NthToDefault Class Reference

N-th to default swap. More...

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

Inheritance diagram for NthToDefault:

Classes
class	engine
	NTD base engine. More...

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.
bool	isExpired () const override
	returns whether the instrument might have value greater than zero.
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
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, ext::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.
Public Member Functions inherited from LazyObject
void	update () override
bool	isCalculated () const
void	forwardFirstNotificationOnly ()
void	alwaysForwardNotifications ()
void	recalculate ()
void	freeze ()
void	unfreeze ()
Public Member Functions inherited from Observable
	Observable (const Observable &)
Observable &	operator= (const Observable &)
	Observable (Observable &&)=delete
Observable &	operator= (Observable &&)=delete
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 set_type::iterator	iterator
Protected Member Functions inherited from Instrument
void	calculate () const override
void	performCalculations () const override
Protected Attributes inherited from Instrument
Real	NPV_
Real	errorEstimate_
Date	valuationDate_
std::map< std::string, ext::any >	additionalResults_
ext::shared_ptr< PricingEngine >	engine_
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.)

Member Function Documentation

isExpired()

bool isExpired ( ) const

overridevirtual

returns whether the instrument might have value greater than zero.

Implements Instrument.

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.

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.