protected double getResidual(
final double fwd, final double expiry, final double[] ks, final double[] vols) {
// Check for trivial case where cutoff is so low that there's no effective value in the option
final double cutoffPrice =
BlackFormulaRepository.price(fwd, ks[0], expiry, vols[0], ks[0] > fwd);
if (CompareUtils.closeEquals(cutoffPrice, 0)) {
return 0.0; // i.e. the tail function is never used
}
// The typical case - fit a ShiftedLognormal to the two strike-vol pairs
final ShiftedLognormalVolModel leftExtrapolator =
new ShiftedLognormalVolModel(fwd, expiry, ks[0], vols[0], ks[1], vols[1]);
// Now, handle behaviour near zero strike. ShiftedLognormalVolModel has non-zero put price for
// zero strike.
// What we do is to find the strike, k_min, at which f(k) = p(k)/k^2 begins to blow up, by
// finding the minimum of this function, k_min
// then setting f(k) = f(k_min) for k < k_min. This ensures the implied volatility and the
// integrand are well behaved in the limit k -> 0.
final Function1D<Double, Double> shiftedLnIntegrand =
new Function1D<Double, Double>() {
@Override
public Double evaluate(final Double strike) {
return leftExtrapolator.priceFromFixedStrike(strike) / (strike * strike);
}
};
final double kMin = new BrentMinimizer1D().minimize(shiftedLnIntegrand, EPS, EPS, ks[0]);
final double fMin = shiftedLnIntegrand.evaluate(kMin);
double res = fMin * kMin; // the (hopefully) very small rectangular bit between zero and kMin
res += _integrator.integrate(shiftedLnIntegrand, kMin, ks[0]);
return res;
}
