First(t => string.Equals(rasterNorthWestName, Path.GetFileName(t.LocalName))).LocalName, fileType))
using (var rasterNE = _rasterService.OpenFile(tiles.First(t => string.Equals(rasterNorthEastName, Path.GetFileName(t.LocalName))).LocalName, fileType))
using (var rasterSW = _rasterService.OpenFile(tiles.First(t => string.Equals(rasterSouthWestName, Path.GetFileName(t.LocalName))).LocalName, fileType))
using (var rasterSE = _rasterService.OpenFile(tiles.First(t => string.Equals(rasterSouthEastName, Path.GetFileName(t.LocalName))).LocalName, fileType))
{
var elevNW = rasterNW.GetElevationAtPoint(rasterNW.ParseMetaData(dataSet.FileFormat), rasterSize - 1, rasterSize - 1);
var elevNE = rasterNE.GetElevationAtPoint(rasterNE.ParseMetaData(dataSet.FileFormat), 0, rasterSize - 1);
var elevSW = rasterSW.GetElevationAtPoint(rasterSW.ParseMetaData(dataSet.FileFormat), rasterSize - 1, 0);
var elevSE = rasterSE.GetElevationAtPoint(rasterSE.ParseMetaData(dataSet.FileFormat), 0, 0);
BilinearInterpolator interpolator = new BilinearInterpolator();
var elev0 = interpolator.Interpolate(elevSW, elevSE, elevNW, elevNE, 0.25, 0.25);
var apiElev0 = _elevationService.GetPointElevation(lat + amounty, lon - amountx, dataSet);
Assert.True((elev0 - apiElev0.Elevation.Value) < double.Epsilon);
var elev1 = interpolator.Interpolate(elevSW, elevSE, elevNW, elevNE, 0.75, 0.25);
var apiElev1 = _elevationService.GetPointElevation(lat + amounty, lon + amountx, dataSet);
Assert.True((elev1 - apiElev1.Elevation.Value) < double.Epsilon);
var elev2 = interpolator.Interpolate(elevSW, elevSE, elevNW, elevNE, 0.25, 0.75);
var apiElev2 = _elevationService.GetPointElevation(lat - amounty, lon - amountx, dataSet);
Assert.True((elev2 - apiElev2.Elevation.Value) < double.Epsilon);
var elev3 = interpolator.Interpolate(elevSW, elevSE, elevNW, elevNE, 0.75, 0.75);
var apiElev3 = _elevationService.GetPointElevation(lat - amounty, lon + amountx, dataSet);
Assert.True((elev3 - apiElev3.Elevation.Value) < double.Epsilon);
}
}
else
{
using (var rasterNW = _rasterService.OpenFile(tiles.First(t => string.Equals(rasterNorthWestName, Path.GetFileName(t.LocalName))).LocalName, fileType))
using (var rasterNE = _rasterService.OpenFile(tiles.First(t => string.Equals(rasterNorthEastName, Path.GetFileName(t.LocalName))).LocalName, fileType))
using (var rasterSW = _rasterService.OpenFile(tiles.First(t => string.Equals(rasterSouthWestName, Path.GetFileName(t.LocalName))).LocalName, fileType))
using (var rasterSE = _rasterService.OpenFile(tiles.First(t => string.Equals(rasterSouthEastName, Path.GetFileName(t.LocalName))).LocalName, fileType))
{
// Northen row, west to east
var elevN0 = rasterNW.GetElevationAtPoint(rasterNW.ParseMetaData(dataSet.FileFormat), rasterSize - 1, rasterSize - 1);
var elevN1 = rasterNW.GetElevationAtPoint(rasterNW.ParseMetaData(dataSet.FileFormat), rasterSize, rasterSize - 1);
var elevN2 = rasterNE.GetElevationAtPoint(rasterNE.ParseMetaData(dataSet.FileFormat), 1, rasterSize - 1);
// middle row, west to east
var elevM0 = rasterNW.GetElevationAtPoint(rasterNW.ParseMetaData(dataSet.FileFormat), rasterSize - 1, rasterSize);
var elevM1 = rasterNW.GetElevationAtPoint(rasterNW.ParseMetaData(dataSet.FileFormat), rasterSize, rasterSize);
var elevM2 = rasterNE.GetElevationAtPoint(rasterNE.ParseMetaData(dataSet.FileFormat), 1, rasterSize);
// Sourthen row, west to east
var elevS0 = rasterSW.GetElevationAtPoint(rasterSW.ParseMetaData(dataSet.FileFormat), rasterSize - 1, 1);
var elevS1 = rasterSW.GetElevationAtPoint(rasterSW.ParseMetaData(dataSet.FileFormat), rasterSize, 1);
var elevS2 = rasterSE.GetElevationAtPoint(rasterSE.ParseMetaData(dataSet.FileFormat), 1, 1);
BilinearInterpolator interpolator = new BilinearInterpolator();
var elev0 = interpolator.Interpolate(elevM0, elevM1, elevN0, elevN1, 0.75, 0.75);
var apiElev0 = _elevationService.GetPointElevation(lat + amounty, lon - amountx, dataSet);
Assert.True((elev0 - apiElev0.Elevation.Value) < double.Epsilon);
var elev1 = interpolator.Interpolate(elevM1, elevM2, elevN1, elevN2, 0.25, 0.75);
var apiElev1 = _elevationService.GetPointElevation(lat + amounty, lon + amountx, dataSet);
Assert.True((elev1 - apiElev1.Elevation.Value) < double.Epsilon);
var elev2 = interpolator.Interpolate(elevS0, elevS1, elevM0, elevM1, 0.75, 0.25);
var apiElev2 = _elevationService.GetPointElevation(lat - amounty, lon - amountx, dataSet);
Assert.True((elev2 - apiElev2.Elevation.Value) < double.Epsilon);
var elev3 = interpolator.Interpolate(elevS1, elevS2, elevM1, elevM2, 0.25, 0.25);
var apiElev3 = _elevationService.GetPointElevation(lat - amounty, lon + amountx, dataSet);
Assert.True((elev3 - apiElev3.Elevation.Value) < double.Epsilon);
}
}
}
public VanillaCapFloor(string tenor, IRateCurve curve, BilinearInterpolator capletVolMatrix, double nominal)
{
Ini(tenor, curve, capletVolMatrix, nominal);
}
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);
}
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 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));
}
// Update VolMatrix
public virtual void SetNewVolMatrix(BilinearInterpolator newCapletVolMatrix)
{
Ini(stringTenor, rateCurve, newCapletVolMatrix, N);
}
// Constructor
public VanillaCap(string tenor, IRateCurve curve, BilinearInterpolator capletVolMatrix, double nominal)
: base(tenor, curve, capletVolMatrix, nominal)
{
IsCap = true; // if true is a cap
}
abstract public double Price(double[] sigma, double strike); // array of sigma abstract public double Price(BilinearInterpolator CapletVolMatrix, double strike); // you can customize it
