/// <summary>
/// Evaluates the function.
/// </summary>
/// <param name="context">The evaluation context instance.</param>
/// <param name="args">The function arguments.</param>
/// <returns>The result value of the function evaluation.</returns>
public override EvaluationValue Evaluate(EvaluationContext context, params IFunctionParameter[] args)
{
if (context == null)
{
throw new ArgumentNullException("context");
}
if (args == null)
{
throw new ArgumentNullException("args");
}
IFunction function = DataType.SubsetFunction;
if ((function.Evaluate(
context,
new EvaluationValue(args[0], args[0].GetType(context)), new EvaluationValue(args[1], args[1].GetType(context))) == EvaluationValue.True) &&
(function.Evaluate(
context,
new EvaluationValue(args[1], args[1].GetType(context)), new EvaluationValue(args[0], args[0].GetType(context))) == EvaluationValue.True))
{
return(EvaluationValue.True);
}
else
{
return(EvaluationValue.False);
}
}
public static IFunction Integrate(IFunction func, double xMin, double xMax, int granularity)
{
var points = new List <Point>();
double xDiff = xMax - xMin;
double delta = xDiff / granularity;
double x = xMin;
double yPrev = 0;
for (int i = 0; i < granularity; ++i)
{
double xa = x;
double xb = x + delta;
double ya = func.Evaluate(xa);
double yb = func.Evaluate(xb);
double area = delta * (ya + yb) / 2;
double y = yPrev + area;
points.Add(new Point(x, y));
x += delta;
yPrev = y;
}
return(new LinearInterpolation(points));
}
/// <summary>
/// Evaluates the function.
/// </summary>
/// <param name="context">The evaluation context instance.</param>
/// <param name="args">The function arguments.</param>
/// <returns>The result value of the function evaluation.</returns>
public override EvaluationValue Evaluate(EvaluationContext context, params IFunctionParameter[] args)
{
if (context == null)
{
throw new ArgumentNullException("context");
}
if (args == null)
{
throw new ArgumentNullException("args");
}
var retBag = new BagValue(DataType);
IFunction functionDup = DataType.IsInFunction;
foreach (object par1 in args[0].Elements)
{
EvaluationValue retVal = functionDup.Evaluate(context, new EvaluationValue(par1, args[0].GetType(context)), retBag);
if (!retVal.BoolValue)
{
retBag.Add(new EvaluationValue(par1, args[0].GetType(context)));
}
}
foreach (object par2 in args[1].Elements)
{
EvaluationValue retVal = functionDup.Evaluate(context, new EvaluationValue(par2, args[1].GetType(context)), retBag);
if (!retVal.BoolValue)
{
retBag.Add(new EvaluationValue(par2, args[1].GetType(context)));
}
}
return(new EvaluationValue(retBag, DataType));
}
private double Integrate(int index, double a, double b)
{
IFunction function = functions[index];
if (!IsInvalid(function.Evaluate(a)) && !IsInvalid(function.Evaluate(b)))
{
return(integrator.Integrate(function, a, b).value);
}
return(0);
}
public double Integrate(IFunction <double> fx, Range <double> range)
{
var x0 = range.Start;
var sum = 0d;
foreach (var x1 in range.All.Skip(1))
{
sum += TrapezoidalRule(x1, x0, fx.Evaluate(x1), fx.Evaluate(x0));
x0 = x1;
}
return(sum);
}
protected override double EstimateIntegralOver(IFunction <double> fx, double x0, double x2)
{
// Simpson's method
var H = x2 - x0;
var h = 0.5 * H;
var x1 = x0 + h;
var fx0 = fx.Evaluate(x0);
var fx1 = fx.Evaluate(x1);
var fx2 = fx.Evaluate(x2);
return((h / 3) * (fx0 + 4 * fx1 + fx2));
}
/// <summary>
/// Method called by the EvaluationEngine to evaluate the function.
