public static void InterpolationExample()
{
ExcelMechanisms exl = new ExcelMechanisms();
// I Create initial t and r arrays.
Vector <double> t = new Vector <double>(new double[] { 0.1, 1, 4, 9, 20, 30 }, 0);
Vector <double> r = new Vector <double>(new double[] { 0.081, 0.07, 0.044, 0.07, 0.04, 0.03 }, 0);
// A Compute log df
Vector <double> logDF = new Vector <double>(r.Size, r.MinIndex);
for (int n = logDF.MinIndex; n <= logDF.MaxIndex; ++n)
{
logDF[n] = Math.Log(Math.Exp(-t[n] * r[n]));
}
// II Hyman interpolator
HymanHermiteInterpolator_V4 myInterpolatorH =
new HymanHermiteInterpolator_V4(t, logDF);
int M = 299;
Vector <double> term = new Vector <double>(M, 1);
term[term.MinIndex] = 0.1;
double step = 0.1;
for (int j = term.MinIndex + 1; j <= term.MaxIndex; j++)
{
term[j] = term[j - 1] + step;
}
// III Compute interpolated values
Vector <double> interpolatedlogDFH = myInterpolatorH.Curve(term);
exl.printOneExcel <double>(term, interpolatedlogDFH, "Hyman cubic", "t", "CS", "int logDF");
// IV Compute continuously compounded rate from the ZCB Z(0,t),
// using equation (3) Hagan and West (2008).
Vector <double> rCompounded = new Vector <double>(interpolatedlogDFH.Size, interpolatedlogDFH.MinIndex);
for (int j = rCompounded.MinIndex; j <= rCompounded.MaxIndex; j++)
{
rCompounded[j] = -interpolatedlogDFH[j] / term[j];
}
exl.printOneExcel <double>(term, rCompounded, "RCompound Hyman Cubic", "term", "r cns compound", "r com");
// V Compute discrete forward rates using equation (6)
// from Hagan and West (2008)
Vector <double> f = new Vector <double>(rCompounded.Size, rCompounded.MinIndex);
f[f.MinIndex] = 0.081;
for (int j = f.MinIndex + 1; j <= rCompounded.MaxIndex; j++)
{
f[j] = (rCompounded[j] * term[j] - rCompounded[j - 1] * term[j - 1]) / (term[j] - term[j - 1]);
}
exl.printOneExcel <double>(term, f, "Hyman Cubic", "term", "discrete fwd", "dis fwd");
}
public static void SimplifiedMonotoneConvex()
{
SortedList <double, double> TermRate = new SortedList <double, double>();
#region using a different contructor
double[] t = new double[] { 0.1, 1, 4, 9, 20, 30 };
double[] r = new double[] { 0.081, 0.07, 0.044, 0.07, 0.04, 0.03 };
#endregion
// We consider inputs as continuous rates and negative forwards are not allowed
// Monotone Convex interpolator (Hagan-West approach)
MonotoneConvex HaganWest = new MonotoneConvex(t, r);
List <double> rr = new List <double>();
List <double> fwd = new List <double>();
List <double> tt = new List <double>();
double step = 0.01;
int MaxIndex = System.Convert.ToInt32((100 * HaganWest.dTerms.Last() + 20));
double x_ = 0.0;
for (int i = 0; i <= MaxIndex; i++)
{
x_ = step * i;
tt.Add(x_);
double k = HaganWest.Interpolant(x_);
rr.Add(HaganWest.Interpolant(x_));
fwd.Add(HaganWest.Forward(x_));
}
// Create the abscissa values
double[] terms = tt.ToArray();
// Compute interpolated values
double[] rates = HaganWest.GetInterpolatedRate(terms);
double[] forwards = HaganWest.GetInterpolatedFwd(terms);
// My excel mechanism
ExcelMechanisms exl = new ExcelMechanisms();
exl.printOneExcel <double>(new Vector <double>(tt.ToArray()), new Vector <double>(forwards)
, "Monotone Convex", "time", "discrete forward", "dis fwd");
exl.printOneExcel <double>(new Vector <double>(tt.ToArray()), new Vector <double>(rates)
, "Monotone Convex", "time", "discrete forward", "dis fwd");
}
// 13.12.3 Cubic Spline Interpolation
#region CubicSplineInterpolator
public static void LogisticI()
{
Console.WriteLine("Vectors initialised: ");
int N = 280;
double a = -15.0; // Left of interval
double b = 15.0; // Right of interval
double h = (b - a) / N;
int startIndex = 0;
Vector <double> xarr = new Vector <double>(N + 1, startIndex, 0.0);
Vector <double> yarr = new Vector <double>(N + 1, startIndex, 0.0);
for (int j = xarr.MinIndex; j <= xarr.MaxIndex; j++)
{
xarr[j] = a + h * j;
yarr[j] = Potpourri.Sigmoid1(xarr[j]);
// yarr[j] = Potpourri.Sigmoid2(xarr[j]);
}
Console.WriteLine("Vectors initialised: ");
int FirstDeriv = 1;
CubicSplineInterpolator csi
= new CubicSplineInterpolator(xarr, yarr, FirstDeriv, 10, 10);
// Display arrays in Excel
ExcelMechanisms exl = new ExcelMechanisms();
exl.printOneExcel <double>(xarr, csi.Curve(), "Logistic I", "x", "value", "I");
// Now choose 1st order derivative at zero
double leftBC = 1.0;
double rightBC = -1.0;
CubicSplineInterpolator csi2 = new CubicSplineInterpolator(xarr, yarr, FirstDeriv, leftBC, rightBC);
// Display arrays in Excel
exl.printOneExcel(xarr, csi2.Curve(), "Logistic II", "x", "value", "II");
}
public static void Main()
{
// 1. Create the option (Factory Method pattern)
Option myOption = CreateOption();
// 2. Define the pde of concern (Bridge pattern)
IIBVPImp pde = new BSIBVPImp(myOption);
// 3. Discrete mesh sizes.
