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<

Size size

bool

returns whether the instrument might have value greater than zero.

Rate fairPremium

Rate premiumValue

Rate protectionValue

Size error

**Additional Inherited Members**

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:

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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) |
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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} |
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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.

**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)`**)
Parameters:**

*attachment* fraction of the LGD where protection starts *
detachment* fraction of the LGD where protection ends

nominals

basket

copula

protectionSeller

premiumSchedule

premiumRate

dayCounter

recoveryRate

upfrontPremiumRate

yieldTS

nBuckets

integrationStep

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