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CDO − collateralized debt obligation


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

Inherits Instrument.

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
Real lgd
Real attachment
Real detachment
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

Additional Inherited Members

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. ].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)

ight] $ of the

Determine the expected value $ E_i = E_{t_i}t[Pay(LGD) protection payoff $ Pay(LGD) $ at each time $ t_i$ where Pay(L) = min g i n { a r r a y } { l (D_1, LGD) - min (D_2, LGD) = t c 0 &;& LGD < D_1 \ isplaystyle LGD - l } i s p l a y s t y l D_1 &;& D_1 LGD D_2 \ isplaystyle D_2 - D_1 &;& LGD > D_2ight. ] \nd{array}

The protection value is then calculated as V_1 = _{i=1}^N (E_i - E_{i-1})

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

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 (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))

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


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