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and similar to the basic model used in this book, the CreditRisk+ model
allows for ¬rms to be in only one of two states, solvency or default. Thus
CreditRisk+ is essentially a model of default risk that is not designed,
for instance, to mark portfolios to market when one or more of their
components are downgraded.
The incorporation of default correlation into the CreditRisk+ framework
is, in some aspects, analogous to the approach adopted by CreditMetrics
and Moody™s KMV. In particular, individual default probabilities are
assumed to be functions of several “risk factors” that are common across
di¬erent assets in the portfolio.
A key di¬erence between CreditRisk+ and the models discussed in
Sections 22.1 and 22.2 regards technical assumptions regarding the random
nature of defaults. Rather than relying either on the normal or empiri-
cal distributions for modeling the evolution of risk factors, CreditRisk+
assumes the factors to be independently distributed according to the
gamma distribution, which, subject to some approximations, allows the
model to produce analytical results for unconditional probabilities of
various losses in the portfolio. In contrast, the reader may recall that
the derivation of the loss distribution function of a given portfolio gen-
erally involved either Monte Carlo simulations or, for large portfolios,
approximation methods.
264 22. A Quick Tour of Commercial Models

Methodologically, CreditRisk+ also di¬ers from CreditMetrics and
Moody™s KMV in that, while these two latter models are structural mod-
els that follow the spirit of the BSM framework discussed in Chapter 17,
CreditRisk+ is closer to the reduced-form approach, also discussed in that
chapter. In particular, CreditRisk+ is based on actuarial methods that
have long been used in the insurance industry to analyze event risk. Similar
to intensity-based models, CreditRisk+ does not explicitly link the likeli-
hood of default to the fundamentals of the ¬rm. Instead, defaults occur
exogenously according to the probabilities implied by the model.
Credit Suisse Financial Products (1997)[67] describes the CreditRisk+
model in further detail. The model is also summarized by Gordy (2000)[35],
who compares and contrasts it to the CreditMetrics approach.


22.4 Moody™s Binomial Expansion Technique
In Chapter 19 we showed that, conditioned on the common factor ±, indi-
vidual defaults were uncorrelated in the basic credit risk model, and the
(conditional) loss distribution function of the homogeneous portfolio was
given by the binomial probability distribution”see equations (19.20) and
(19.21). As we saw then, one attractive feature of the conditional loss dis-
tribution function implied by the basic model was that its computation
involved no Monte Carlo simulations, which can be computer-intensive,
and no approximation methods, such as the large-portfolio method.
Moody™s binomial expansion technique is designed to take advantage of
this convenient feature of portfolios with zero default correlation.
For a given credit portfolio with J potentially correlated assets, Moody™s
BET essentially aims at arriving at an otherwise equivalent homogeneous
equally weighted portfolio with D uncorrelated assets, where D is dic-
tated by the “diversity score” of the original portfolio. We say that this
idealized portfolio is otherwise equivalent to the actual portfolio we are
interested in because it shares many of the fundamental characteristics
of the original portfolio. For instance, the individual default probability
of each constituent of the idealized portfolio is set to the average default
probability of the assets included in the original portfolio.
The diversity score of the original portfolio is a measure conceived by
Moody™s to capture the degree of industry diversi¬cation represented in
the portfolio. For instance, a portfolio with a high degree of concentration
in a given industry would be one with a low diversity score, resulting in an
idealized portfolio with a number of assets, D, that could fall well short of
the actual number of assets in the original portfolio. Intuitively, the smaller
number of assets in the idealized portfolio controls for the fact that the large
number of assets in the original portfolio tends to overstate the portfolio™s
true degree of diversi¬cation when two or more of its constituents have a
tendency to default together.
22.5 Concluding Remarks 265

Once the idealized portfolio is constructed, and the main characteristics
of the actual portfolio are mapped into it, one can derive its loss distri-
bution function in a way that is entirely analogous to the derivation of
the conditional loss distribution function in Chapter 19. In particular, the
probability of, say, k defaults in the idealized portfolio can be derived from
the binomial distribution as in
D!
ω k (1 ’ ω)D’k
Prob [k defaults] = (22.2)
k!(D ’ k)!

where ω is the probability of default of each reference entity represented in
the idealized portfolio.
Armed with equation (22.2), as well as Moody™s estimates of the diversity
score and of individual default probabilities in the portfolio, it is then rela-
tively straightforward to value, for instance the tranches of a CDO. Indeed,
the BET method is an important component of Moody™s rating method-
ology for rating both traditional and synthetic CDOs”see, for instance,
Cifuentes and O™Connor (1996)[12] and Yoshizawa (2003)[75]. Other com-
ponents include qualitative adjustments made to take other features of
individual CDOs into account, such as the legal aspects of the structure.
Moody™s has found the BET approach to work well for relatively homo-
geneous portfolios, but less so for portfolios where individual assets™ default
probabilities are markedly di¬erent. For such situations, Moody™s has devel-
oped a modi¬ed approach, dubbed the double binomial expansion method,
whereby the portfolio is divided with di¬erent portions that are mutu-
ally uncorrelated, but where each portion has a di¬erent individual default
probability”see Cifuentes and Wilcox (1998)[13]. A further variation on
the method, called the multiple binomial method, is employed for portfolios
with further heterogeneity in individual default probabilities (Yoshizawa,
2003)[75].