/// </summary>
/// <param name="context">The evaluation context instance.</param>
/// <param name="args">The IFuctionParameters that will be used as arguments to the function.</param>
/// <returns></returns>
public override EvaluationValue Evaluate(EvaluationContext context, params IFunctionParameter[] args)
{
if (context == null)
{
throw new ArgumentNullException("context");
}
if (args == null)
{
throw new ArgumentNullException("args");
}
IFunction function = args[0].GetFunction(0);
if (!args[1].IsBag)
{
return(EvaluationValue.False);
}
var retVal = new BagValue(args[1].GetType(context));
foreach (var par in args[1].Elements)
{
retVal.Add(
function.Evaluate(
context,
new EvaluationValue(par, args[1].GetType(context))));
}
return(new EvaluationValue(retVal, args[1].GetType(context)));
}
public HestonCallSimulationOptimizationProblem(EquityCalibrationData equityCalData, Vector matBound, Vector strikeBound)
: base(equityCalData, matBound, strikeBound)
{
//this.dyFunc = equityCalData.dyFunc;
this.dyFunc = CallEstimator.IstantaneousDividendYield(equityCalData);
this.zrFunc = equityCalData.zrFunc;
// Generates common random numbers
I = (int)Math.Ceiling(cpmd.Maturity[Range.End] / dt);
epsilon = new Matrix(I, 2 * N);
NewRandomNumbers();
// Precalculates istantaneous growth rates
growth = new Vector(I);
for (int i = 0; i < I; i++)
{
double t = i * dt;
double zr_t = zrFunc.Evaluate(t);
growth[i] = zr_t + FunctionHelper.Partial(zr_t, zrFunc, new Vector()
{
t
}, 0, dt) * t - dyFunc.Evaluate(t);
}
Console.WriteLine("Heston Simulation Calibration: Paths=" + N);
}
/// <summary>
/// Method called by the EvaluationEngine to evaluate the function.
/// </summary>
/// <param name="context">The evaluation context instance.</param>
/// <param name="args">The IFuctionParameters that will be used as arguments to the function.</param>
/// <returns></returns>
public override EvaluationValue Evaluate(EvaluationContext context, params IFunctionParameter[] args)
{
if (context == null)
{
throw new ArgumentNullException("context");
}
if (args == null)
{
throw new ArgumentNullException("args");
}
IFunction function = args[0].GetFunction(0);
if (!Equals(function.Returns, DataTypeDescriptor.Boolean))
{
return(EvaluationValue.Indeterminate);
}
foreach (var par1 in args[1].Elements)
{
foreach (var par2 in args[2].Elements)
{
EvaluationValue retVal = function.Evaluate(
context,
new EvaluationValue(par1, args[1].GetType(context)), new EvaluationValue(par2, args[2].GetType(context)));
if (!retVal.BoolValue)
{
return(EvaluationValue.False);
}
}
}
return(EvaluationValue.True);
}
/// <summary>
/// Evaluates the function.
/// </summary>
/// <param name="context">The evaluation context instance.</param>
/// <param name="args">The function arguments.</param>
/// <returns>The result value of the function evaluation.</returns>
public override EvaluationValue Evaluate(EvaluationContext context, params IFunctionParameter[] args)
{
if (context == null)
{
throw new ArgumentNullException("context");
}
if (args == null)
{
throw new ArgumentNullException("args");
}
IFunction function = DataType.EqualFunction;
foreach (object par1 in args[0].Elements)
{
foreach (object par2 in args[1].Elements)
{
EvaluationValue retVal = function.Evaluate(
context,
new EvaluationValue(par1, args[0].GetType(context)),
new EvaluationValue(par2, args[1].GetType(context)));
if (retVal.BoolValue)
{
return(EvaluationValue.True);
}
}
}
return(EvaluationValue.False);
}
/// <summary>
/// Evaluates the function.
/// </summary>
/// <param name="context">The evaluation context instance.</param>
/// <param name="args">The function arguments.</param>
/// <returns>The result value of the function evaluation.</returns>
public override EvaluationValue Evaluate(EvaluationContext context, params IFunctionParameter[] args)
{
if (context == null)
{
throw new ArgumentNullException("context");
}
if (args == null)
{
throw new ArgumentNullException("args");
}
if (args[1].IsBag)
{
IFunction function = DataType.EqualFunction;
foreach (object value in args[1].Elements)
{
if (function.Evaluate(
context,
new EvaluationValue(args[0], args[0].GetType(context)),
new EvaluationValue(value, args[1].GetType(context))) == EvaluationValue.True)
{
return(EvaluationValue.True);
}
}
}
return(EvaluationValue.False);
}
/// <summary>
/// Method called by the EvaluationEngine to evaluate the function.
