/**
* General method when you wish to compute the expected variance from a log-moneyness
* parametrised surface to within a certain tolerance
*
* @param surface log-moneyness parametrised volatility surface
* @return expected variance
*/
@SuppressWarnings("synthetic-access")
@Override
public Double visitLogMoneyness(final BlackVolatilitySurfaceLogMoneyness surface) {
final double atmVol = surface.getVolatilityForLogMoneyness(_t, 0.0);
if (_t < 1e-4) {
return atmVol * atmVol;
}
final double rootT = Math.sqrt(_t);
final double invNorTol = NORMAL.getInverseCDF(_tol);
final Function1D<Double, Double> integrand = getLogMoneynessIntegrand(surface);
double putPart;
if (_addResidual) {
putPart = _integrator.integrate(integrand, Math.log(_lowStrikeCutoff / _f), 0.0);
putPart += _residual;
} else {
final double l = invNorTol * atmVol * rootT; // initial estimate of lower limit
putPart = _integrator.integrate(integrand, l, 0.0);
double rem = integrand.evaluate(l);
double error = rem / putPart;
int step = 1;
while (error > _tol) {
putPart += _integrator.integrate(integrand, (step + 1) * l, step * l);
step++;
rem = integrand.evaluate((step + 1) * l);
error = rem / putPart;
}
putPart +=
rem; // add on the (very small) remainder estimate otherwise we'll always underestimate
// variance
}
final double u =
_f * Math.exp(-invNorTol * atmVol * rootT); // initial estimate of upper limit
double callPart = _integrator.integrate(integrand, 0.0, u);
double rem = integrand.evaluate(u);
double error = rem / callPart;
int step = 1;
while (error > _tol) {
callPart += _integrator.integrate(integrand, step * u, (1 + step) * u);
step++;
rem = integrand.evaluate((1 + step) * u);
error = rem / putPart;
}
// callPart += rem;
// don't add on the remainder estimate as it is very conservative, and likely too large
return 2 * (putPart + callPart) / _t;
}
@SuppressWarnings("synthetic-access")
@Override
public Double visitStrike(final BlackVolatilitySurfaceStrike surface) {
final double atmVol = surface.getVolatility(_t, _f);
if (_t < 1e-4) {
return atmVol * atmVol;
}
final double rootT = Math.sqrt(_t);
final double invNorTol = NORMAL.getInverseCDF(_tol);
final Function1D<Double, Double> integrand = getStrikeIntegrand(surface);
final Function1D<Double, Double> remainder =
new Function1D<Double, Double>() {
@Override
public Double evaluate(final Double strike) {
if (strike == 0) {
return 0.0;
}
final boolean isCall = strike >= _f;
final double vol = surface.getVolatility(_t, strike);
final double otmPrice = BlackFormulaRepository.price(_f, strike, _t, vol, isCall);
final double res = (isCall ? otmPrice / strike : otmPrice / 2 / strike);
return res;
}
};
double putPart;
if (_addResidual) {
putPart = _integrator.integrate(integrand, _lowStrikeCutoff, _f);
putPart += _residual;
} else {
double l = _f * Math.exp(invNorTol * atmVol * rootT); // initial estimate of lower limit
putPart = _integrator.integrate(integrand, l, _f);
double rem = remainder.evaluate(l);
double error = rem / putPart;
while (error > _tol) {
l /= 2.0;
putPart += _integrator.integrate(integrand, l, 2 * l);
rem = remainder.evaluate(l);
error = rem / putPart;
}
putPart +=
rem; // add on the (very small) remainder estimate otherwise we'll always underestimate
// variance
}
double u = _f * Math.exp(-invNorTol * atmVol * rootT); // initial estimate of upper limit
double callPart = _integrator.integrate(integrand, _f, u);
double rem = remainder.evaluate(u);
double error = rem / callPart;
while (error > _tol) {
callPart += _integrator.integrate(integrand, u, 2 * u);
u *= 2.0;
rem = remainder.evaluate(u);
error = rem / putPart;
}
// callPart += rem/2.0;
// don't add on the remainder estimate as it is very conservative, and likely too large
return 2 * (putPart + callPart) / _t;
}
