#include <qle/models/gaussianlhplossmodel.hpp>

Inheritance diagram for GaussianLHPLossModel:

Collaboration diagram for GaussianLHPLossModel:

Public Types
typedef GaussianCopulaPolicy	copulaType

Public Member Functions
	GaussianLHPLossModel (const Handle< Quote > &correlQuote, const std::vector< Handle< QuantLib::RecoveryRateQuote > > &quotes)

	GaussianLHPLossModel (Real correlation, const std::vector< Real > &recoveries)

	GaussianLHPLossModel (const Handle< Quote > &correlQuote, const std::vector< Real > &recoveries)

void	update () override

Real	expectedTrancheLoss (const Date &d, Real recoveryRate=Null< Real >()) const override

Real	probOverLoss (const Date &d, Real remainingLossFraction) const override

Real	expectedShortfall (const Date &d, Probability perctl) const override
	Returns the ESF as an absolute amount (rather than a fraction) More...

Real	percentile (const Date &d, Real perctl) const override
	Value at Risk given a default loss percentile. More...

Probability	averageProb (const Date &d) const

Real	averageRecovery (const Date &d) const

Protected Member Functions
Real	percentilePortfolioLossFraction (const Date &d, Real perctl) const

Real	expectedRecovery (const Date &d, Size iName, const DefaultProbKey &ik) const override

Protected Member Functions inherited from DefaultLossModel
	DefaultLossModel ()

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 QuantLib::Real	correlation () const

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

Real	expectedTrancheLossImpl (Real remainingNot, Real prob, Real averageRR, Real attachLimit, Real detachLimit) const

Private Attributes
Real	sqrt1minuscorrel_

Handle< Quote >	correl_

std::vector< Handle< QuantLib::RecoveryRateQuote > >	rrQuotes_

Real	beta_

BivariateCumulativeNormalDistribution	biphi_

Static Private Attributes
static CumulativeNormalDistribution const	phi_ = CumulativeNormalDistribution()

Additional Inherited Members
Protected Attributes inherited from DefaultLossModel
RelinkableHandle< QuantExt::Basket >	basket_

Detailed Description

Portfolio loss model with analytical expected tranche loss for a large homogeneous pool with Gaussian one-factor copula. See for example "The Normal Inverse Gaussian Distribution for Synthetic CDO pricing.", Anna Kalemanova, Bernd Schmid, Ralf Werner, Journal of Derivatives, Vol. 14, No. 3, (Spring 2007), pp. 80-93. http://www.defaultrisk.com/pp_crdrv_91.htm

It can be used to price a credit derivative or to provide risk metrics of a portfolio.

Definition at line 62 of file gaussianlhplossmodel.hpp.

Member Typedef Documentation

◆ copulaType

typedef GaussianCopulaPolicy copulaType

Definition at line 64 of file gaussianlhplossmodel.hpp.

Constructor & Destructor Documentation

◆ GaussianLHPLossModel() [1/3]

GaussianLHPLossModel	(	const Handle< Quote > &	correlQuote,
		const std::vector< Handle< QuantLib::RecoveryRateQuote > > &	quotes
	)

◆ GaussianLHPLossModel() [2/3]

GaussianLHPLossModel	(	Real	correlation,
		const std::vector< Real > &	recoveries
	)

Definition at line 46 of file gaussianlhplossmodel.cpp.

    : LatentModel<GaussianCopulaPolicy>(sqrt(correlation), recoveries.size(),
                                        // g++ complains default value not seen as typename
                                        GaussianCopulaPolicy::initTraits()),
      sqrt1minuscorrel_(std::sqrt(1. - correlation)),
      correl_(Handle<Quote>(QuantLib::ext::make_shared<SimpleQuote>(correlation))), beta_(sqrt(correlation)),
      biphi_(-sqrt(correlation)) {
    for (Size i = 0; i < recoveries.size(); i++)
        rrQuotes_.push_back(Handle<RecoveryRateQuote>(QuantLib::ext::make_shared<RecoveryRateQuote>(recoveries[i])));
}

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◆ GaussianLHPLossModel() [3/3]

GaussianLHPLossModel	(	const Handle< Quote > &	correlQuote,
		const std::vector< Real > &	recoveries
	)

Definition at line 57 of file gaussianlhplossmodel.cpp.

    : LatentModel<GaussianCopulaPolicy>(sqrt(correlQuote->value()), recoveries.size(),
                                        // g++ complains default value not seen as typename
                                        GaussianCopulaPolicy::initTraits()),
      sqrt1minuscorrel_(std::sqrt(1. - correlQuote->value())), correl_(correlQuote), beta_(sqrt(correlQuote->value())),
      biphi_(-sqrt(correlQuote->value())) {
    registerWith(correl_);
    for (Size i = 0; i < recoveries.size(); i++)
        rrQuotes_.push_back(Handle<RecoveryRateQuote>(QuantLib::ext::make_shared<RecoveryRateQuote>(recoveries[i])));
}

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Member Function Documentation

◆ update()

void update ( )

override

Definition at line 73 of file gaussianlhplossmodel.hpp.