/// </summary>
/// <param name="context">The evaluation context instance.</param>
/// <param name="args">The IFuctionParameters that will be used as arguments to the function.</param>
/// <returns></returns>
public override EvaluationValue Evaluate(EvaluationContext context, params IFunctionParameter[] args)
{
if (context == null)
{
throw new ArgumentNullException("context");
}
if (args == null)
{
throw new ArgumentNullException("args");
}
IFunction function = args[0].GetFunction(0);
foreach (var par1 in args[1].Elements)
{
bool hasFound = false;
foreach (var par2 in args[2].Elements)
{
EvaluationValue retVal = function.Evaluate(
context,
new EvaluationValue(par1, args[1].GetType(context)),
new EvaluationValue(par2, args[2].GetType(context)));
if (retVal.BoolValue)
{
hasFound = true;
break;
}
}
if (!hasFound)
{
return(EvaluationValue.False);
}
}
return(EvaluationValue.True);
}
/// <summary>
/// Method called by the EvaluationEngine to evaluate the function.
/// </summary>
/// <param name="context">The evaluation context instance.</param>
/// <param name="args">The IFuctionParameters that will be used as arguments to the function.</param>
/// <returns></returns>
public override EvaluationValue Evaluate(EvaluationContext context, params IFunctionParameter[] args)
{
if (context == null)
{
throw new ArgumentNullException("context");
}
if (args == null)
{
throw new ArgumentNullException("args");
}
IFunction function = args[0].GetFunction(0);
var value = new EvaluationValue(args[1], args[1].GetType(context));
foreach (var par in args[2].Elements)
{
EvaluationValue retVal = function.Evaluate(
context, value,
new EvaluationValue(par, args[2].GetType(context)));
if (retVal.BoolValue)
{
return(retVal);
}
}
return(EvaluationValue.False);
}
private bool UnsatisfiedRoot(IFunction function, double i1, double d1, double i2, double d2)
{
if (Math.Sign(d1) != Math.Sign(d2))
{
double root = EMath.Geometry.Line.Root(i1, d1, i2, d2);
if (!((decimal)root >= (decimal)i1 && (decimal)root <= (decimal)i2 &&
Math.Abs(function.Evaluate(root)) < rootTolerance))
{
Debug.Log(Math.Abs(function.Evaluate(root)));
Debug.Log("Unsatisfied Root!!!");
return(true);
}
}
return(false);
}
public double Integrate(IFunction <double> fx, Range <double> range)
{
var x0 = range.Start;
var sum = 0d;
foreach (var x2 in range.All.Skip(1))
{
var h = x2 - x0;
var x1 = x0 + 0.5 * h;
var fx0 = fx.Evaluate(x0);
var fx1 = fx.Evaluate(x1);
var fx2 = fx.Evaluate(x2);
sum += (h / 6) * (fx0 + 4 * fx1 + fx2);
x0 = x2;
}
return(sum);
}
private Matrix LocVolMatrixFromImpliedVol(CallPriceMarketData Hdataset, IFunction impVol, out Vector locVolMat, out Vector locVolStr)
{
int nmat = calibrationSettings.LocalVolatilityMaturities;
int nstrike = calibrationSettings.LocalVolatilityStrikes;
double lastMat = Hdataset.Maturity[Range.End];
double lastStr = Hdataset.Strike[Range.End];
locVolMat = Vector.Linspace(Hdataset.Maturity[0], lastMat, nmat);
locVolStr = Vector.Linspace(Hdataset.Strike[0], lastStr, nstrike);
Matrix locVolMatrix = new Matrix(nmat, nstrike);
Integrate integrate = new Integrate(this);
double sigma, dSigmadk, num, y, den, avgGrowthRate;
Vector x = new Vector(2);
for (int i = 0; i < nmat; i++)
{
avgGrowthRate = integrate.AdaptLobatto(0.0, locVolMat[i]);
int j = 0;
x[0] = locVolMat[i];
x[1] = locVolStr[j];
sigma = impVol.Evaluate(x);
dSigmadk = impVol.Partial(x, 1);
num = Math.Pow(sigma, 2) + 2.0 * sigma * x[0] * impVol.Partial(x, 0);
den = 1.0;
locVolMatrix[i, j] = Math.Sqrt(num / den);
// The rest of the cycle.
