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);
}
private double GetDeltaStrikeForAbs(double fwd, double strike, double maturity)
{
var cp = strike < 0 ? OptionType.Put : OptionType.Call;
Func <double, double> testFunc = (deltaK =>
{
var interpForStrike = InterpolatorFactory.GetInterpolator(ExpiriesDouble, ExpiriesDouble.Select(e => GetVolForDeltaStrike(deltaK, e, fwd)).ToArray(), TimeInterpolatorType);
var vol2 = interpForStrike.Interpolate(maturity);
var absK = BlackFunctions.AbsoluteStrikefromDeltaKAnalytic(fwd, deltaK, 0, maturity, vol2);
return(absK - strike);
});
var solvedStrike = -Math.Solvers.Brent.BrentsMethodSolve(testFunc, -0.99999999999, -0.00000000001, 1e-8);
if (solvedStrike == 0.00000000001 || solvedStrike == 0.99999999999) //out of bounds
{
var upperK = testFunc(-0.00000000001);
var lowerK = testFunc(-0.99999999999);
if (Abs(upperK - fwd) < Abs(lowerK - fwd))
{
solvedStrike = 0.00000000001;
}
else
{
solvedStrike = 0.99999999999;
}
}
return(solvedStrike);
}
private double GetAbsStrikeForDelta(double fwd, double deltaStrike, double maturity)
{
var cp = deltaStrike < 0 ? OptionType.Put : OptionType.Call;
Func <double, double> testFunc = (absK =>
{
var interpForStrike = InterpolatorFactory.GetInterpolator(ExpiriesDouble, ExpiriesDouble.Select(e => GetVolForAbsoluteStrike(absK, e, fwd)).ToArray(), TimeInterpolatorType);
var vol2 = interpForStrike.Interpolate(maturity);
var deltaK = BlackFunctions.BlackDelta(fwd, absK, 0, maturity, vol2, cp);
return(deltaK - deltaStrike);
});
var solvedStrike = Math.Solvers.Brent.BrentsMethodSolve(testFunc, 0.000000001, 50 * fwd, 1e-8);
return(solvedStrike);
}
