Real GaussianLHPLossModel::expectedShortfall(const Date& d,
Probability perctl) const
{
// loss as a fraction of the live portfolio
Real ptflLossPerc = percentilePortfolioLossFraction(d, perctl);
Real remainingAttachAmount = basket_->remainingAttachmentAmount();
Real remainingDetachAmount = basket_->remainingDetachmentAmount();
const Real remainingNot = basket_->remainingNotional(d);
const Real attach =
std::min(remainingAttachAmount / remainingNot, 1.);
const Real detach =
std::min(remainingDetachAmount / remainingNot, 1.);
if(ptflLossPerc >= detach-QL_EPSILON)
return remainingNot * (detach-attach);//equivalent
Real maxLossLevel = std::max(attach, ptflLossPerc);
Probability prob = averageProb(d);
Real averageRR = averageRecovery(d);
Real valA = expectedTrancheLossImpl(remainingNot, prob,
averageRR, maxLossLevel, detach);
Real valB = // probOverLoss(d, maxLossLevel);//in live tranche units
// from fraction of basket notional to fraction of tranche notional
probOverLoss(d, std::min(std::max((maxLossLevel - attach)
/(detach - attach), 0.), 1.));
return ( valA + (maxLossLevel - attach) * remainingNot * valB )
/ (1.-perctl);
}
// same as percentilePortfolio but tranched
Real percentile(const Date& d, Real perctl) const {
const Real remainingNot = basket_->remainingNotional(d);
Real remainingAttachAmount = basket_->remainingAttachmentAmount();
Real remainingDetachAmount = basket_->remainingDetachmentAmount();
const Real attach =
std::min(remainingAttachAmount / remainingNot, 1.);
const Real detach =
std::min(remainingDetachAmount / remainingNot, 1.);
return remainingNot *
std::min(std::max(percentilePortfolioLossFraction(d, perctl)
- attach, 0.), detach - attach);
}