collateralized debt obligation More...

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

Inheritance diagram for CDO:

Public Member Functions
	CDO (Real attachment, Real detachment, const std::vector< Real > &nominals, const std::vector< Handle< DefaultProbabilityTermStructure > > &basket, const Handle< OneFactorCopula > &copula, bool protectionSeller, const Schedule &premiumSchedule, Rate premiumRate, const DayCounter &dayCounter, Rate recoveryRate, Rate upfrontPremiumRate, const Handle< YieldTermStructure > &yieldTS, Size nBuckets, const Period &integrationStep=Period(10, Years))

Real	nominal () const

Real	lgd () const

Real	attachment () const

Real	detachment () const

std::vector< Real >	nominals ()

Size	size ()

bool	isExpired () const
	returns whether the instrument might have value greater than zero.

Rate	fairPremium () const

Rate	premiumValue () const

Rate	protectionValue () const

Size	error () const

Public Member Functions inherited from Instrument
Real	NPV () const
	returns the net present value of the instrument.

Real	errorEstimate () const
	returns the error estimate on the NPV when available.

const Date &	valuationDate () const
	returns the date the net present value refers to.

template<typename T >
T	result (const std::string &tag) const
	returns any additional result returned by the pricing engine.

const std::map< std::string, boost::any > &	additionalResults () const
	returns all additional result returned by the pricing engine.

void	setPricingEngine (const ext::shared_ptr< PricingEngine > &)
	set the pricing engine to be used. More...

virtual void	setupArguments (PricingEngine::arguments *) const

virtual void	fetchResults (const PricingEngine::results *) const

Public Member Functions inherited from LazyObject
void	update ()

void	recalculate ()

void	freeze ()

void	unfreeze ()

void	alwaysForwardNotifications ()

Public Member Functions inherited from Observable
	Observable (const Observable &)

Observable &	operator= (const Observable &)

void	notifyObservers ()

Public Member Functions inherited from Observer
	Observer (const Observer &)

Observer &	operator= (const Observer &)

std::pair< iterator, bool >	registerWith (const ext::shared_ptr< Observable > &)

void	registerWithObservables (const ext::shared_ptr< Observer > &)

Size	unregisterWith (const ext::shared_ptr< Observable > &)

void	unregisterWithAll ()

virtual void	deepUpdate ()

Additional Inherited Members
Public Types inherited from Observer
typedef boost::unordered_set< ext::shared_ptr< Observable > >	set_type

typedef set_type::iterator	iterator

Protected Member Functions inherited from Instrument
void	calculate () const

Protected Member Functions inherited from LazyObject
Protected Attributes inherited from Instrument
Real	NPV_

Real	errorEstimate_

Date	valuationDate_

std::map< std::string, boost::any >	additionalResults_

ext::shared_ptr< PricingEngine >	engine_

Protected Attributes inherited from LazyObject
bool	calculated_

bool	frozen_

bool	alwaysForward_

Detailed Description

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:

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)
Determine the expected value \( E_i = E_{t_i}\,\left[Pay(LGD)\right] \) of the protection payoff \( Pay(LGD) \) at each time \( t_i\) where
\[ Pay(L) = min (D_1, LGD) - min (D_2, LGD) = \left\{ \begin{array}{lcl} \displaystyle 0 &;& LGD < D_1 \\ \displaystyle LGD - D_1 &;& D_1 \leq LGD \leq D_2 \\ \displaystyle D_2 - D_1 &;& LGD > D_2 \end{array} \right. \]
The protection value is then calculated as
\[ V_1 \:=\: \sum_{i=1}^N (E_i - E_{i-1}) \cdot d_i \]
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.

Constructor & Destructor Documentation

◆ CDO()

CDO	(	Real	attachment,
		Real	detachment,
		const std::vector< Real > &	nominals,
		const std::vector< Handle< DefaultProbabilityTermStructure > > &	basket,
		const Handle< OneFactorCopula > &	copula,
		bool	protectionSeller,
		const Schedule &	premiumSchedule,
		Rate	premiumRate,
		const DayCounter &	dayCounter,
		Rate	recoveryRate,
		Rate	upfrontPremiumRate,
		const Handle< YieldTermStructure > &	yieldTS,
		Size	nBuckets,
		const Period &	integrationStep = `Period(10, Years)`
	)

Parameters

attachment	fraction of the LGD where protection starts
detachment	fraction of the LGD where protection ends
nominals	vector of basket nominal amounts
basket	default basket represented by a vector of default term structures that allow computing single name default probabilities depending on time
copula	one-factor copula
protectionSeller	sold protection if set to true, purchased otherwise
premiumSchedule	schedule for premium payments
premiumRate	annual premium rate, e.g. 0.05 for 5% p.a.
dayCounter	day count convention for the premium rate
recoveryRate	recovery rate as a fraction
upfrontPremiumRate	premium as a tranche notional fraction
yieldTS	yield term structure handle
nBuckets	number of distribution buckets
integrationStep	time step for integrating over one premium period; if larger than premium period length, a single step is taken

Public Member Functions

Additional Inherited Members

Detailed Description

Constructor & Destructor Documentation

◆ CDO()