# QuantLib_CDO man page

CDO — collateralized debt obligation

## Synopsis

`#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)
- 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

## Author

Generated automatically by Doxygen for QuantLib from the source code.

## Referenced By

The man pages CDO(3), detachment(3), fairPremium(3), lgd(3), premiumValue(3), protectionValue(3), ql-attachment(3) and ql-error(3) are aliases of QuantLib_CDO(3).