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 SABRParamToIVFacts()
{
//for beta==1 and zero nu and rho we get a flat surface with vol==alpha
var vol = SABR.CalcImpVol_Beta1(100, 100, 1, 0.32, 0, 0);
Assert.Equal(0.32, vol, 10);
vol = SABR.CalcImpVol_Beta1(100, 150, 1, 0.32, 0, 0);
Assert.Equal(0.32, vol, 10);
vol = SABR.CalcImpVol_Beta1(100, 50, 1, 0.32, 0, 0);
Assert.Equal(0.32, vol, 10);
//for positive rho should see upside vols > downside
var volU = SABR.CalcImpVol_Beta1(100, 150, 1, 0.32, 0.5, 0.16);
var volD = SABR.CalcImpVol_Beta1(100, 75, 1, 0.32, 0.5, 0.16);
Assert.True(volU > volD);
//for negative rho should see upside vols < downside
volU = SABR.CalcImpVol_Beta1(100, 150, 1, 0.32, -0.5, 0.16);
volD = SABR.CalcImpVol_Beta1(100, 75, 1, 0.32, -0.5, 0.16);
Assert.True(volU < volD);
//for larger nu should see upside wing vols higher
volU = SABR.CalcImpVol_Beta1(100, 150, 1, 0.32, 0, 0.16);
volD = SABR.CalcImpVol_Beta1(100, 75, 1, 0.32, 0, 0.16);
var wingLow = volU + volD;
volU = SABR.CalcImpVol_Beta1(100, 150, 1, 0.32, 0, 0.32);
volD = SABR.CalcImpVol_Beta1(100, 75, 1, 0.32, 0, 0.32);
var wingHigh = volU + volD;
Assert.True(wingHigh > wingLow);
//for GB parameterization, should see no sensitivity to rho and nu at ATM
var volA = SABR.CalcImpVol_GB(100, 100, 1, 0.32, 0, 0.16);
var volB = SABR.CalcImpVol_GB(100, 100, 1, 0.32, -0.5, 0.26);
Assert.Equal(volA, volB, 10);
//for hagan and berestycki, should see agreement in most cases
var volHa = SABR.CalcImpVol_Hagan(100, 100, 1, 0.32, 0.9, 0.5, 0.16);
var volBe = SABR.CalcImpVol_Berestycki(100, 100, 1, 0.32, 0.9, 0.5, 0.16);
Assert.Equal(volHa, volBe, 5);
volHa = SABR.CalcImpVol_Hagan(100, 150, 1, 0.32, 0.5, 0.5, 0.16);
volBe = SABR.CalcImpVol_Berestycki(100, 150, 1, 0.32, 0.5, 0.5, 0.16);
Assert.Equal(volHa, volBe, 3);
}
public double GetVolForAbsoluteStrike(double strike, double maturity, double forward)
{
var alpha = _alphaInterp.Interpolate(maturity);
var beta = _betaInterp.Interpolate(maturity);
var nu = _nuInterp.Interpolate(maturity);
var rho = _rhoInterp.Interpolate(maturity);
var fwd = forward;
if (beta >= 1.0)
{
return(SABR.CalcImpVol_Beta1(fwd, strike, maturity, alpha, rho, nu));
}
else
{
return(SABR.CalcImpVol_Hagan(fwd, strike, maturity, alpha, beta, rho, nu));
}
}
public double CalcImpVol_Beta1(double k, SABRParameters currentSABR) => SABR.CalcImpVol_Beta1(_fwd, k, _tExp, currentSABR.Alpha, currentSABR.Rho, currentSABR.Nu);
public static double GetVolForAbsoluteStrike(double strike, double maturity, double forward, SABRParameters sabrParams) => sabrParams.Beta >= 1.0
? SABR.CalcImpVol_Beta1(forward, strike, maturity, sabrParams.Alpha, sabrParams.Rho, sabrParams.Nu)
: SABR.CalcImpVol_Hagan(forward, strike, maturity, sabrParams.Alpha, sabrParams.Beta, sabrParams.Rho, sabrParams.Nu);