QuantLib_SyntheticCDO man page

SyntheticCDO — Synthetic Collateralized Debt Obligation.

Synopsis

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

Inherits Instrument.

Classes

class engine
CDO base engine.

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, boost::optional< Real > notional=boost::none)

const 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

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

Disposable< std::vector< Real > > expectedTrancheLoss () const

Size error () const

void setupArguments (PricingEngine::arguments *) const

void fetchResults (const PricingEngine::results *) const

Additional Inherited Members

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. ].PP 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 \ isplaystyle D_2 - D_1 &;& LGD > D_2 \nd{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 ].PP 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

SyntheticCDO (const boost::shared_ptr< Basket > & basket, Protection::Side side, const Schedule & schedule, Rate upfrontRate, Rate runningRate, const DayCounter & dayCounter, BusinessDayConvention paymentConvention, boost::optional< Real > notional = boost::none)

Parameters:

notional Tranche notional. If the notional exceeds the basket inception tranche notional the cdo is leveraged by that factor.

Member Function Documentation

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., Real accuracy = 1.0e-3) 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.

Disposable<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.

Author

Generated automatically by Doxygen for QuantLib from the source code.

Referenced By

fairUpfrontPremium(3), implicitCorrelation(3), leverageFactor(3) and SyntheticCDO(3) are aliases of QuantLib_SyntheticCDO(3).

Fri Sep 23 2016 Version 1.8.1 QuantLib