NthToDefault Class Reference

N-th to default swap. More...

#include <nthtodefault.hpp>

Inheritance diagram for NthToDefault:

Collaboration diagram for NthToDefault:

Classes
class	arguments
class	engine
	NTD base engine. More...
class	results

Public Member Functions
	NthToDefault (const ext::shared_ptr< Basket > &basket, Size n, Protection::Side side, Schedule premiumSchedule, Rate upfrontRate, Rate premiumRate, const DayCounter &dayCounter, Real nominal, bool settlePremiumAccrual)
	This product is 'digital'; the basket might be tranched but this is. More...
bool	isExpired () const override
	returns whether the instrument might have value greater than zero. More...
Rate	premium () const
Real	nominal () const
DayCounter	dayCounter () const
Protection::Side	side () const
Size	rank () const
Size	basketSize () const
const Date &	maturity () const
const ext::shared_ptr< Basket > &	basket () const
Rate	fairPremium () const
Real	premiumLegNPV () const
Real	protectionLegNPV () const
Real	errorEstimate () const
void	setupArguments (PricingEngine::arguments *) const override
void	fetchResults (const PricingEngine::results *) const override
Public Member Functions inherited from Instrument
	Instrument ()
Real	NPV () const
	returns the net present value of the instrument. More...
Real	errorEstimate () const
	returns the error estimate on the NPV when available. More...
const Date &	valuationDate () const
	returns the date the net present value refers to. More...
template<typename T >
T	result (const std::string &tag) const
	returns any additional result returned by the pricing engine. More...
const std::map< std::string, ext::any > &	additionalResults () const
	returns all additional result returned by the pricing engine. More...
void	setPricingEngine (const ext::shared_ptr< PricingEngine > &)
	set the pricing engine to be used. More...
Public Member Functions inherited from LazyObject
	LazyObject ()
	~LazyObject () override=default
void	update () override
bool	isCalculated () const
void	forwardFirstNotificationOnly ()
void	alwaysForwardNotifications ()
void	recalculate ()
void	freeze ()
void	unfreeze ()
Public Member Functions inherited from Observable
	Observable ()
	Observable (const Observable &)
Observable &	operator= (const Observable &)
	Observable (Observable &&)=delete
Observable &	operator= (Observable &&)=delete
virtual	~Observable ()=default
void	notifyObservers ()
Public Member Functions inherited from Observer
	Observer ()=default
	Observer (const Observer &)
Observer &	operator= (const Observer &)
virtual	~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	update ()=0
virtual void	deepUpdate ()

Private Member Functions
void	setupExpired () const override

Private Attributes
ext::shared_ptr< Basket >	basket_
Size	n_
Protection::Side	side_
Real	nominal_
Schedule	premiumSchedule_
Rate	premiumRate_
Rate	upfrontRate_
DayCounter	dayCounter_
bool	settlePremiumAccrual_
Leg	premiumLeg_
Rate	premiumValue_
Real	protectionValue_
Real	upfrontPremiumValue_
Real	fairPremium_
Real	errorEstimate_

Additional Inherited Members
Public Types inherited from Observer
typedef set_type::iterator	iterator
Protected Member Functions inherited from Instrument
void	calculate () const override
void	performCalculations () const override
Protected Member Functions inherited from LazyObject
Protected Attributes inherited from Instrument
Real	NPV_
Real	errorEstimate_
Date	valuationDate_
std::map< std::string, ext::any >	additionalResults_
ext::shared_ptr< PricingEngine >	engine_
Protected Attributes inherited from LazyObject
bool	calculated_ = false
bool	frozen_ = false
bool	alwaysForward_

Detailed Description

N-th to default swap.

A NTD instrument exchanges protection against the nth default in a basket of underlying credits for premium payments based on the protected notional amount.

The pricing is analogous to the pricing of a CDS instrument which represents protection against default of a single underlying credit. The only difference is the calculation of the probability of default. In the CDS case, it is the probabilty of single name default; in the NTD case the probability of at least N defaults in the portfolio of underlying credits.

This probability is computed using the algorithm 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 algorithm allows for varying probability of default across the basket. Otherwise, for identical probabilities of default, the probability of n defaults is given by the binomial distribution.

Default correlation is modeled using a one-factor Gaussian copula approach.

The class is tested against data in Hull-White (see reference above.)

