double LmmVanillaSwapPricer::swapNPV_Analytical_2(const VanillaSwap& vanillaSwap, const std::vector<double>& liborsInitValue) const // initLibor[i] = L_i[T_0]
{
assert(pLMMTenorStructure_->get_horizon()+1 == liborsInitValue.size());
assert(pLMMTenorStructure_->get_horizon() >= vanillaSwap.get_indexEnd()); // if not cannot price this swap;
size_t horizon = pLMMTenorStructure_->get_horizon();
const double & floatingLegdelta_T = vanillaSwap.get_floatingLegTenorType().YearFraction();
const double & fixedLegdelta_T = vanillaSwap.get_fixedLegTenorType().YearFraction();
//! ZC[i] = P(T_0,T_i)
std::vector<double> ZC(horizon+2);
ZC[0] = 1.0;
for(size_t i=1; i<ZC.size(); ++i)
{
ZC[i] = ZC[i-1]/(1+floatingLegdelta_T*liborsInitValue[i-1]);
}
//! numeraire
std::vector<double> numeraire(ZC.size() ); // determinisitc IR
for(size_t i=0; i<ZC.size(); ++i)
{
numeraire[i] = 1.0/ZC[i];
}
//! pvFloatingLeg: 1 - 1
const std::vector<LMM::Index>& floatingLegPaymentIndexSchedule = vanillaSwap.get_floatingLegPaymentIndexSchedule();
//size_t floatingLegTenorLmmTenorRatio = vanillaSwap.get_floatingLegTenorLmmTenorRatio();
LMM::Index indexFloatingLegStart = floatingLegPaymentIndexSchedule.front();
LMM::Index indexFloatingLegEnd = floatingLegPaymentIndexSchedule.back();
double pvFloatingLegValue = ZC[indexFloatingLegStart-1] - ZC[indexFloatingLegEnd];
////! pvFloatingLeg: exact
//double pvFloatingLeg = 0.0;
//const std::vector<LMM::Index>& floatingLegPaymentIndexSchedule = vanillaSwap.get_floatingLegPaymentIndexSchedule();
//for(size_t itr = 0; itr < floatingLegPaymentIndexSchedule.size(); ++itr)
//{
// //! At time T_{i+1}, pay: L_i(T_i)
// size_t floatingLegPaymentIndex = floatingLegPaymentIndexSchedule[itr]; // = i+1
// size_t indexLibor = floatingLegPaymentIndex-1; // =i, because : floatingTenor = lmmTenor
// pvFloatingLeg += floatingLegdelta_T*initLibor[indexLibor]*ZC[floatingLegPaymentIndex];
//}
LMM::Index indexValuationDate = 0;
double pvFixedLegValue = pvFixedLeg(indexValuationDate,vanillaSwap,numeraire);
return pvFloatingLegValue - pvFixedLegValue;
}
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;
}