const Real Gaussian1dModel::zerobondOption(
const Option::Type &type, const Date &expiry, const Date &valueDate,
const Date &maturity, const Rate strike, const Date &referenceDate,
const Real y, const Handle<YieldTermStructure> &yts, const Real yStdDevs,
const Size yGridPoints, const bool extrapolatePayoff,
const bool flatPayoffExtrapolation) const {
calculate();
Time fixingTime = termStructure()->timeFromReference(expiry);
Time referenceTime =
referenceDate == Null<Date>()
? 0.0
: termStructure()->timeFromReference(referenceDate);
Array yg = yGrid(yStdDevs, yGridPoints, fixingTime, referenceTime, y);
Array z = yGrid(yStdDevs, yGridPoints);
Array p(yg.size());
for (Size i = 0; i < yg.size(); i++) {
Real expValDsc = zerobond(valueDate, expiry, yg[i], yts);
Real discount =
zerobond(maturity, expiry, yg[i], yts) / expValDsc;
p[i] =
std::max((type == Option::Call ? 1.0 : -1.0) * (discount - strike),
0.0) /
numeraire(fixingTime, yg[i], yts) * expValDsc;
}
CubicInterpolation payoff(
z.begin(), z.end(), p.begin(), CubicInterpolation::Spline, true,
CubicInterpolation::Lagrange, 0.0, CubicInterpolation::Lagrange, 0.0);
Real price = 0.0;
for (Size i = 0; i < z.size() - 1; i++) {
price += gaussianShiftedPolynomialIntegral(
0.0, payoff.cCoefficients()[i], payoff.bCoefficients()[i],
payoff.aCoefficients()[i], p[i], z[i], z[i], z[i + 1]);
}
if (extrapolatePayoff) {
if (flatPayoffExtrapolation) {
price += gaussianShiftedPolynomialIntegral(
0.0, 0.0, 0.0, 0.0, p[z.size() - 2], z[z.size() - 2],
z[z.size() - 1], 100.0);
price += gaussianShiftedPolynomialIntegral(0.0, 0.0, 0.0, 0.0, p[0],
z[0], -100.0, z[0]);
} else {
if (type == Option::Call)
price += gaussianShiftedPolynomialIntegral(
0.0, payoff.cCoefficients()[z.size() - 2],
payoff.bCoefficients()[z.size() - 2],
payoff.aCoefficients()[z.size() - 2], p[z.size() - 2],
z[z.size() - 2], z[z.size() - 1], 100.0);
if (type == Option::Put)
price += gaussianShiftedPolynomialIntegral(
0.0, payoff.cCoefficients()[0], payoff.bCoefficients()[0],
payoff.aCoefficients()[0], p[0], z[0], -100.0, z[0]);
}
}
return numeraire(referenceTime, y, yts) * price;
}
extern std::vector
< std::unique_ptr< math::API::InterpolationTableIntegral > > referenceIntegrals;
SCENARIO("The composite interpolation table's integral functions correctly",
"[math], [CompositeInterpolationTable], [integral]"){
GIVEN("An CompositeInterpolationTable and "
"the vector of integral tables generated from it's components"){
WHEN("queried for their xGrid and yGrids"){
THEN("the stored values will be equal"){
LOG(INFO) << "Test " << ++testNumber
<< ": [integral] No Errors Expected";
auto integralTable = cit->integral(0);
auto xGrids = integralTable->xGrid();
auto xGrid = xGrids.begin();
auto yGrids = integralTable->yGrid();
auto yGrid = yGrids.begin();
for (auto& referenceIntegral : referenceIntegrals){
auto refXGrids = referenceIntegral->xGrid();
auto& refXGrid = refXGrids[0];
REQUIRE(true == std::equal(refXGrid.begin(), refXGrid.end(),
xGrid->begin(), xGrid->end()));
auto refYGrids = referenceIntegral->yGrid();
auto& refYGrid = refYGrids[0];
REQUIRE(true == std::equal(refYGrid.begin(), refYGrid.end(),
yGrid->begin(), yGrid->end()));
++xGrid;
++yGrid;
}
}
}
