Classes | Public Member Functions | List of all members
SyntheticCDO Class Reference

Synthetic Collateralized Debt Obligation. More...

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

Inheritance diagram for SyntheticCDO:
Inheritance graph
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Classes

class  engine
 CDO base engine. More...
 

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, const Handle< YieldTermStructure > &yieldTS)
 
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
 
std::vector< Real > expectedTrancheLoss () const
 
Size error () const
 
void setupArguments (PricingEngine::arguments *) const
 
void fetchResults (const PricingEngine::results *) 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 boost::shared_ptr< PricingEngine > &)
 set the pricing engine to be used. More...
 
- Public Member Functions inherited from LazyObject
void update ()
 
void recalculate ()
 
void freeze ()
 
void unfreeze ()
 
- 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< std::set
< boost::shared_ptr
< Observable > >::iterator,
bool > 		registerWith (const boost::shared_ptr< Observable > &)
 
Size unregisterWith (const boost::shared_ptr< Observable > &)
 
void unregisterWithAll ()
 

Additional Inherited Members

- Protected Member Functions inherited from Instrument
void calculate () const
 
virtual void performCalculations () const
 
- Protected Member Functions inherited from LazyObject
- Protected Attributes inherited from Instrument
boost::shared_ptr< PricingEngine > engine_
 
Real NPV_
 
Real errorEstimate_
 
Date valuationDate_
 
std::map< std::string, boost::any > additionalResults_
 
- Protected Attributes inherited from LazyObject
bool calculated_
 
bool frozen_
 

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 $,

\[ V = V_1 - V_2. \]

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.

Possible enhancements:
Investigate and fix cases $ E_{i+1} < E_i. $

Member Function Documentation

Real remainingNotional ( ) const

Total outstanding tranche notional, not wiped out

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.

Reimplemented from Instrument.

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