for (j = 1; j < nstrike; j++)
{
x[1] = locVolStr[j];
sigma = impVol.Evaluate(x);
dSigmadk = impVol.Partial(x, 1);
num = Math.Pow(sigma, 2) + 2.0 * sigma * x[0] *
(impVol.Partial(x, 0) + avgGrowthRate * x[1] * dSigmadk);
y = Math.Log(locVolStr[j] / Hdataset.S0) + avgGrowthRate;
den = System.Math.Pow(1.0 - x[1] * y * dSigmadk / sigma, 2) + x[1] * sigma * x[0] *
(dSigmadk - 0.25 * x[1] * sigma * x[0] * dSigmadk * dSigmadk + x[1] * impVol.Partial2(x, 1));
locVolMatrix[i, j] = Math.Sqrt(num / den);
}
}
return(locVolMatrix);
}
internal void RegisterFunction(IFunction function)
{
this.CheckForExistingFunctionName(function.Name);
this.registeredFunctions.Add(function.Name, (p, a) =>
{
function.Variables = a;
return(function.Evaluate(p, this.options));
});
}
private void AddFunctionLine(IFunction function, double i, double ih, double b, Material material,
List <Point> points, int index)
{
double d = function.Evaluate(i);
if (IsInvalid(d))
{
SetInvalidContinuity(points, index);
return;
}
Point start = GetPoint(i, d);
points.Add(start);
double dh = function.Evaluate(ih);
if (IsInvalid(dh))
{
SetInvalidContinuity(ih, b, points, index);
return;
}
Point end = GetPoint(ih, dh);
if ((decimal)ih >= (decimal)b)
{
points.Add(end);
}
if (UnsatisfiedRoot(function, i, d, ih, dh))
{
SetInvalidContinuity(ih, b, points, index);
return;
}
PlotLine(start, end, material);
}
public double Evaluate(double x)
{
if (_validateDomain)
{
if (!_domain.IsValid(x))
{
throw new ArgumentOutOfRangeException($"{x} does not fall within domain {_domain}.");
}
}
return(_function.Evaluate(x));
}
/// <summary>
/// Linear Differential Equation of the form y` = P(t)y + G(t)
/// </summary>
/// <param name="Pt">function of t to multiply with y</param>
/// <param name="Gt">function of t to add to result</param>
/// <returns>differential equation</returns>
public static FirstOrderDE <T> Linear(IFunction <T> Pt, IFunction <T> Gt)
{
var calc = Pt.Calculator ?? Gt.Calculator;
return(new FirstOrderDE <T>(
new NativeFunction2 <T>(calc, ((T, T)args) => {
var x = args.Item1;
var y = args.Item2;
return calc.Subtract(
calc.Multiply(Pt.Evaluate(x), y),
Gt.Evaluate(x)
);
})
static double Mean(IFunction f, double a, double b)
{
double sum = 0;
int N = 20;
double h = b - a;
double dt = h / N;
for (int z = 0; z < N; z++)
{
sum += f.Evaluate(a + (dt * z)) * dt;
}
return(sum / h);
}
/* not tochable */ //----------------------------------------------------------------------------------
private void Button1_Click(object sender, EventArgs e) /*plot derivative*/
{
if (coordinates != null)
{
foreach (var item in coordinates)
{
coordinates.Remove(item);
}
}
/*plot on the pictureBox*/
zoomValue = trackBar1.Value;
orgX = pictureBox1.Width / 2;
orgY = pictureBox1.Height / 2;
derivativePen = new Pen(Brushes.Red, 2.0F);
/* plot Newton's derivative with pen purple */
derivativePen = new Pen(Brushes.Purple, 2.0F);
for (float i = -orgX; i <= pictureBox1.Height / 2; i += 0.01f)
{
double h = 0.01;
double Y1 = ((root.Evaluate(i + h) - root.Evaluate(i)) / h); //f(x+h) - f(x) / h
double Y2 = ((root.Evaluate(i + (0.01) + h) - root.Evaluate(i + (0.01))) / h);
Y1 = ((-1) * Y1 * zoomValue) + orgY;
Y2 = ((-1) * Y2 * zoomValue) + orgY;
double X = (zoomValue * i) + orgX;
