InhomogeneousPoolLossModel< copulaPolicy > Class Template Reference

Default loss distribution convolution for finite non homogeneous pool. More...

#include <qle/models/inhomogeneouspooldef.hpp>

Inheritance diagram for InhomogeneousPoolLossModel< copulaPolicy >:

Collaboration diagram for InhomogeneousPoolLossModel< copulaPolicy >:

Public Types
typedef copulaPolicy	copulaType

Public Member Functions
	InhomogeneousPoolLossModel (const QuantLib::ext::shared_ptr< ConstantLossLatentmodel< copulaPolicy > > &copula, Size nBuckets, Real max=5., Real min=-5., Real nSteps=50)
Real	expectedTrancheLoss (const Date &d, bool zeroRecovery=false) const
Real	percentile (const Date &d, Real percentile) const
	Value at Risk given a default loss percentile. More...
Real	expectedShortfall (const Date &d, Probability percentile) const

Protected Member Functions
Distribution	lossDistrib (const Date &d, bool zeroRecovery=false) const
Protected Member Functions inherited from DefaultLossModel
	DefaultLossModel ()
virtual Real	expectedTrancheLoss (const Date &d, Real recoveryRate=Null< Real >()) const
virtual Probability	probOverLoss (const Date &d, Real lossFraction) const
virtual Real	expectedShortfall (const Date &d, Real percentile) const
	Expected shortfall given a default loss percentile. More...
virtual std::vector< Real >	splitVaRLevel (const Date &d, Real loss) const
	Associated VaR fraction to each counterparty. More...
virtual std::vector< Real >	splitESFLevel (const Date &d, Real loss) const
	Associated ESF fraction to each counterparty. More...
virtual std::map< Real, Probability >	lossDistribution (const Date &) const
	Full loss distribution. More...
virtual Real	densityTrancheLoss (const Date &d, Real lossFraction) const
	Probability density of a given loss fraction of the basket notional. More...
virtual std::vector< Probability >	probsBeingNthEvent (Size n, const Date &d) const
virtual Real	defaultCorrelation (const Date &d, Size iName, Size jName) const
	Pearsons' default probability correlation. More...
virtual Probability	probAtLeastNEvents (Size n, const Date &d) const
virtual Real	expectedRecovery (const Date &, Size iName, const DefaultProbKey &) const
virtual QuantLib::Real	correlation () const

Protected Attributes
const QuantLib::ext::shared_ptr< ConstantLossLatentmodel< copulaPolicy > >	copula_
Size	nBuckets_
Real	attach_
Real	detach_
Real	notional_
Real	attachAmount_
Real	detachAmount_
std::vector< Real >	notionals_
Protected Attributes inherited from DefaultLossModel
RelinkableHandle< QuantExt::Basket >	basket_

Private Member Functions
void	resetModel ()
	Concrete models do now any updates/inits they need on basket reset. More...

Private Attributes
const Real	max_
const Real	min_
const Real	nSteps_
const Real	delta_

Detailed Description

template<class copulaPolicy>
class QuantExt::InhomogeneousPoolLossModel< copulaPolicy >

Default loss distribution convolution for finite non homogeneous pool.

Definition at line 47 of file inhomogeneouspooldef.hpp.

Member Typedef Documentation

copulaType

typedef copulaPolicy copulaType

Definition at line 53 of file inhomogeneouspooldef.hpp.

Constructor & Destructor Documentation

InhomogeneousPoolLossModel()

InhomogeneousPoolLossModel	(	const QuantLib::ext::shared_ptr< ConstantLossLatentmodel< copulaPolicy > > &	copula,
		Size	nBuckets,
		Real	max = 5.,
		Real	min = -5.,
		Real	nSteps = 50
	)

Definition at line 55 of file inhomogeneouspooldef.hpp.

        : copula_(copula), nBuckets_(nBuckets), max_(max), min_(min), nSteps_(nSteps), delta_((max - min) / nSteps) {
        QL_REQUIRE(copula->numFactors() == 1, "Inhomogeneous model not implemented for multifactor");
    }

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Member Function Documentation

resetModel()

void resetModel ( )

privatevirtual

Concrete models do now any updates/inits they need on basket reset.

Implements DefaultLossModel.

Definition at line 126 of file inhomogeneouspooldef.hpp.

                                                                    {
    // need to be capped now since the limit amounts might be over the
    //  remaining notional (think amortizing)
    attach_ = std::min(basket_->remainingAttachmentAmount() / basket_->remainingNotional(), 1.);
    detach_ = std::min(basket_->remainingDetachmentAmount() / basket_->remainingNotional(), 1.);
    notional_ = basket_->remainingNotional();
    notionals_ = basket_->remainingNotionals();
    attachAmount_ = basket_->remainingAttachmentAmount();
    detachAmount_ = basket_->remainingDetachmentAmount();
 
    copula_->resetBasket(basket_.currentLink());
}

lossDistrib()

Distribution lossDistrib ( const Date &  d, bool  zeroRecovery = false  ) const

protected

Definition at line 139 of file inhomogeneouspooldef.hpp.

