SyntheticCDO (3) - Linux Manuals

SyntheticCDO: Synthetic Collateralized Debt Obligation.

Command to display SyntheticCDO manual in Linux: $ man 3 SyntheticCDO

NAME

QuantLib::SyntheticCDO - Synthetic Collateralized Debt Obligation.

SYNOPSIS

#include <ql/experimental/credit/syntheticcdo.hpp>

Inherits QuantLib::Instrument.

Classes

class engine
CDO base engine.

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 = (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},
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_{i-1}) 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_{i-1,i},d_i ].PPwhere $ 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.

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.