Definition at line 70 of file nthtodefault.hpp.

Constructor & Destructor Documentation

NthToDefault()

NthToDefault	(	const ext::shared_ptr< Basket > &	basket,
		Size	n,
		Protection::Side	side,
		Schedule	premiumSchedule,
		Rate	upfrontRate,
		Rate	premiumRate,
		const DayCounter &	dayCounter,
		Real	nominal,
		bool	settlePremiumAccrual
	)

This product is 'digital'; the basket might be tranched but this is.

Definition at line 31 of file nthtodefault.cpp.

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Member Function Documentation

isExpired()

bool isExpired ( ) const

overridevirtual

returns whether the instrument might have value greater than zero.

Implements Instrument.

Definition at line 68 of file nthtodefault.cpp.

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premium()

Rate premium

(

)

const

Definition at line 91 of file nthtodefault.hpp.

nominal()

Real nominal

(

)

const

Definition at line 92 of file nthtodefault.hpp.

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dayCounter()

DayCounter dayCounter

(

)

const

Definition at line 93 of file nthtodefault.hpp.

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side()

Protection::Side side

(

)

const

Definition at line 94 of file nthtodefault.hpp.

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rank()

Size rank

(

)

const

Definition at line 95 of file nthtodefault.hpp.

basketSize()

Size basketSize

(

)

const

Definition at line 66 of file nthtodefault.cpp.

maturity()

const Date & maturity

(

)

const

Definition at line 98 of file nthtodefault.hpp.

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basket()

const ext::shared_ptr< Basket > & basket

(

)

const

Definition at line 100 of file nthtodefault.hpp.

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fairPremium()

Rate fairPremium

(

)

const

Definition at line 72 of file nthtodefault.cpp.

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premiumLegNPV()

Real premiumLegNPV

(

)

const

Definition at line 79 of file nthtodefault.cpp.

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protectionLegNPV()

Real protectionLegNPV

(

)

const

Definition at line 88 of file nthtodefault.cpp.

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errorEstimate()

Real errorEstimate

(

)

const

Definition at line 95 of file nthtodefault.cpp.

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setupArguments()

void setupArguments ( PricingEngine::arguments *  ) const

overridevirtual

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.

Definition at line 113 of file nthtodefault.cpp.

fetchResults()

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

overridevirtual

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.

Reimplemented from Instrument.

Definition at line 126 of file nthtodefault.cpp.

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setupExpired()

void setupExpired ( ) const

overrideprivatevirtual

This method must leave the instrument in a consistent state when the expiration condition is met.

Reimplemented from Instrument.

Definition at line 103 of file nthtodefault.cpp.

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Member Data Documentation

basket_

ext::shared_ptr<Basket> basket_

private

Definition at line 114 of file nthtodefault.hpp.

n_

Size n_

private

Definition at line 115 of file nthtodefault.hpp.

side_

Protection::Side side_

private

Definition at line 116 of file nthtodefault.hpp.

nominal_

Real nominal_

private

Definition at line 117 of file nthtodefault.hpp.

premiumSchedule_

Schedule premiumSchedule_

private

Definition at line 118 of file nthtodefault.hpp.

premiumRate_

Rate premiumRate_

private

Definition at line 119 of file nthtodefault.hpp.

upfrontRate_

Rate upfrontRate_

private

Definition at line 120 of file nthtodefault.hpp.

dayCounter_

DayCounter dayCounter_

private

Definition at line 121 of file nthtodefault.hpp.

settlePremiumAccrual_

bool settlePremiumAccrual_

private

Definition at line 122 of file nthtodefault.hpp.

premiumLeg_

Leg premiumLeg_

private

Definition at line 124 of file nthtodefault.hpp.

premiumValue_

Rate premiumValue_

mutableprivate

Definition at line 127 of file nthtodefault.hpp.

protectionValue_

Real protectionValue_

mutableprivate

Definition at line 128 of file nthtodefault.hpp.

upfrontPremiumValue_

Real upfrontPremiumValue_

mutableprivate

Definition at line 129 of file nthtodefault.hpp.

fairPremium_

Real fairPremium_

mutableprivate

Definition at line 130 of file nthtodefault.hpp.

errorEstimate_

Real errorEstimate_

mutableprivate

Definition at line 131 of file nthtodefault.hpp.