                                                                                                                   {
    LossDistBucketing bucktLDistBuff(nBuckets_, detachAmount_);
 
    std::vector<Real> lgd; // switch to a mutable cache member
    // RL: additional option used to set set recovery rates to zero
    std::vector<Real> recoveries =
        zeroRecovery ? std::vector<Real>(copula_->recoveries().size(), 0.0) : copula_->recoveries();
    std::transform(recoveries.begin(), recoveries.end(), std::back_inserter(lgd), [](Real x) { return 1.0 - x; });
    std::transform(lgd.begin(), lgd.end(), notionals_.begin(), lgd.begin(), std::multiplies<Real>());
    std::vector<Real> prob = basket_->remainingProbabilities(d);
    for (Size iName = 0; iName < prob.size(); iName++)
        prob[iName] = copula_->inverseCumulativeY(prob[iName], iName);
 
    // integrate locally (1 factor).
    // use explicitly a 1D latent model object?
    // \todo Use a library integrator here and in the homogeneous case.
    Distribution dist(nBuckets_, 0.0, detachAmount_);
    // notional_);
    std::vector<Real> mkft(1, min_ + delta_ / 2.);
    for (Size i = 0; i < nSteps_; i++) {
        std::vector<Real> conditionalProbs;
        for (Size iName = 0; iName < notionals_.size(); iName++)
            conditionalProbs.push_back(copula_->conditionalDefaultProbabilityInvP(prob[iName], iName, mkft));
        Distribution d = bucktLDistBuff(lgd, conditionalProbs);
        Real densitydm = delta_ * copula_->density(mkft);
        // also, instead of calling the static method it could be wrapped
        // through an inlined call in the latent model
        for (Size j = 0; j < nBuckets_; j++) {
            dist.addDensity(j, d.density(j) * densitydm);
            dist.addAverage(j, d.average(j) * densitydm); // RL
        }
        mkft[0] += delta_;
    }
    return dist;
}

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expectedTrancheLoss()

Real expectedTrancheLoss	(	const Date &	d,
		bool	zeroRecovery = false
	)		const

Definition at line 69 of file inhomogeneouspooldef.hpp.

                                                                             {
        Distribution dist = lossDistrib(d, zeroRecovery);
        // RL: dist.trancheExpectedValue() using x = dist.average(i)
        // FIXME: some remaining inaccuracy in dist.cumulativeDensity(detachAmount_)
        Real expectedLoss = 0;
        dist.normalize();
        for (Size i = 0; i < dist.size(); i++) {
            // Real x = dist.x(i) + dist.dx(i)/2; // in QL distribution.cpp
            Real x = dist.average(i);
            if (x < attachAmount_)
                continue;
            if (x > detachAmount_)
                break;
            expectedLoss += (x - attachAmount_) * dist.dx(i) * dist.density(i);
        }
        expectedLoss += (detachAmount_ - attachAmount_) * (1.0 - dist.cumulativeDensity(detachAmount_));
        return expectedLoss;
 
        return lossDistrib(d, zeroRecovery).cumulativeExcessProbability(attachAmount_, detachAmount_);
        // This one if the distribution is over the whole loss structure:
        // but it becomes very expensive
        /*
        return lossDistrib(d).trancheExpectedValue(
            attachAmount_, detachAmount_);
        */
    }

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percentile()

Real percentile ( const Date &  d, Real  percentile  ) const

virtual

Value at Risk given a default loss percentile.

Reimplemented from DefaultLossModel.

Definition at line 95 of file inhomogeneouspooldef.hpp.

                                                          {
        Real portfLoss = lossDistrib(d).confidenceLevel(percentile);
        return std::min(std::max(portfLoss - attachAmount_, 0.), detachAmount_ - attachAmount_);
    }

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expectedShortfall()

Real expectedShortfall	(	const Date &	d,
		Probability	percentile
	)		const

Definition at line 99 of file inhomogeneouspooldef.hpp.

                                                                        {
        Distribution dist = lossDistrib(d);
        dist.tranche(attachAmount_, detachAmount_);
        return dist.expectedShortfall(percentile);
    }

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Member Data Documentation

copula_

const QuantLib::ext::shared_ptr<ConstantLossLatentmodel<copulaPolicy> > copula_

protected

Definition at line 106 of file inhomogeneouspooldef.hpp.

nBuckets_

Size nBuckets_

protected

Definition at line 107 of file inhomogeneouspooldef.hpp.

attach_

Real attach_

mutableprotected

Definition at line 108 of file inhomogeneouspooldef.hpp.

detach_

Real detach_

protected

Definition at line 108 of file inhomogeneouspooldef.hpp.

notional_

Real notional_

protected

Definition at line 108 of file inhomogeneouspooldef.hpp.

attachAmount_

Real attachAmount_

protected

Definition at line 108 of file inhomogeneouspooldef.hpp.

detachAmount_

Real detachAmount_

protected

Definition at line 108 of file inhomogeneouspooldef.hpp.

notionals_

std::vector<Real> notionals_

mutableprotected

Definition at line 109 of file inhomogeneouspooldef.hpp.

max_

const Real max_

private

Definition at line 115 of file inhomogeneouspooldef.hpp.

min_

const Real min_

private

Definition at line 116 of file inhomogeneouspooldef.hpp.

nSteps_

const Real nSteps_

private

Definition at line 117 of file inhomogeneouspooldef.hpp.

delta_

const Real delta_

private

Definition at line 118 of file inhomogeneouspooldef.hpp.