Synthetic Collateralized Debt Obligation. More...
#include <qle/instruments/syntheticcdo.hpp>
Classes | |
class | arguments |
class | engine |
CDO base engine. More... | |
class | results |
Public Member Functions | |
SyntheticCDO (const boost::shared_ptr< QuantExt::Basket > &basket, Protection::Side side, const Schedule &schedule, Rate upfrontRate, Rate runningRate, const DayCounter &dayCounter, BusinessDayConvention paymentConvention, bool settlesAccrual=true, const QuantLib::CreditDefaultSwap::ProtectionPaymentTime protectionPaymentTime=QuantLib::CreditDefaultSwap::ProtectionPaymentTime::atDefault, Date protectionStart=Date(), Date upfrontDate=Date(), boost::optional< Real > notional=boost::none, Real recoveryRate=Null< Real >(), const DayCounter &lastPeriodDayCounter=DayCounter()) | |
const boost::shared_ptr< QuantExt::Basket > & | basket () const |
bool | isExpired () const override |
Rate | fairPremium () const |
Rate | fairUpfrontPremium () const |
Rate | premiumValue () const |
Rate | protectionValue () const |
Real | premiumLegNPV () const |
Real | protectionLegNPV () const |
Real | recoveryRate () const |
Returns the recovery rate for fixed recovery CDO, otherwise returns Null<Real>() | |
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 |
std::vector< Real > | expectedTrancheLoss () const |
Size | error () const |
void | setupArguments (PricingEngine::arguments *) const override |
void | fetchResults (const PricingEngine::results *) const override |
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 \( V_2 \),
\[ V = V_1 - V_2. \]
The protection leg is priced as follows:
\[ Pay(L) = min (D_1, LGD) - min (D_2, LGD) = \left\{ \begin{array}{lcl} \displaystyle 0 &;& LGD < D_1 \\ \displaystyle LGD - D_1 &;& D_1 \leq LGD \leq D_2 \\ \displaystyle D_2 - D_1 &;& LGD > D_2 \end{array} \right. \]
\[ V_1 \:=\: \sum_{i=1}^N (E_i - E_{i-1}) \cdot d_i \]
where \( d_i\) is the discount factor at time/date \( t_i \)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
\[ V_2 =m \, \cdot \sum_{i=1}^N \,(D_2 - D_1 - E_i) \cdot \Delta_{i-1,i}\,d_i \]
where \( m \) is the premium rate, \( \Delta_{i-1, i}\) is the day count fraction between date/time \( t_{i-1}\) and \( t_i.\)
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.
SyntheticCDO | ( | const boost::shared_ptr< QuantExt::Basket > & | basket, |
Protection::Side | side, | ||
const Schedule & | schedule, | ||
Rate | upfrontRate, | ||
Rate | runningRate, | ||
const DayCounter & | dayCounter, | ||
BusinessDayConvention | paymentConvention, | ||
bool | settlesAccrual = true , |
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const QuantLib::CreditDefaultSwap::ProtectionPaymentTime | protectionPaymentTime = QuantLib::CreditDefaultSwap::ProtectionPaymentTime::atDefault , |
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Date | protectionStart = Date() , |
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Date | upfrontDate = Date() , |
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boost::optional< Real > | notional = boost::none , |
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Real | recoveryRate = Null< Real >() , |
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const DayCounter & | lastPeriodDayCounter = DayCounter() |
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) |
If the notional exceeds the basket inception tranche notional, the cdo is leveraged by that factor.
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. , |
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Real | accuracy = 1.0e-3 |
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) | 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.
std::vector<Real> expectedTrancheLoss | ( | ) | const |
Expected tranche loss for all payment dates