SyntheticCDO Class Reference

Synthetic Collateralized Debt Obligation. More...

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

Inheritance diagram for SyntheticCDO:

List of all members.

Classes

class  engine
 CDO base engine. More...

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< Basketbasket () 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 $,

\[ V = V_1 - V_2. \]

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}\,\left[Pay(LGD)\right] $ of the protection payoff $ Pay(LGD) $ at each time $ t_i$ where

    \[ Pay(L) = min (D_1, LGD) - min (D_2, LGD) = \left\{ \begin{array}{lcl} \displaystyle 0 &;& LGD < D_1 \\ \displaystyle LGD - D_1 &;& D_1 \leq LGD \leq D_2 \\ \displaystyle D_2 - D_1 &;& LGD > D_2 \end{array} \right. \]

  • The protection value is then calculated as

    \[ V_1 \:=\: \sum_{i=1}^N (E_i - E_{i-1}) \cdot d_i \]

    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.

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.