detachment (3) - Linux Manuals

detachment: collateralized debt obligation

NAME

QuantLib::CDO - collateralized debt obligation

SYNOPSIS

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

Inherits QuantLib::Instrument.

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 is still tradable.
Rate fairPremium () const

Rate premiumValue () const

Rate protectionValue () const

Size error () const

Detailed Description

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. $

Constructor & Destructor Documentation

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))

Parameters:

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
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
upfrontPremiumRate premium as a tranche notional fraction
yieldTS yield term structure handle
integrationStep time step for integrating over one premium period; if larger than premium period length, a single step is taken

Author

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