- QuantLib
- CDO
 
collateralized debt obligation More...
#include <ql/experimental/credit/cdo.hpp>

| 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 | 
collateralized debt obligation
The instrument prices a mezzanine CDO tranche with loss given default between attachment point  and detachment point
 and detachment point  .
.
For purchased protection, the instrument value is given by the difference of the protection value  and premium value
 and premium value  ,
,
![\[ V = V_1 - V_2. \]](form_70.png) 
The protection leg is priced as follows:
 (before recovery) or Loss Given Default
 (before recovery) or Loss Given Default  at times/dates
 at times/dates  (premium schedule times with intermediate steps)
 (premium schedule times with intermediate steps)![$ E_i = E_{t_i}\,\left[Pay(LGD)\right] $](form_73.png) of the protection payoff
 of the protection payoff  at each time
 at each time  where
 where 
![\[ Pay(L) = min (D_1, LGD) - min (D_2, LGD) = \left\{ \begin{array}{lcl} \displaystyle 0 &;& LGD < D_1 \\ \displaystyle LGD - D_1 &;& D_1 \leq LGD \leq D_2 \\ \displaystyle D_2 - D_1 &;& LGD > D_2 \end{array} \right. \]](form_76.png) 
![\[ V_1 \:=\: \sum_{i=1}^N (E_i - E_{i-1}) \cdot d_i \]](form_77.png) 
 is the discount factor at time/date
 is the discount factor at time/date 
The premium is paid on the protected notional amount, initially  This notional amount is reduced by the expected protection payments
 This notional amount is reduced by the expected protection payments  at times
 at times  so that the premium value is calculated as
 so that the premium value is calculated as
![\[ V_2 = m \, \cdot \sum_{i=1}^N \,(D_2 - D_1 - E_i) \cdot \Delta_{i-1,i}\,d_i \]](form_82.png) 
where  is the premium rate,
 is the premium rate,  is the day count fraction between date/time
 is the day count fraction between date/time  and
 and 
The construction of the portfolio loss distribution  is based on the probability bucketing algorithm described in
 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) | ||
| ) | 
| attachment | fraction of the LGD where protection starts | 
| detachment | fraction of the LGD where protection ends | 
| nominals | vector of basket nominal amounts | 
| basket | default basket represented by a vector of default term structures that allow computing single name default probabilities depending on time | 
| copula | one-factor copula | 
| protectionSeller | sold protection if set to true, purchased otherwise | 
| premiumSchedule | schedule for premium payments | 
| premiumRate | annual premium rate, e.g. 0.05 for 5% p.a. | 
| dayCounter | day count convention for the premium rate | 
| recoveryRate | recovery rate as a fraction | 
| upfrontPremiumRate | premium as a tranche notional fraction | 
| yieldTS | yield term structure handle | 
| nBuckets | number of distribution buckets | 
| integrationStep | time step for integrating over one premium period; if larger than premium period length, a single step is taken |