22.5 Concluding Remarks
There is obviously much more to the credit risk models discussed in this
chapter than has been covered in this brief overview. In addition, there
are a number of other well-regarded commercially available models that
we did not address here. Our choice of models, as well as the coverage
provided for each model discussed in this chapter, was driven by a main
guiding principle, which was to provide some insight into how the key
concepts and methods described in Chapters 15 through 21 have actually
been incorporated into credit risk analytical services that are bought and
sold in the marketplace.
23
Modeling Counterparty Credit Risk




In the context of the credit derivatives market, counterparty credit risk
refers mainly to the chance that a protection seller will fail to make
good on its promise to make previously agreed-upon payments in the
event of quali¬ed defaults by reference entities.1 We have thus far mostly
sidestepped the issue of counterparty credit risk when discussing the valua-
tion of credit derivative contracts. We have done so in part because existing
arrangements among market participants”such as collateralization agree-
ments and netting”help mitigate such a risk, but also for analytical
convenience”factoring counterparty credit risk into the valuation exercise
often adds a layer of complexity to the analysis that, for the most part, goes
beyond the scope of this book. We say “for the most part” because we can
in fact use a variant of the simple model discussed in Chapters 19 through
21 to capture some of the key insights regarding the role of counterparty
credit risk in the valuation of credit derivatives.


1
Strictly speaking, the protection seller is also subject to the risk that the buyer
will fail to make the agreed-upon protection premium payments. The seller™s potential
exposure, however, is essentially limited to the marked-to-market value of the contract,
which, as we saw in Chapter 16, is a function of the di¬erence between the premium
written into the contract and the one prevailing in the market place at the time of
default by the protection buyer. Thus the contract could well have negative market
value to the seller, which would be the case if the credit quality of the reference entity
had deteriorated since the inception of the contract. Under such circumstances, the
seller would in principle experience a windfall upon default by the buyer, although,
before defaulting, the buyer would likely have a strong incentive to seek to monetize the
positive market value of the contract.
268 23. Modeling Counterparty Credit Risk

Our focus will be on the ubiquitous single-name credit default swap,
which we discussed in some detail in Chapter 6. We shall assume that the
CDS contracts examined in this chapter are uncollateralized agreements
that are not subject to netting and that do not include any other credit
enhancement mechanism. Towards the end of the chapter we outline ways
to extend the model for the analysis of more complex contracts, such as
baskets and portfolio default swaps.


23.1 The Single-Name CDS as a “Two-Asset
Portfolio”
One might wonder why include a discussion of counterparty credit risk”
especially one that focuses on single-name credit default swaps”in this part
of the book, which, after all, deals with portfolio credit risk. The answer
lies in the following simple insight: In the presence of counterparty credit
risk, and from the perspective of the protection buyer, one can think of a
single-name CDS as being akin to a portfolio involving risk exposures to two
entities: the one referenced in the CDS and the protection seller. Indeed, the
protection buyer has a default-contingent exposure to the protection seller,
in that it will have to rely on the seller to cover any losses resulting from a
default by the reference entity. Thus, the protection buyer e¬ectively also
has some residual exposure to the reference entity because, if the protection
seller does not make good on its commitment, the buyer will have to bear
any losses associated with a default by the reference entity.
We have to be careful not to take the portfolio analogy too far, how-
ever. In contrast to a traditional portfolio setting, the protection buyer
only really bears a loss upon default by the reference entity if that entity
happens to default at around the same time as the protection seller. (Or if
the reference entity defaults after a default by the seller, and the original
contract was not replaced.) Still, the basic insight that an uncollateralized
single-name CDS shares some of the basic characteristics of a two-asset
portfolio has some insightful implications for the analysis of counterparty
credit risk. Indeed, as we shall see below, we can examine the e¬ects of
counterparty credit risk on the valuation of CDS contracts by relying on
a modi¬ed version of the portfolio credit risk model that we discussed in
Chapters 19 through 21.


23.2 The Basic Model
To admit explicitly the possibility that the protection seller can default
on its obligations under the CDS contract, we assume that the seller is a
23.2 The Basic Model 269

risky entity whose standardized returns Rp,t follow the same basic model
introduced in Chapter 19:

1 ’ βp
2
Rp,t = βp ±t + (23.1)
p,t


where, as indicated in that chapter, ±t is a common factor (systematic risk)
driving the returns on the protection seller; p,t represents a risk factor that
is speci¬c to the protection seller (idiosyncratic risk); and βp denotes the
degree of correlation between Rp,t and the common factor ±t .
We assume that any protection payment owed by the protection seller
will be made only on one of the premium payment dates of the CDS. In
addition, we de¬ne a default by the protection seller as the ¬rst instance
when its return Rp is equal to or below its default barrier Cp on any of
those dates.2
Given equation (23.1), and assuming that ± and p have zero mean and
unit variance and are mutually independent and normally distributed, we
saw in Chapter 19 that, conditional on all information available at time
t, and given survival through that time, the risk-neutral probability that
Rp,T will be at or below Cp,T at some future date T is

