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SyntheticCDO

NAME

SyntheticCDO − Synthetic Collateralized Debt Obligation.

SYNOPSIS

#include <ql/experimental/credit/syntheticcdo.hpp>

Inherits Instrument.

Classes

class engine
CDO base engine.

Public Member Functions

SyntheticCDO (const boost::shared_ptr< Basket > &basket, Protection::Side side, const Schedule &schedule, Rate upfrontRate, Rate runningRate, const DayCounter &dayCounter, BusinessDayConvention paymentConvention, boost::optional< Real > notional=boost::none)
const boost::shared_ptr< Basket > & basket () const
bool isExpired () const
returns whether the instrument might have value greater than zero.
Rate fairPremium () const
Rate fairUpfrontPremium () const
Rate premiumValue () const
Rate protectionValue () const
Real premiumLegNPV () const
Real protectionLegNPV () const
Real remainingNotional () const
Real leverageFactor () const
const Date & maturity () const
Last protection date.
Real implicitCorrelation (const std::vector< Real > &recoveries, const Handle< YieldTermStructure > &discountCurve, Real targetNPV=0., Real accuracy=1.0e−3) const
Disposable< std::vector< Real > > expectedTrancheLoss () const
Size error () const
void setupArguments (PricingEngine::arguments *) const
void fetchResults (const PricingEngine::results *) const

Additional Inherited Members

Detailed Description

Synthetic Collateralized Debt Obligation.

The instrument prices a mezzanine CDO tranche with loss given default between attachment point $ D_1$ and detachment point $ D_2 > D_1 $.

For purchased protection, the instrument value is given by the difference of the protection value $ V_1 $ and premium value $ V_2 $,

V = V_1 - V_2. ].PP The protection leg is priced as follows:

	•		Build the probability distribution for volume of defaults $ L $ (before recovery) or Loss Given Default $ LGD = (1-r)L $ at times/dates $ t_i, i=1, ..., N$ (premium schedule times with intermediate steps)
	•

ight] $ of the

			Determine the expected value $ E_i = E_{t_i}t[Pay(LGD) protection payoff $ Pay(LGD) $ at each time $ t_i$ where Pay(L) = min g i n { a r r a y } { l (D_1, LGD) - min (D_2, LGD) = t c 0 &;& LGD < D_1 \ isplaystyle LGD - l } i s p l a y s t y l D_1 &;& D_1 LGD D_2 \ isplaystyle D_2 - D_1 &;& LGD > D_2ight. ] \nd{array}
	•		The protection value is then calculated as V_1 = _{i=1}^N (E_i - E_{i-1})

The premium is paid on the protected notional amount, initially $ D_2 - D_1. $ This notional amount is reduced by the expected protection payments $ E_i $ at times $ t_i, $ so that the premium value is calculated as

V_2 =m

The construction of the portfolio loss distribution $ E_i $ is based on the probability bucketing algorithm described in

John Hull and Alan White, ’Valuation of a CDO and nth to default CDS without Monte Carlo simulation’, Journal of Derivatives 12, 2, 2004

The pricing algorithm allows for varying notional amounts and default termstructures of the underlyings.

Constructor & Destructor Documentation

SyntheticCDO (const boost::shared_ptr< Basket > & basket, Protection::Side side, const Schedule & schedule, Rate upfrontRate, Rate runningRate, const DayCounter & dayCounter, BusinessDayConvention paymentConvention, boost::optional< Real > notional = boost::none)
If the notional exceeds the basket inception tranche notional, the cdo is leveraged by that factor.

Member Function Documentation

Real remainingNotional () const
Total outstanding tranche notional, not wiped out

Real leverageFactor () const
The number of times the contract contains the portfolio tranched notional.

Real implicitCorrelation (const std::vector< Real > & recoveries, const Handle< YieldTermStructure > & discountCurve, Real targetNPV = 0., Real accuracy = 1.0e−3) const
The Gaussian Copula LHP implied correlation that makes the contract zero value. This is for a flat correlation along time and portfolio loss level.

Disposable<std::vector<Real> > expectedTrancheLoss () const
Expected tranche loss for all payment dates

void setupArguments (PricingEngine::arguments *) const [virtual]
When a derived argument structure is defined for an instrument, this method should be overridden to fill it. This is mandatory in case a pricing engine is used.

Reimplemented from Instrument.

void fetchResults (const PricingEngine::results * r) const [virtual]
When a derived result structure is defined for an instrument, this method should be overridden to read from it. This is mandatory in case a pricing engine is used.