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 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);