Hp (t, T ) ≡ Probt [Rp,T ¤ Cp,T ] = N (Cp,T ) (23.2)

where N (.) is the standard normal cumulative distribution function. More
generally, Hp (t, Tj ) is the time-t probability that Rp,Tj will be at or below
Cp,Tj at time Tj .
The evolution of returns associated with the entity referenced in the
CDS is modeled in an entirely analogous way. If we let Rr,t denote the
standardized return on the reference entity, and make the same assumptions
made for the protection seller, we have:

1 ’ βr
2
Rr,t = βr ±t + (23.3)
r,t

Hr (t, T ) ≡ Prob[Rr,T ¤ Cr,T ] = N (Cr,T ) (23.4)

Equations (23.1) through (23.4) constitute our basic framework for ana-
lyzing the e¬ects of counterparty credit risk in credit default swaps. As we
will see later in this chapter, these equations capture two important deter-
minants of counterparty credit risk e¬ects: the credit quality of the pro-
tection seller (Hp ) and the degree of default correlation between the seller

2
In contrast to Chapters 19 through 22, where we limited ourselves to one-year con-
tracts, we are now dealing with multi-period contracts. That is why we are characterizing
the time of default as the ¬rst premium payment date in which Rp touches the default
barrier from above.
270 23. Modeling Counterparty Credit Risk

and the reference entity, which is mainly determined by their respective
values of β.
We should note that, although it may not be clear from the simpli¬ed
notation used thus far, the basic model is ¬‚exible enough to allow for
time-varying, even stochastic, probabilities of default. Such features could
be incorporated, for instance, by modeling the evolution of the default
thresholds accordingly.



23.3 A CDS with No Counterparty Credit Risk
If collateralization and other credit enhancement mechanisms embedded
in the contract are such that the protection seller poses no risk to the
protection buyer, we can proceed as if Hp (t, T ) = 0 for all T , and we
can thus ignore equations (23.1) and (23.2) when valuing the CDS. In
essence, this is what we did in Part III of this book. We shall take the case
of no counterparty credit risk as a benchmark against which to compare
valuations derived from our counterparty credit risk model, but ¬rst we
recast some of the main results derived in Part III in terms of the modeling
framework described in the previous section.
Let us consider a J-year CDS written on the ¬rm described by equa-
tions (23.3) and (23.4). We assume that the CDS has a notional amount of
$1, is entered into at time t, and involves the annual payment of premiums,
at dates T1 , T2 , . . . , TJ , i.e.,

δj ≡ Tj ’ Tj’1 = 1 year

for all j. For notational convenience we set T0 = t. As we saw in Chapter 16,
valuing such a swap involves, ¬rst, ¬nding the expected present values (PV)
of its protection and premium legs and, second, determining the value of
the premium Sr,J such that the CDS has zero market value at its inception.
We follow the spirit of Merton™s (1974)[59] model and assume that a default
by the reference entity, if any, only occurs at speci¬c times. In the context
of this chapter, those times are the premium payment dates of the CDS.
As we saw in Chapter 16, the expected (risk-adjusted) present value of
the premium leg for this CDS can be written as

J
PV[premiums]t = Z(t, Tj )Qr (t, Tj )Sr,J (23.5)
j=1


where Qr (t, Tj ) is the risk-neutral probability, conditional on all informa-
tion available at time t and given no default by that time, that the reference
23.3 A CDS with No Counterparty Credit Risk 271

entity will survive through time Tj , and Z(t, Tj ) is the time-t price of a risk-
less zero-coupon bond that matures at time Tj ”Z(t, Tj ) is the time-t value
of a dollar that will be received/paid at time Tj .3
The relationship between Qr and Hr at time T1 is straightforward:

Qr (t, T1 ) = 1 ’ Hr (t, T1 ) = 1 ’ N (Cr,T1 ) (23.6)

and, generalizing for j > 1,

j
[1 ’ N (Cr,Ti )]
Qr (t, Tj ) = (23.7)
i=1

where the last equation follows from the fact that Rr,Tj is serially
uncorrelated, i.e.,4 , 5

Qr (t,Tj ) ≡ Probt [Rr,T1 > Cr,T1 and Rr,T2 > Cr,T2 and ... Rr,Tj > Cr,Tj ]
= Probt [Rr,T1 > Cr,T1 ] Probt [Rr,T2 > Cr,T2 ] ... Probt [Rr,Tj > Cr,Tj ]
j
= Probt [Rr,Ti > Cr,Ti ]
i=1


In Chapter 16 we also showed that the expected risk-adjusted present
value of the protection leg can be written as

J
Z(t, Tj )[Qr (t, Tj’1 ) ’ Qr (t, Tj )](1 ’ Xr )
PV[protection]t = (23.8)
j=1


where Xr is the recovery rate associated with the reference entity (0 ¤
Xr < 1).

