collateralized debt obligation More...
#include <ql/experimental/credit/cdo.hpp>
Inheritance diagram for CDO: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 |
Public Member Functions inherited from Instrument | |
| virtual void | setupArguments (PricingEngine::arguments *) const |
| virtual void | fetchResults (const PricingEngine::results *) const |
| Real | NPV () const |
| returns the net present value of the instrument. | |
| Real | errorEstimate () const |
| returns the error estimate on the NPV when available. | |
| const Date & | valuationDate () const |
| returns the date the net present value refers to. | |
| template<typename T > | |
| T | result (const std::string &tag) const |
| returns any additional result returned by the pricing engine. | |
| const std::map< std::string, boost::any > & | additionalResults () const |
| returns all additional result returned by the pricing engine. | |
| void | setPricingEngine (const boost::shared_ptr< PricingEngine > &) |
| set the pricing engine to be used. More... | |
Public Member Functions inherited from LazyObject | |
| void | update () |
| void | recalculate () |
| void | freeze () |
| void | unfreeze () |
Public Member Functions inherited from Observable | |
| Observable (const Observable &) | |
| Observable & | operator= (const Observable &) |
| void | notifyObservers () |
Public Member Functions inherited from Observer | |
| Observer (const Observer &) | |
| Observer & | operator= (const Observer &) |
| std::pair< iterator, bool > | registerWith (const boost::shared_ptr< Observable > &) |
| void | registerWithObservables (const boost::shared_ptr< Observer > &) |
| Size | unregisterWith (const boost::shared_ptr< Observable > &) |
| void | unregisterWithAll () |
Additional Inherited Members | |
Public Types inherited from Observer | |
| typedef std::set< boost::shared_ptr< Observable > > | set_type |
| typedef set_type::iterator | iterator |
Protected Member Functions inherited from Instrument | |
| void | calculate () const |
Protected Member Functions inherited from LazyObject | |
Protected Attributes inherited from Instrument | |
| boost::shared_ptr< PricingEngine > | engine_ |
| Real | NPV_ |
| Real | errorEstimate_ |
| Date | valuationDate_ |
| std::map< std::string, boost::any > | additionalResults_ |
Protected Attributes inherited from LazyObject | |
| bool | calculated_ |
| bool | frozen_ |
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 \( V_2 \),
\[ V = V_1 - V_2. \]
The protection leg is priced as follows:
\[ Pay(L) = min (D_1, LGD) - min (D_2, LGD) = \left\{ \begin{array}{lcl} \displaystyle 0 &;& LGD < D_1 \\ \displaystyle LGD - D_1 &;& D_1 \leq LGD \leq D_2 \\ \displaystyle D_2 - D_1 &;& LGD > D_2 \end{array} \right. \]
\[ V_1 \:=\: \sum_{i=1}^N (E_i - E_{i-1}) \cdot d_i \]
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
\[ V_2 = m \, \cdot \sum_{i=1}^N \,(D_2 - D_1 - E_i) \cdot \Delta_{i-1,i}\,d_i \]
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.
| 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 |