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 |
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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. | |
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void | update () |
void | recalculate () |
void | freeze () |
void | unfreeze () |
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Observable (const Observable &) | |
Observable & | operator= (const Observable &) |
void | notifyObservers () |
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Observer (const Observer &) | |
Observer & | operator= (const Observer &) |
std::pair< std::set < boost::shared_ptr < Observable > >::iterator, bool > | registerWith (const boost::shared_ptr< Observable > &) |
Size | unregisterWith (const boost::shared_ptr< Observable > &) |
void | unregisterWithAll () |
Additional Inherited Members | |
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void | calculate () const |
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boost::shared_ptr< PricingEngine > | engine_ |
Real | NPV_ |
Real | errorEstimate_ |
Date | valuationDate_ |
std::map< std::string, boost::any > | additionalResults_ |
collateralized debt obligation
The instrument prices a mezzanine CDO tranche with loss given default between attachment point and detachment point
.
For purchased protection, the instrument value is given by the difference of the protection value and premium value
,
The protection leg is priced as follows: - Build the probability distribution for volume of defaults
(before recovery) or Loss Given Default
at times/dates
(premium schedule times with intermediate steps)
The premium is paid on the protected notional amount, initially This notional amount is reduced by the expected protection payments
at times
so that the premium value is calculated as
where \form#39 is the premium rate, \form#83 is the day count fraction between date/time \form#84 and
The construction of the portfolio loss distribution \form#80@_fakenl is based on the probability bucketing algorithm described in <strong> John Hull and Alan White, "Valuation of a CDO and nth to default CDS without Monte Carlo simulation", Journal of Derivatives 12, 2, 2004 </strong> 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 |