3
Equation (23.5) implicitly assumes that no accrued premium is due to the protection
seller upon a default by the reference entity. This simplifying assumption, and a simple
approach to relax it, was discussed in Chapter 16.
4
As we saw in Chapter 19, serial uncorrelation of Rr , which is normally distributed
with zero mean and unit variance, means that Rr,T and Rr,T ’s are uncorrelated random
variables for all nonzero values of s. Thus, for instance,
Probt [Rr,T > C and Rr,T ’s > C] = Probt [Rr,T > C]Probt [Rr,T ’s > C]
5 j
The notation G(i), for any function G(i) of i, denotes the product operator:
i=1
j
G(i) ≡ G(1)G(2) . . . G(j)
i=1
272 23. Modeling Counterparty Credit Risk

Given equations (23.5) and (23.8), the fair value of the CDS premium
when there is no counterparty credit risk is
J
Z(t, Tj )[Qr (t, Tj’1 ) ’ Qr (t, Tj )](1 ’ Xr )
j=1
Sr,J|Hp = 0 = (23.9)
J
Z(t, Tj )Qr (t, Tj )
j=1

and, thus, the model-implied CDS premium in the absence of counterparty
credit is
J j’1
’ N (Cr,Ti )]N (Cr,Tj )(1 ’ Xr )
Z(t, Tj ) i = 1 [1
j=1
Sr,J|Hp = 0 = (23.10)
J j
’ N (Cr,Ti )]
Z(t, Tj ) i = 1 [1
j=1



23.4 A CDS with Counterparty Credit Risk
A ¬rst step in understanding how the model presented in Section 23.2
can be used to value a CDS that involves counterparty credit risk is to
lay out the possible default outcomes regarding the contract and then to
compute the risk-neutral probabilities associated with each outcome, just
as we did with baskets and portfolio default swaps in Chapters 20 and 21.
As noted earlier, we shall approach this problem from the perspective of
the protection buyer in a CDS.
The protection buyer will pay the premium due on the dates Tj speci¬ed
in the contract, j = 1, . . . , J, for as long as both the protection seller and
the reference entity remain solvent on those dates. Let Qrp (t, Tj ) denote
the probability of such an event at time Tj , conditional on all available
information at time t and given survival by both entities through that
time. If we also assume that the protection seller is entitled to no accrued
premium upon its own default, we can write the expected present value of
the premium leg of a CDS that is subject to counterparty credit risk as:
J
PV[premiums]t = Z(t, Tj )Qrp (t, Tj )Sr,J (23.11)
j=1


which is entirely analogous to equation (23.5), except that we have replaced
the survival probability of the reference entity with the probability that
both the reference entity and the protection seller will survive through
di¬erent dates in the future. The intuition is quite clear. If either the protec-
tion seller or the reference entity defaults at Tj , the protection buyer has no
reason to continue to make premium payments. In the former case (seller™s
default), the default protection provided by the contract becomes worth-
less; in the latter case (reference entity™s default) the contract is triggered
and it is the seller that owes a payment to the buyer.
23.4 A CDS with Counterparty Credit Risk 273

As for the protection leg of the swap, the buyer will receive the protection
payment at a given time Tj only if two events occur at that time: the refer-
ence entity defaults and the protection seller is solvent. Let H(t, Tj ) denote
the probability that these events take place at Tj , conditional on all infor-
mation available at time t and on survival by both entities through t. Then,
similar to equation (23.8), the expected present value of the protection
leg is:
J
Z(t, Tj )H(t, Tj )(1 ’ Xr )
PV[protection]t = (23.12)
j=1


where, for simplicity, we assume a zero recovery rate associated with the
protection seller.6
Given equations (23.11) and (23.12), the fair value of the credit default
swap premium in the presence of counterparty credit risk is:
J
j = 1 Z(t, Tj )H(t, Tj )(1 ’ Xr )
Sr,J|Hp >0 = (23.13)
J
j = 1 Z(t, Tj )Qrp (t, Tj )

Equation (23.13) is a model-independent expression for the premium for
a CDS that is subject to counterparty credit risk. To obtain expressions for
the probabilities H(t, Tj ) and Qrp (t, Tj ), we need to go back to the credit
risk model. We discuss below two methods for doing so. The ¬rst is based
on deriving explicit solutions for these probabilities in terms of parameters
of the model”Cp,Tj , Cr,Tj , βp , and βr . The second is based on Monte Carlo
simulation methods and is similar in spirit to the approach emphasized in
Chapters 20 and 21.

23.4.1 Analytical Derivation of Joint Probabilities of
Default
Unlike the case of no counterparty credit risk, where the probabilities
included in the formula for the CDS premium depended only on the

6
Extending the framework to allow for a nonzero recovery rate for the protection
seller would be relatively straightforward. We would add terms involving Xp (1 ’ Xr )”
where 0 ¤ Xp < 1 is the recovery rate of the protection seller”and the risk-neutral
conditional probabilities, G(t, Tj ), associated with a default by both entities at time Tj ,
as in
J J
Z(t, Tj )H(t, Tj )(1 ’ Xr ) + Z(t, Tj )G(t, Tj )Xp (1 ’ Xr )
PV[protection leg]t =
j=1 j=1

To keep things simpler, however, and because this extension is relatively trivial, we
choose to set Xp to zero and leave the nonzero Xp case as an exercise for the reader.
274 23. Modeling Counterparty Credit Risk