double X2 = (zoomValue * i) + orgX + 0.01f;
if (Y1 <= pictureBox1.Height && Y2 <= pictureBox1.Height && Y1 >= 0 && Y2 >= 0)
{
g.DrawLine(derivativePen, (float)X, (float)Y1, (float)X2, (float)Y2);
}
}
/* plot the Analytical derivative and plotting the tree*/
IFunction p;
p = root.derivative();
DrawBinaryTree(p);
derivativePen = new Pen(Brushes.Green, 2.0F);
for (float i = -orgX; i <= pictureBox1.Height; i += 0.01f)
{
double X = (double)i;
float Y = (float)p.Evaluate(X) * zoomValue;
float Y2 = ((float)p.Evaluate(i + 0.1) * zoomValue);
if (Y <= pictureBox1.Height / 2 && Y2 <= pictureBox1.Height / 2 && Y >= -200 && Y2 >= -200)
{
g.DrawLine(derivativePen, (float)(X * zoomValue) + orgX, orgY - Y, (float)(orgX + (X * zoomValue) + 0.1), orgY - Y2);
}
}
}
public DefiniteIntegral Integrate(IFunction function, double a, double b)
{
double c1 = (b + a) / 2.0;
double c2 = (b - a) / 2.0;
double sum = 0;
for (int i = 0; i < polynomials.n; i++)
{
sum += polynomials.weights[i] * function.Evaluate(c1 + c2 * polynomials.roots[i]);
}
return(new DefiniteIntegral(c2 * sum));
}
public static IFunction Differentiate(IFunction func, double xMin, double xMax, int granularity)
{
var points = new List <Point>();
double xDiff = xMax - xMin;
double delta = xDiff / granularity;
double x = xMin;
for (int i = 0; i < granularity; ++i)
{
double xa = x - delta / 2;
double xb = x + delta / 2;
double ya = func.Evaluate(xa);
double yb = func.Evaluate(xb);
double slope = (yb - ya) / (xb - xa);
points.Add(new Point(x, slope));
x += delta;
}
return(new LinearInterpolation(points));
}
protected static void SaveCsv(string name, IFunction <double> approx, IFunction <double> real, Range <double> range)
{
if (!Directory.Exists(".data"))
{
Directory.CreateDirectory(".data");
}
using (var writer = new StreamWriter(Path.Combine(".data", $"{name}.xy.csv"))) {
writer.WriteLine("x, y, ~y");
foreach (var x in range.All)
{
writer.WriteLine($"{x},{real.Evaluate(x)},{approx.Evaluate(x)}");
}
}
}
protected static void SaveCsv(string name, IFunction <double> approx, Func <double, double> real)
{
if (!Directory.Exists(".data"))
{
Directory.CreateDirectory(".data");
}
using (var writer = new StreamWriter(Path.Combine(".data", $"{name}.xy.csv"))) {
writer.WriteLine("x, y, y`");
for (var x = -10d; x <= 10d; x += 0.1d)
{
writer.WriteLine($"{x},{real(x)},{approx.Evaluate(x)}");
}
}
}
/// <summary>
/// Returns the Strike vector embedded in the volatility matrix.
/// The method manage the convention that if rates/strikes [defined in .ColumnValues fields] are equal to -1,
/// the strike vector is ATM and must be derived from the term structure.
/// </summary>
/// <param name="normalVol">The matrix</param>
/// <param name="zr">The term structure.</param>
/// <returns>The strike vector.</returns>
static Vector GetStrikes(MatrixMarketData normalVol, IFunction zr)
{
if (IsAtmMatrix(normalVol))
{
// builds the vector of ATM strikes
var s = new Vector(normalVol.RowValues.Length);
for (int j = 0; j < s.Length; j++)
{
s[j] = zr.Evaluate(normalVol.RowValues[j]);
}
return(s);
}
else
{
return(normalVol.ColumnValues);
}
}
/// <summary>
/// Registers the supplied <paramref name="function"/> for use within compiling and evaluating an <see cref="Expression"/>.
