expectedTrancheLoss (3)  Linux Manuals
expectedTrancheLoss: Synthetic Collateralized Debt Obligation.
NAME
QuantLib::SyntheticCDO  Synthetic Collateralized Debt Obligation.
SYNOPSIS
#include <ql/experimental/credit/syntheticcdo.hpp>
Inherits QuantLib::Instrument.
Classes
Public Member Functions
SyntheticCDO (const boost::shared_ptr< Basket > basket, Protection::Side side, const Schedule &schedule, Rate upfrontRate, Rate runningRate, const DayCounter &dayCounter, BusinessDayConvention paymentConvention, const Handle< YieldTermStructure > &yieldTS)
boost::shared_ptr< Basket > basket () const
bool isExpired () const
returns whether the instrument is still tradable.
Rate fairPremium () const
Rate fairUpfrontPremium () const
Rate premiumValue () const
Rate protectionValue () const
Real remainingNotional () const
std::vector< Real > expectedTrancheLoss () const
Size error () const
void setupArguments (PricingEngine::arguments *) const
void fetchResults (const PricingEngine::results *) const
Detailed Description
Synthetic 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 = (1r),L $ at times/dates $ t_i, i=1, ..., N$ (premium schedule times with intermediate steps)
 *

Determine the expected value $ E_i = E_{t_i},
protection payoff $ Pay(LGD) $ at each time $ t_i$ where [ Pay(L) = min (D_1, LGD)  min (D_2, LGD) =
LGD  D_1 &;& D_1
protection value is then calculated as [ V_1 :=: um_{i=1}^N (E_i  E_{i1}) dot 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 , dot um_{i=1}^N ,(D_2  D_1  E_i) dot Delta_{i1,i},d_i ].PPwhere $ m $ is the premium rate, $ Delta_{i1, i}$ is the day count fraction between date/time $ t_{i1}$ 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.
Possible enhancements
 Investigate and fix cases $ E_{i+1} < E_i. $
Member Function Documentation
Real remainingNotional () const
Total outstanding tranche notional, not wiped out
std::vector<Real> expectedTrancheLoss () const
Expected tranche loss for all payment dates
void setupArguments (PricingEngine::arguments *) const [virtual]
When a derived argument structure is defined for an instrument, this method should be overridden to fill it. This is mandatory in case a pricing engine is used.
Reimplemented from Instrument.
void fetchResults (const PricingEngine::results * r) const [virtual]
When a derived result structure is defined for an instrument, this method should be overridden to read from it. This is mandatory in case a pricing engine is used.
Reimplemented from Instrument.
Author
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