FIGURE 23.1. Diagrammatic Representation of Probabilities of Defaulting at
Time T1


distribution of future returns for the reference entity, we now need to
use equations (23.1) through (23.4) to compute joint probabilities of var-
ious default and survival scenarios involving the reference entity and the
protection seller. As we saw in Chapter 19, the derivation of these joint
probabilities can quickly become very messy for a portfolio with several
assets, even for the simplest case of a homogeneous portfolio. But comput-
ing joint default and survival probabilities for the “two-asset portfolio”
implicit in a CDS with counterparty credit risk can be a signi¬cantly
simpler exercise.
Consider, for instance, the derivation of Qrp (t, T1 ) and H(t, T1 ).
Figure 23.1 shows a diagrammatic representation of the probabilities
attached to possible default and survival outcomes involving the refer-
ence entity and the protection seller at T1 .7 In particular, the area labeled
Hr (t, T1 ) represents the conditional risk-neutral probability that the ref-
erence entity will default at time T1 , and the one labeled Hp (t, T1 ) is
analogously de¬ned for the protection seller. The region of overlap between
the two areas, labeled Hrp (t, T1 ) in the ¬gure, is the probability that both
the reference entity and the protection seller will default at time T1 .8
Relying on the same arguments laid out in the beginning of Chapter 19,
the probability that both the protection seller and the reference entity will
survive through time T1 is

Qrp (t, T1 ) = 1 ’ [Hr (t, T1 ) + Hp (t, T1 ) ’ Hrp (t, T1 )] (23.14)

7
We ¬rst discussed the use of such diagrams in Chapter 19.
8
We continue to assume that these probabilities are conditional on all information
available at time t, given survival by both entities through t.
23.4 A CDS with Counterparty Credit Risk 275

which is simply one minus the probability that at least one of the two
entities”the protection seller and the reference entity”will default by
time T1 .
Given the de¬nition of default events”equations (23.2) and (23.4)”
Hrp (t, T1 ) can also be characterized as the probability that both Rp,T1 and
Rr,T1 will fall below their respective default thresholds. Because both Rp,T1
and Rp,T1 are normally distributed and, as we saw in Chapter 19, have a
coe¬cient of correlation equal to βp βr , this probability is given by

Hrp (t, T1 ) = N2 (Cr,T1 , Cp,T1 , βp βr ) (23.15)

where N2 () is the cumulative distribution function of the bivariate normal
distribution.9
Thus, in terms of the model parameters, the probability that both the
reference entity and the protection seller will not default at time T1 is:10

Qrp (t, T1 ) = 1 ’ [N (Cr,T1 ) + N (Cp,T1 ) ’ N2 (Cr,T1 , Cp,T1 , βp βr )] (23.16)

Going back to Figure 23.1, it is relatively straightforward to see that the
probability that the reference entity will default at time T1 and that the
protection seller will remain solvent is

H(t, T1 ) = Hr (t, T1 ) ’ Hrp (t, T1 ) = N (Cr,T1 ) ’ N2 (Cr,T1 , Cp,T1 , βp βr )
(23.17)

The derivation of expressions for Qrp (t, Tj ) and H(t, Tj ) for j ≥ 2
requires only a bit more work than the computations just described for
Qrp (t, T1 ) and H(t, T1 ). Take, for instance, the computation of Qrp (t, T2 ).
If we let PS and RE denote the protection seller and reference entity,
respectively, and de¬ne RTj ≡ [Rr,Tj , Rp,Tj ] and CTj ≡ [Cr,Tj , Cp,Tj ] we
can write

Qrp (t, T2 ) ≡ Probt [PS and RE survive through T2 ]
= Probt [RT1 > CT1 and RT2 > CT2 ]

= Probt [RT1 > CT1 ] Probt [RT2 > CT2 ]


9
Appendix B provides a brief overview of the bivariate normal distribution.
10
Those familiar with the bivariate normal distribution have probably noticed that
the right-hand side of (23.16) is equivalent to N2 (’Cr,T1 , ’Cp,T1 , βp βr ).
276 23. Modeling Counterparty Credit Risk

where, as in the case of no counterparty credit risk, the last equality follows
from the fact that returns are serially uncorrelated.11
Thus, given

Probt [RTi > CTi ] ≡ Probt [Rr,Ti > Cr,Ti and Rp,Ti > Cp,Ti ] (23.18)

it is straightforward to see that we can write:

2
{1 ’ [Hr (t, Ti ) + Hp (t, Ti ) ’ Hrp (t, Ti )]}
Qrp (t, T2 ) = (23.19)
i=1


As for the derivation of a model-implied expression for H(t, T2 ), we once
again recall its de¬nition:

H(t, T2 ) ≡ Probt [RE defaults at T2 and PS survives through T2 ]
= Probt [(RE def. and PS surv. at T2 ) and

(PS and RE surv. through T1 )]

Serial uncorrelation of returns implies that the two events in parenthesis
above are independent. Thus we can write:

H(t, T2 ) = Probt [RE def. and PS surv. at T2 ]
— Probt [PS and RE surv. through T1 ]

The expressions for the two probabilities on the right-hand side of the above
equation are entirely analogous to the ones derived for T1 . Thus,

H(t, T2 ) = [Hr (t, T2 ) ’ Hrp (t, T2 )]Qrp (t, T1 ) (23.20)

Generalizing for Tj , j ≥ 2, and expressing all probabilities in terms of
the parameters of the model, we obtain:

j
{1 ’ [N (Cr,Ti ) + N (Cp,Ti ) ’ N2 (Cr,Ti , Cp,Ti , βr βp )]}
Qrp (t, Tj ) =
i=1
(23.21)

H(t, Tj ) = [N (Cr,Tj ) ’ N2 (Cr,Tj , Cp,Tj , βr βp )]Qrp (t, Tj’1 ) (23.22)

11
Rp and Rr are only contemporaneously correlated. Serial uncorrelation of Z, which
is the only source of contemporaneous correlation between Rp and Rr implies that
returns on the protection seller and the reference entity are intertemporally uncorrelated.
23.4 A CDS with Counterparty Credit Risk 277

which we can substitute into equation (23.13) to write an explicit formula
for the CDS premium in the presence of counterparty credit risk.