/// </summary>
/// <param name="function">The <see cref="IFunction"/> to perform the function evaluation.</param>
/// <param name="force">Whether to forcefully override any existing function.</param>
public void RegisterFunction(IFunction function, bool force = false)
{
if (function is null)
{
throw new ArgumentNullException(nameof(function));
}
this.RegisterFunction(
function.Name,
(p, a) =>
{
function.Variables = a;
return(function.Evaluate(p, this));
},
force);
}
internal static Matrix ToMatrix(IFunction func)
{
int n = 20;
double ub = 5;
var sup = func as ISupport1D;
if (sup != null)
{
ub = sup.Support[1];
}
var mat = new Matrix(n, 2);
for (int i = 0; i < n; i++)
{
double x = i * ub / n;
mat[i, 0] = x;
mat[i, 1] = func.Evaluate(x);
}
return(mat);
}
public void RegisterFunction(IFunction function, bool force = false)
{
ExecFunction exec = new ExecFunction((p, a, c) =>
{
return(function.Evaluate(p, a, c));
});
if (force)
{
this[function.Name] = exec;
}
else if (!this.ContainsKey(function.Name))
{
this.Add(function.Name, exec);
}
else
{
throw new FunctionNameAlreadyRegisteredException(function.Name);
}
}
static double Mean(IFunction f, double a, double b)
{
double sum = 0;
int N = 20;
double h = b - a;
double dt = h / N;
for (int z = 0; z < N; z++)
sum += f.Evaluate(a + (dt * z)) * dt;
return sum / h;
}
/// <summary>
/// Evaluates a function and also validates it's return value and parameter data types
/// </summary>
/// <param name="context">The evaluation context instance.</param>
/// <param name="functionInstance">The function to call</param>
/// <param name="arguments">The function arguments</param>
/// <returns>The return value of the function</returns>
public static EvaluationValue EvaluateFunction(EvaluationContext context, IFunction functionInstance, params IFunctionParameter[] arguments)
{
if (context == null) throw new ArgumentNullException("context");
// If the caller is in a missing attribute state the function should not be called
if (context.IsMissingAttribute)
{
context.Trace("There's a missing attribute in the parameters");
return EvaluationValue.Indeterminate;
}
else
{
// Validate function defined arguments
int functionArgumentIdx;
for (functionArgumentIdx = 0; functionArgumentIdx < functionInstance.Arguments.Length; functionArgumentIdx++)
{
// Validate the value is not an Indeterminate value
if (arguments[functionArgumentIdx] is EvaluationValue &&
((EvaluationValue)arguments[functionArgumentIdx]).IsIndeterminate)
{
if (!context.IsMissingAttribute)
{
context.ProcessingError = true;
}
context.Trace("There's a parameter with Indeterminate value");
return EvaluationValue.Indeterminate;
}
// Compare the function and the value data type
if (((functionInstance.Arguments[functionArgumentIdx] != arguments[functionArgumentIdx].GetType(context)) &&
((functionInstance.Arguments[functionArgumentIdx] != DataTypeDescriptor.Bag) && (arguments[functionArgumentIdx] is BagValue))))
{
context.ProcessingError = true;
context.Trace("There's a parameter with an invalid datatype");
return EvaluationValue.Indeterminate;
}
}
//If the function supports variable arguments, the last datatype is used to validate the
//rest of the parameters
if (functionInstance.VarArgs)
{
functionArgumentIdx--;
for (int argumentValueIdx = functionArgumentIdx; argumentValueIdx < arguments.Length; argumentValueIdx++)
{
// Validate the value is not an Indeterminate value
if (arguments[argumentValueIdx] is EvaluationValue && ((EvaluationValue)arguments[argumentValueIdx]).IsIndeterminate)
{
if (!context.IsMissingAttribute)
{
context.ProcessingError = true;
}
context.Trace("There's a parameter with Indeterminate value");
return EvaluationValue.Indeterminate;
}
// Compare the function and the value data type