                           {
        sqrt1minuscorrel_ = std::sqrt(1. - correl_->value());
        beta_ = std::sqrt(correl_->value());
        biphi_ = BivariateCumulativeNormalDistribution(-beta_);
        // tell basket to notify instruments, etc, we are invalid
        if (!basket_.empty())
            basket_->notifyObservers();
    }

◆ resetModel()

void resetModel ( )

overrideprivatevirtual

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

Implements DefaultLossModel.

Definition at line 83 of file gaussianlhplossmodel.hpp.

83{}

◆ expectedTrancheLossImpl()

Real expectedTrancheLossImpl	(	Real	remainingNot,
		Real	prob,
		Real	averageRR,
		Real	attachLimit,
		Real	detachLimit
	)		const

private

Parameters

attachLimit as a fraction of the underlying live portfolio notional

Definition at line 68 of file gaussianlhplossmodel.cpp.

                                                                                             {
 
    if (attachLimit >= detachLimit)
        return 0.; // or is it an error?
    // expected remaining notional:
    if (remainingNot == 0.)
        return 0.;
 
    const Real one = 1.0 - 1.0e-12; // FIXME DUE TO THE INV CUMUL AT 1
    const Real k1 = std::min(one, attachLimit / (1.0 - averageRR)) + QL_EPSILON;
    const Real k2 = std::min(one, detachLimit / (1.0 - averageRR)) + QL_EPSILON;
 
    if (prob > 0) {
        const Real ip = InverseCumulativeNormal::standard_value(prob);
        const Real invFlightK1 = (ip - sqrt1minuscorrel_ * InverseCumulativeNormal::standard_value(k1)) / beta_;
        const Real invFlightK2 = (ip - sqrt1minuscorrel_ * InverseCumulativeNormal::standard_value(k2)) / beta_;
 
        return remainingNot * (detachLimit * phi_(invFlightK2) - attachLimit * phi_(invFlightK1) +
                               (1. - averageRR) * (biphi_(ip, -invFlightK2) - biphi_(ip, -invFlightK1)));
    } else
        return 0.0;
}

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◆ expectedTrancheLoss()

Real expectedTrancheLoss	(	const Date &	d,
		Real	recoveryRate = `Null<Real>()`
	)		const

overridevirtual

Reimplemented from DefaultLossModel.

Definition at line 94 of file gaussianlhplossmodel.hpp.

                                                                                             {
        // can calls to Basket::remainingNotional(d) be cached?<<<<<<<<<<<<<
        const Real remainingfullNot = basket_->remainingNotional(d);
        Real averageRR = recoveryRate != Null<Real>() ? recoveryRate : averageRecovery(d);
        Probability prob = averageProb(d);
        Real remainingAttachAmount = basket_->remainingAttachmentAmount();
        Real remainingDetachAmount = basket_->remainingDetachmentAmount();
 
        // const Real attach = std::min(remainingAttachAmount
        //    / remainingfullNot, 1.);
        // const Real detach = std::min(remainingDetachAmount
        //    / remainingfullNot, 1.);
        const Real attach = remainingAttachAmount / remainingfullNot;
        const Real detach = remainingDetachAmount / remainingfullNot;
 
        return expectedTrancheLossImpl(remainingfullNot, prob, averageRR, attach, detach);
    }

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◆ probOverLoss()

Real probOverLoss	(	const Date &	d,
		Real	remainingLossFraction
	)		const

overridevirtual

The passed remainingLossFraction is in live tranche units, not portfolio as a fraction of the remaining(live) tranche (i.e. a_remaining=0% and det_remaining=100%)

Reimplemented from DefaultLossModel.

Definition at line 95 of file gaussianlhplossmodel.cpp.

                                                                                       {
    // these test goes into basket<<<<<<<<<<<<<<<<<<<<<<<<<
    QL_REQUIRE(remainingLossFraction >= 0., "Incorrect loss fraction.");
    QL_REQUIRE(remainingLossFraction <= 1., "Incorrect loss fraction.");
 
    Real remainingAttachAmount = basket_->remainingAttachmentAmount();
    Real remainingDetachAmount = basket_->remainingDetachmentAmount();
    // live unerlying portfolio loss fraction (remaining portf fraction)
 
    const Real remainingBasktNot = basket_->remainingNotional(d);
    const Real attach = std::min(remainingAttachAmount / remainingBasktNot, 1.);
    const Real detach = std::min(remainingDetachAmount / remainingBasktNot, 1.);
 
    Real portfFract = attach + remainingLossFraction * (detach - attach);
 
    Real averageRR = averageRecovery(d);
    Real maxAttLossFract = (1. - averageRR);
    if (portfFract > maxAttLossFract)
        return 0.;
 
    // for non-equity losses add the probability jump at zero tranche
    //   losses (since this method returns prob of losing more or
    //   equal to)
    if (portfFract <= QL_EPSILON)
        return 1.;
 
    Probability prob = averageProb(d);
 
    Real ip = InverseCumulativeNormal::standard_value(prob);
    Real invFlightK =
        (ip - sqrt1minuscorrel_ * InverseCumulativeNormal::standard_value(portfFract / (1. - averageRR))) / beta_;
 
    return phi_(invFlightK); // probOver
}

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◆ expectedShortfall()

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

override

Returns the ESF as an absolute amount (rather than a fraction)

Definition at line 130 of file gaussianlhplossmodel.cpp.