23.4.2 Simulation-based Approach
Rather than using the model to derive explicit formulae for the proba-
bilities in equation (23.13), one may choose to rely on a Monte Carlo
simulation approach similar to the one described in Chapter 19 and used
in Chapters 20 and 21. In the context of the J-year CDS studied thus far,
each simulation of the model involves relying on equations (23.1) through
(23.4) to generate J values for the vector RTj ≡ [Rp,Tj , Rr,Tj ], for j = 1 to
J. For each generated pair of returns, we record whether any of the two
basic default outcomes of interest”survival by both entities and default by
the reference entity while the protection seller survives”took place.
Thus, for j = 1 to J, we de¬ne
• q(j) ≡ total number of simulations where both the reference entity
and the protection seller survive through time Tj
• h(j) ≡ total number of simulations where the reference entity defaults
at time Tj and the protection seller survives through Tj .12

After running a su¬ciently large number of simulations, we can compute
approximate values of Qrp (t, Tj ) as

q(i)
Qrp (t, Tj ) ≈ (23.23)
M

Likewise, we can approximate H(t, Tj ) as

h(j)
H(t, Tj ) ≈ (23.24)
M

where M is the total number of simulations of the model. Thus, the method
involves generating M values of Rr and Rp for each of the J premium
payment dates of the CDS.
To improve the accuracy of the results, it is common practice to perform
these computations a large number of times and then report the average of
the results obtained. For instance, we may run M = 500,000 simulations of
the model 200 times and compute the average of the 200 results obtained.

12
Recall that the time of default is de¬ned as the ¬rst time that the asset return
reaches or falls below the default barrier on a premium payment date.
278 23. Modeling Counterparty Credit Risk

23.4.3 An Example
We examine the e¬ects of counterparty credit risk on the valuation of a
¬ve-year CDS written on a reference entity with a 5 percent risk-neutral
probability of default over the next year and a ¬‚at credit curve. We assume
that the swap involves no credit enhancement mechanisms such as collat-
eralization and netting, that βr = βp = β, and that the premium is paid
annually.
Figure 23.2 shows premiums for the CDS just described under various
assumptions regarding the credit quality of the protection seller and for
di¬erent values of β. Accordingly, β varies from zero to .99, and Hp (t, Tj )
ranges from zero to 4 percent. These results are based on the analytical
results derived in Section 23.4.1 and were con¬rmed by Monte Carlo sim-
ulations.13 Before we proceed, we should note that this exercise involves
several simplifying assumptions, such as a zero recovery rate for the pro-
tection seller and no accrued premiums or interest in the event of default
by the reference entity. In more realistic settings, these factors should not
be ignored.14
Each curve in the ¬gure corresponds to a given value of β. For instance,
the solid line shows values of the CDS premium when β = 0, which corre-
sponds to the case of no default correlation between the protection seller
and the reference entity. The values along the horizontal axis correspond
to risk-neutral default probabilities of potential protection sellers in this
contract.
Consistent with one™s intuition, Figure 23.2 shows that, for a given degree
of default correlation between the reference entity and the protection seller,
the fair value of the CDS premium declines as the credit quality of the pro-
tection seller deteriorates. Nonetheless, such an e¬ect is barely noticeable
for very low levels of default correlation. This occurs as the protection
and premium legs of the CDS are about equally a¬ected by counterparty
credit risk when the coe¬cient of default correlation between the protec-
tion seller and the reference entity is low. Take the case of a protection
seller that has a risk-neutral default probability of 4 percent, which is only
marginally below the risk-neutral default probability of the reference entity.
With β = .2”a coe¬cient of default correlation of about 1 percent”the
fair value of the CDS premium that such a seller would be able to charge
is only about 3 basis points lower than that charged in a contract that
involves no counterparty credit risk.



13
We assume a ¬‚at credit curve for the protection seller.
14
For instance, a nonzero recovery rate associated with the protection seller would lead
to a smaller e¬ect of counterparty credit risk on CDS premiums than the one suggested
by this example.
23.4 A CDS with Counterparty Credit Risk 279

400



350



300
basis points




250



200



150 beta=0
beta=.2
beta=.6
beta=.99
100
0 0.5 1 1.5 2 2.5 3 3.5 4
default probability of protection seller (percent)


FIGURE 23.2. E¬ects of Counterparty Credit Risk on Five-year CDS Premi-
ums. (The reference entity is assumed to have a recovery rate
of 30 percent. The riskless yield curve is assumed to be ¬‚at at
5 percent.)




