public void Build(DateTime originDate, double[][] strikes, DateTime[] expiries, double[][] vols, Func <double, double> forwardCurve)
{
OriginDate = originDate;
Expiries = expiries;
ExpiriesDouble = Expiries.Select(t => TimeBasis.CalculateYearFraction(originDate, t)).ToArray();
if (Expiries.Length != strikes.Length)
{
throw new InvalidOperationException("Expiries and first dimension of Strikes must of same length");
}
if (Expiries.Length != vols.Length)
{
throw new InvalidOperationException("Expiries and first dimension of Vols must of same length");
}
Alphas = new double[Expiries.Length];
Betas = new double[Expiries.Length];
Nus = new double[Expiries.Length];
Rhos = new double[Expiries.Length];
for (var i = 0; i < expiries.Length; i++)
{
var vs = vols[i];
var ks = strikes[i];
var t = ExpiriesDouble[i];
var fwd = forwardCurve(t);
Betas[i] = 1.0;
Func <double[], double[]> errorFunc = (x =>
{
var err = ks.Select((k, ix) => vs[ix] - SABR.CalcImpVol_Beta1(fwd, k, t, x[0], x[1], x[2]));
return(err.ToArray());
});
var n2Sol = new Math.Solvers.GaussNewton
{
ObjectiveFunction = errorFunc,
InitialGuess = new double[] { vs.Average(), 0.1, 0.1 },
Tollerance = 1e-8,
JacobianBump = 0.0000001
};
var paramArr = n2Sol.Solve();
Alphas[i] = paramArr[0];
Rhos[i] = paramArr[1];
Nus[i] = paramArr[2];
}
var fwds = ExpiriesDouble.Select(x => forwardCurve(x)).ToArray();
_alphaInterp = InterpolatorFactory.GetInterpolator(ExpiriesDouble, Alphas, TimeInterpolatorType);
_betaInterp = InterpolatorFactory.GetInterpolator(ExpiriesDouble, Betas, TimeInterpolatorType);
_rhoInterp = InterpolatorFactory.GetInterpolator(ExpiriesDouble, Rhos, TimeInterpolatorType);
_nuInterp = InterpolatorFactory.GetInterpolator(ExpiriesDouble, Nus, TimeInterpolatorType);
_fwdsInterp = InterpolatorFactory.GetInterpolator(ExpiriesDouble, fwds, TimeInterpolatorType);
}
public void CanSolveTameExample()
{
var n2Sol = new Math.Solvers.GaussNewton
{
ObjectiveFunction = Residuals,
InitialGuess = new double[] { 6, 0.3 },
Tollerance = 1e-8
};
var output = n2Sol.Solve();
var functionOutput = Residuals(output);
var functionOutputUp = Residuals(output.Select(x => x + 0.0001).ToArray());
var functionOutputDown = Residuals(output.Select(x => x - 0.0001).ToArray());
//verify that the solution is better than two neighboruing solutions
Assert.True(functionOutput.Select(x => x * x).Sum() < functionOutputUp.Select(x => x * x).Sum());
Assert.True(functionOutput.Select(x => x * x).Sum() < functionOutputDown.Select(x => x * x).Sum());
}
public void Dim2NRFacts()
{
var ws0 = new double[] { 76, 5, -2 };
var nExamples = 100;
var predictors = new double[nExamples][];
var predictions = new double[nExamples];
var R = new System.Random();
for (var e = 0; e < nExamples; e++)
{
predictors[e] = new double[2] {
R.NextDouble(), R.NextDouble()
};
}
var testFunc = new Func <double[], double[], double>((xs, ws) =>
{
var intercept = ws[0];
var w1 = ws[1];
var w2 = ws[2];
return(intercept + xs[0] * w1 + xs[1] * w2);
});
var solveFunc = new Func <double[], double[]>(ws =>
{
return(predictors.Select(x => testFunc(x, ws) - testFunc(x, ws0)).ToArray());
});
var solver = new Math.Solvers.GaussNewton
{
ObjectiveFunction = solveFunc,
InitialGuess = new double[3]
};
var weights = solver.Solve();
Assert.Equal(ws0[0], weights[0], 8);
Assert.Equal(ws0[1], weights[1], 8);
Assert.Equal(ws0[2], weights[2], 8);
}