                                                                                    {
    // 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);
}

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◆ percentilePortfolioLossFraction()

Real percentilePortfolioLossFraction	(	const Date &	d,
		Real	perctl
	)		const

protected

Definition at line 154 of file gaussianlhplossmodel.cpp.

                                                                                           {
    // this test goes into basket<<<<<<<<<<<<<<<<<<<<<<<<<
    QL_REQUIRE(perctl >= 0. && perctl <= 1., "Percentile argument out of bounds.");
 
    if (perctl == 0.)
        return 0.; // portfl == attach
    if (perctl == 1.)
        perctl = 1. - QL_EPSILON; // portfl == detach
 
    return (1. - averageRecovery(d)) * phi_((InverseCumulativeNormal::standard_value(averageProb(d)) +
                                             beta_ * InverseCumulativeNormal::standard_value(perctl)) /
                                            sqrt1minuscorrel_);
}

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◆ expectedRecovery()

Real expectedRecovery	(	const Date &	,
		Size	iName,
		const DefaultProbKey &
	)		const

overrideprotectedvirtual

Expected RR for name conditinal to default by that date.

Reimplemented from DefaultLossModel.

Definition at line 131 of file gaussianlhplossmodel.hpp.

                                                                                              {
        return rrQuotes_[iName].currentLink()->value();
    }

◆ percentile()

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

overridevirtual

Value at Risk given a default loss percentile.

Reimplemented from DefaultLossModel.

Definition at line 137 of file gaussianlhplossmodel.hpp.

                                                               {
        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);
    }

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◆ averageProb()

Probability averageProb ( const Date & d ) const

Definition at line 147 of file gaussianlhplossmodel.hpp.

                                                 { // not an overload of Deflossmodel ???<<<<<???
        // weighted average by programmed exposure.
        const std::vector<Probability> probs = basket_->remainingProbabilities(d); // use remaining basket
        const std::vector<Real> remainingNots = basket_->remainingNotionals(d);
        return std::inner_product(probs.begin(), probs.end(), remainingNots.begin(), 0.) /
               basket_->remainingNotional(d);
    }

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◆ averageRecovery()

Real averageRecovery ( const Date & d ) const

Definition at line 163 of file gaussianlhplossmodel.hpp.

    {
        const std::vector<Probability> probs = basket_->remainingProbabilities(d);
        std::vector<Real> recoveries;
        for (Size i = 0; i < basket_->remainingSize(); i++)
            recoveries.push_back(rrQuotes_[i]->value());
        std::vector<Real> notionals = basket_->remainingNotionals(d);
        Real denominator = std::inner_product(notionals.begin(), notionals.end(), probs.begin(), 0.);
        if (denominator == 0.)
            return 0.;
 
        std::transform(notionals.begin(), notionals.end(), probs.begin(), notionals.begin(), std::multiplies<Real>());
 
        return std::inner_product(recoveries.begin(), recoveries.end(), notionals.begin(), 0.) / denominator;
    }

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Member Data Documentation

◆ sqrt1minuscorrel_

Real sqrt1minuscorrel_

mutableprivate

Definition at line 181 of file gaussianlhplossmodel.hpp.

◆ correl_

Handle<Quote> correl_

private

Definition at line 183 of file gaussianlhplossmodel.hpp.

◆ rrQuotes_

std::vector<Handle<QuantLib::RecoveryRateQuote> > rrQuotes_

private

Definition at line 184 of file gaussianlhplossmodel.hpp.

◆ beta_

Real beta_

private

Definition at line 196 of file gaussianlhplossmodel.hpp.

◆ biphi_

BivariateCumulativeNormalDistribution biphi_

private

Definition at line 197 of file gaussianlhplossmodel.hpp.

◆ phi_

CumulativeNormalDistribution const phi_ = CumulativeNormalDistribution()

staticprivate

Definition at line 198 of file gaussianlhplossmodel.hpp.

Public Types

Public Member Functions

Protected Member Functions

Private Member Functions

Private Attributes

Static Private Attributes

Additional Inherited Members

Detailed Description

Member Typedef Documentation

◆ copulaType

Constructor & Destructor Documentation

◆ GaussianLHPLossModel() [1/3]

◆ GaussianLHPLossModel() [2/3]

◆ GaussianLHPLossModel() [3/3]

Member Function Documentation

◆ update()

◆ resetModel()

◆ expectedTrancheLossImpl()

◆ expectedTrancheLoss()

◆ probOverLoss()

◆ expectedShortfall()

◆ percentilePortfolioLossFraction()

◆ expectedRecovery()

◆ percentile()

◆ averageProb()

◆ averageRecovery()

Member Data Documentation

◆ sqrt1minuscorrel_

◆ correl_

◆ rrQuotes_

◆ beta_

◆ biphi_

◆ phi_