Figure 23.2 also illustrates the e¬ect of default correlation on the CDS
premium. As one would expect, higher correlation (higher β) increases the
likelihood that the seller and the reference entity will default together and,
thus, makes the CDS less valuable to the protection buyer, resulting in a
lower premium. For instance, with β = .6, which amounts to a default cor-
relation of approximately 12 percent, the drop-o¬ in premiums as the credit
quality of the protection seller declines is much steeper than in comparable
cases with lower default correlation. Under this scenario, the same pro-
tection seller described in the previous paragraph”one with a risk-neutral
default probability of 4 percent”would have to o¬er roughly a 40 basis
point concession on the ¬ve-year premium relative to the premium charged
in a comparable contract with no counterparty credit risk.
Taken together, the results in Figure 23.2 suggest that, although coun-
terparty credit risk can have a signi¬cant e¬ect on the extent of default
protection e¬ectively provided by a CDS, protection buyers can substan-
tially mitigate their exposure to sellers by being mindful of the potential
degree of default correlation between the seller and the reference entity.
That mitigation would be over and above that conferred by relatively com-
mon contractual arrangements such as collateralization and netting, and
280 23. Modeling Counterparty Credit Risk

by the fact that protection sellers tend to have a high credit quality to
begin with.



23.5 Other Models and Approaches
In keeping with the introductory nature of this book, we have focused on
a very simple approach to analyzing the e¬ects of counterparty credit risk
in credit derivatives contracts. Nonetheless, our basic framework captures
many of the key elements and insights of other approaches developed in
the credit risk literature. For instance, a model that is closely related to
the one described in this chapter is the one developed by Hull and White
(2001)[42].
Similar to our basic model, the Hull-White speci¬cation follows the struc-
tural approach to modeling credit risk and assumes that there is a variable
Xj (t) that describes the creditworthiness of entity j at time t and that the
entity defaults at t if Xj (t) falls below a certain level Kj (t). Hull and White
also used their model to examine the valuation of credit default swaps that
are subject to counterparty credit risk. Their model allows for defaults to
occur at any time, not just at the premium payment dates speci¬ed in the
CDS, and also allows for accrued premiums and interest rate payments to
be factored into the valuation exercise. These features are not di¬cult to
incorporate into the model discussed in Sections 23.1 through 23.4. For
instance, accrued premiums can be introduced as noted in Chapter 16.
Many other methods and approaches for modeling the e¬ects of coun-
terparty credit risk exist and have varying degrees of complexity and
e¬ectiveness. For instance, a well-known framework rooted on the intensity-
based approach was proposed by Jarrow and Yu (2001)[47]. Additional
methods are discussed by Arvanitis and Gregory (2001)[2].
One issue that was not explicitly addressed by our basic model is the
replacement value of a credit derivative contract in the event of default by
the protection seller while the reference entity is still solvent. By replace-
ment cost we mean the cost, to the protection buyer, of replacing a contract
where the protection seller has defaulted with another one written on the
same reference entity and with the same remaining maturity.
If the credit quality of the reference entity has not changed since the
inception of the original contract, then the replacement cost is zero. Thus,
for instances of low asset default correlation between the protection seller
and the reference entity, the replacement cost should generally be very
small. For high (positive) correlation, however, the replacement cost of
the contract may be non-trivial, in that the credit quality of the reference
entity is more likely to have deteriorated than improved when that of the
protection seller has worsened to the point of leading it to default on its
23.7 Concluding Thoughts 281

obligations. For negative default correlation between the protection seller
and the reference entity, the replacement cost could actually turn out to
be negative, in which case the protection buyer could experience a windfall
upon a default by the seller.



23.6 Counterparty Credit Risk in Multi-name
Structures
We have thus far focused on approaches for assessing the e¬ects of coun-
terparty credit risk on the pricing of single-name credit default swaps. It
turns out that the basic framework described in Sections 23.1 through 23.4
can be extended for the analysis of more complex structures. For instance,
in the case of the ¬rst-to-default basket, we can expand the set of poss-
ible default outcomes”shown in Table 20.1 for a ¬ve-asset example that
involves no counterparty credit risk”to allow for scenarios where the pro-
tection seller defaults during the life of the basket. By carefully keeping
track of all possible outcomes and their respective risk-neutral probabili-
ties implied by the model, one can rely on Monte Carlo simulation methods
similar to the one described in Section 23.4.2. A similar logic applies to the
valuation of portfolio default swaps, which we discussed in Chapter 21.



23.7 Concluding Thoughts
As we mentioned in the beginning of Part IV, the portfolio credit risk lit-
erature has been growing rapidly and is technically demanding. Indeed, we
have barely scratched its surface in this introductory book. We do hope,
however, that we have managed to provide a broad overview of some of the
main issues that are germane to the valuation of multi-name credit deriva-
tives and of counterparty credit risk. More important, we hope we have
been able to provide a base from which one can expand one™s knowledge of
the subject and grow into this important segment of the credit derivatives
market.
Part V

A Brief Overview of
Documentation and
Regulatory Issues




283
24
Anatomy of a CDS Transaction




This chapter provides an overview of legal and documentation issues involv-
ing credit default swaps (CDS), the most prevalent of all credit derivatives.1
Similar to other over-the-counter derivatives instruments, credit default
swaps are typically initiated with a phone call in which the basic terms
of the transaction are agreed upon by the two prospective counterparties.2
That initial oral agreement is then followed up by a con¬rmation letter,
which, together with any supporting documentation referenced in the let-
ter, spells out the rights and obligations of each counterparty, as well as
the procedures for ful¬lling them.
From a legal standpoint, the con¬rmation letter and related documents
are the core of any CDS transaction and jointly constitute what we shall
refer here as a CDS contract. In this chapter, we take a closer look at
the main features and provisions of CDS contracts and the role that they
have played in the rapid growth of the credit derivatives market. We
also look at how developments in the marketplace have helped shape the
contracts.
In keeping with the scope of this book, we limit ourselves to provid-
ing a broad, and thus necessarily incomplete, overview of documentation


1
Many other credit derivatives instruments are negotiated on the basis of a similar
documentation framework.
2
In recent years, it has become increasingly common for transactions to be initiated
“on-line” via various electronic platforms.
286 24. Anatomy of a CDS Transaction

issues regarding CDS transactions. Needless to say, this chapter does not
constitute legal advice regarding CDS, or any other credit derivatives
contracts.