int J = 325;
int N = J;
Console.Write("NS: ");
J = Convert.ToInt32(Console.ReadLine());
Console.Write("NT (NT ~ O(NS^2 for explicit, NT any value for implicit): ");
N = Convert.ToInt32(Console.ReadLine());
// 4. The domain in which the PDE is defined.
Range <double> rangeX = new Range <double>(0.0, myOption.FarFieldCondition);
Range <double> rangeT = new Range <double>(0.0, myOption.ExpiryDate);
// 5. Create FDM Solver.
Console.Write("Implicit [1] or Explicit Euler [2]: ");
int choice = Convert.ToInt32(Console.ReadLine());
IBVPFDM fdm = new ImplicitEulerIBVP(pde, rangeX, rangeT, J, N);
if (choice != 1)
{
fdm = new ExplicitEulerIBVP(pde, rangeX, rangeT, J, N);
}
// 6. Calculate the matrix result.
NumericMatrix <double> sol = fdm.result();
// 7. Display the results in Excel.
ExcelMechanisms exl = new ExcelMechanisms();
try
{
exl.printOneExcel(fdm.XValues, fdm.vecNew, "Euler method", "Stock", "Value", "V");
}
catch (Exception e)
{
Console.WriteLine(e);
}
}
public static void Main()
{
// 1. Create the option (Factory Method pattern)
Option myOption = CreateOption();
// 2. Define the pde of concern (Bridge pattern)
IBSPde pde = new Pde_BS(myOption);
// 3. Discrete mesh sizes.
int J = 325;
int N = J;
Console.Write("NS: ");
J = Convert.ToInt32(Console.ReadLine());
Console.Write("NT: ");
N = Convert.ToInt32(Console.ReadLine());
// 4. The domain in which the PDE is defined.
Range <double> rangeX = new Range <double>(0.0, myOption.FarFieldCondition);
Range <double> rangeT = new Range <double>(0.0, myOption.ExpiryDate);
// 5. Create FDM Solver.
IBVPFDM fdm = new ADE(pde, rangeX, rangeT, J, N);
// 6. Calculate the matrix result.
NumericMatrix <double> sol = fdm.result();
// 7. Display the results in Excel.
ExcelMechanisms exl = new ExcelMechanisms();
try
{
exl.printOneExcel(fdm.XValues, fdm.vecNew, "ADE method", "Stock", "Value", "V");
}
catch (Exception e)
{
Console.WriteLine(e);
}
}
// RECALL: void printOneExcel(Vector<double> x,
// Vector<double> functionResult,string title)
public void displayinExcel(OptionValueType yval)
{
string text = "Value";
if (yval == OptionValueType.Delta)
{
text = "Delta";
}
if (yval == OptionValueType.Gamma)
{
text = "Gamma";
}
if (yval == OptionValueType.Vega)
{
text = "Vega";
}
if (yval == OptionValueType.Theta)
{
text = "Theta";
}
if (yval == OptionValueType.Rho)
{
text = "Rho";
}
if (yval == OptionValueType.Coc)
{
text = "Coc";
}
Vector <double> yarr = calculate(yval);
// cout << "array ..."; int yy; cin >> yy;
// print(yarr);
ExcelMechanisms excel = new ExcelMechanisms();
excel.printOneExcel(XARR, yarr, text, text, text, text);
}