if ((functionInstance.Arguments[functionArgumentIdx] != arguments[argumentValueIdx].GetType(context)) &&
((arguments[argumentValueIdx] is BagValue) && (functionInstance.Arguments[functionArgumentIdx] != DataTypeDescriptor.Bag)))
{
context.ProcessingError = true;
context.Trace("There's a parameter with an invalid datatype");
return EvaluationValue.Indeterminate;
}
}
}
var sb = new StringBuilder();
// Call the function in a controlled evironment to capture any exception
try
{
sb.Append(functionInstance.Id);
sb.Append("( ");
bool isFirst = true;
foreach (IFunctionParameter param in arguments)
{
if (isFirst)
{
isFirst = false;
}
else
{
sb.Append(", ");
}
sb.Append(param.ToString());
}
sb.Append(" )");
sb.Append(" = ");
EvaluationValue returnValue = functionInstance.Evaluate(context, arguments);
sb.Append(returnValue.ToString());
context.Trace(sb.ToString());
return returnValue;
}
catch (EvaluationException e)
{
context.Trace(sb.ToString());
context.ProcessingError = true;
context.Trace("Error: {0}", e.Message);
return EvaluationValue.Indeterminate;
}
}
}
internal static Matrix ToMatrix(IFunction func)
{
int n = 20;
double ub=5;
var sup = func as ISupport1D;
if (sup != null)
ub = sup.Support[1];
var mat = new Matrix(n,2);
for (int i = 0; i < n; i++)
{
double x = i*ub / n;
mat[i, 0] = x;
mat[i, 1] = func.Evaluate(x);
}
return mat;
}
public HestonCallSimulationOptimizationProblem(EquityCalibrationData equityCalData, Vector matBound, Vector strikeBound)
: base(equityCalData,matBound,strikeBound)
{
//this.dyFunc = equityCalData.dyFunc;
this.dyFunc = CallEstimator.IstantaneousDividendYield(equityCalData);
this.zrFunc = equityCalData.zrFunc;
// Generates common random numbers
I = (int)Math.Ceiling(cpmd.Maturity[Range.End] / dt);
epsilon = new Matrix(I, 2*N);
NewRandomNumbers();
// Precalculates istantaneous growth rates
growth = new Vector(I);
for (int i = 0; i < I; i++)
{
double t = i * dt;
double zr_t = zrFunc.Evaluate(t);
growth[i] = zr_t + FunctionHelper.Partial(zr_t,zrFunc, new Vector() { t }, 0, dt) * t - dyFunc.Evaluate(t);
}
Console.WriteLine("Heston Simulation Calibration: Paths=" + N);
}
public static double LogAverageFactor(double y, IFunction func, Vector x)
{
return (y == func.Evaluate(x)) ? 0.0 : Double.NegativeInfinity;
}
private Matrix LocVolMatrixFromImpliedVol(CallPriceMarketData Hdataset, IFunction impVol, out Vector locVolMat, out Vector locVolStr)
{
int nmat = calibrationSettings.LocalVolatilityMaturities;
int nstrike = calibrationSettings.LocalVolatilityStrikes;
double lastMat = Hdataset.Maturity[Range.End];
double lastStr = Hdataset.Strike[Range.End];
locVolMat = Vector.Linspace(Hdataset.Maturity[0], lastMat, nmat);
locVolStr = Vector.Linspace(Hdataset.Strike[0], lastStr, nstrike);
Matrix locVolMatrix = new Matrix(nmat, nstrike);
Integrate integrate = new Integrate(this);
double sigma, dSigmadk, num, y, den, avgGrowthRate;
Vector x = new Vector(2);
for (int i = 0; i < nmat; i++)
{
avgGrowthRate = integrate.AdaptLobatto(0.0, locVolMat[i]);
int j = 0;
x[0] = locVolMat[i];
x[1] = locVolStr[j];
sigma = impVol.Evaluate(x);
dSigmadk = impVol.Partial(x, 1);
num = Math.Pow(sigma, 2) + 2.0 * sigma * x[0] * impVol.Partial(x, 0);
den = 1.0;
locVolMatrix[i, j] = Math.Sqrt(num / den);
// The rest of the cycle.
for (j = 1; j < nstrike; j++)
{
x[1] = locVolStr[j];
sigma = impVol.Evaluate(x);
dSigmadk = impVol.Partial(x, 1);
num = Math.Pow(sigma, 2) + 2.0 * sigma * x[0] *
(impVol.Partial(x, 0) + avgGrowthRate * x[1] * dSigmadk);
y = Math.Log(locVolStr[j] / Hdataset.S0) + avgGrowthRate;
den = System.Math.Pow(1.0 - x[1] * y * dSigmadk / sigma, 2) + x[1] * sigma * x[0] *
(dSigmadk - 0.25 * x[1] * sigma * x[0] * dSigmadk * dSigmadk + x[1] * impVol.Partial2(x, 1));
locVolMatrix[i, j] = Math.Sqrt(num / den);
}
}
return locVolMatrix;
}