24.1 Standardization of CDS Documentation
As we mentioned in Chapter 2, CDS contracts are largely standardized,
with the marketplace mostly relying on documentation sponsored by the
International Swaps and Derivatives Association (ISDA), a trade group
whose members include major dealers and end-users of over-the-counter
derivatives products ranging from interest rate swaps to credit deriva-
tives. We say “largely” because there are some contractual variations
across national borders. Indeed, while the ISDA documentation for credit
derivatives is preeminent worldwide, it coexists, in a few countries, with
alternative, locally drawn, documentation frameworks.
To appreciate the role that the so-called ISDA contracts for CDS have
played in the development of the credit derivatives market, it is useful to
imagine the counterfactual. Suppose that, to this date, market participants
still had to contend with di¬erent forms of CDS contracts, both within
and across jurisdictions, depending on the counterparty, each with its own
stipulations and de¬nitions of key terms of the agreement. To reduce the
inherent “legal risk” that would prevail in a world with a multitude of con-
tract types, participants, and their lawyers, would have to devote valuable
time and resources to scrutinizing each agreement, often negotiating its
terms on a case-by-case basis. Such a situation would hardly be conducive
to the impressive growth in liquidity and size that the credit derivatives
market has experienced in recent years.
The fact is that, starting in the early days of the credit derivatives
market, participants came to realize the need for a common set of con-
tractual provisions and practices, following the example of other successful
over-the-counter derivatives markets, most notably that for interest rate
swaps. In essence, that is how the ISDA framework has become the most
prevalent standard for documenting CDS transactions both at the national
and international levels. Thus, our discussion of legal and documentation
issues involving CDS transactions is centered entirely on the ISDA legal
framework.
Broadly speaking, the ISDA framework for credit default swap contracts
revolves around the following main components:
• The Master Agreement is a contract between the two prospective
counterparties that often preexists the CDS transaction in which they
are about to enter. The master agreement governs those aspects of the
legal relationship between the two counterparties that are not speci¬c
24.1 Standardization of CDS Documentation 287

to the CDS transaction at hand. For instance, the agreement may
specify that the laws of the state of New York should be the appli-
cable law to any contracts entered into by the two counterparties.
The master agreement may also specify that netting provisions should
be applicable to any over-the-counter derivatives contract entered
by the two counterparties and covered by the master agreement.3
Procedures relating to default by one of the counterparties in any
of the types of contracts covered by the master agreement are gener-
ally also dealt with in this document. Highlighting the general nature
of the master agreement, it is not uncommon for the same agreement
to cover several types of over-the-counter contracts, not just credit
derivatives.
• The Con¬rmation Letter is the document that follows up on the
initial (generally oral) agreement between two prospective counterpar-
ties to enter into a speci¬c CDS. As its name indicates, this document
con¬rms the “economic” terms of the swap such as the identity of the
reference entity, the notional amount of the contract, and the protec-
tion premium. In the early days of the credit derivatives market, the
con¬rmation letter was a relatively lengthy document that described
the terms of the contract in great detail. That so-called long-form of
the CDS con¬rmation letter has e¬ectively been replaced by its short-
form, which is basically a template that allows the counterparties to
“¬ll in the blanks” with the appropriate information and “check” the
boxes that apply for the transaction at hand. For instance, the parties
might have to agree on which types of default events are covered by the
contract. The use of the short-form of the con¬rmation letter became
widespread as the degree of standardization of acceptable provisions
and de¬nitions became signi¬cant enough that those terms and provi-
sions could be listed in a separate document, called the ISDA Credit
Derivatives De¬nitions.
• The ISDA Credit Derivatives De¬nitions, as just noted, is a list
that de¬nes key terms referred to in the con¬rmation letter. Examples
include de¬nitions of the credit events allowable in the con¬rma-
tion letter, as well as additional detail on deliverable obligations and
settlement procedures.
• Supplements are separate documents issued by ISDA that amend,
update, or clarify terms in the De¬nitions.
• Credit Support Documentation involves agreements that call for
the collateralization of net exposures between the counterparties in

3
See Chapter 2 for a brief discussion of netting provisions.
288 24. Anatomy of a CDS Transaction

order to mitigate counterparty credit risk considerations. Not all CDS
contracts include credit support documentation, but contracts that
do are becoming increasingly common, especially when a lower-rated
counterparty is involved.
The legal framework sponsored by ISDA is primarily intended to pro-
mote standardization of legal provisions and market practices, but it does
recognize that some of the legal stipulations of the transaction may need
to be tailored to the needs of the counterparties. For instance, the master
agreement has two parts, the so-called “printed form” and the “schedule.”
While the former contains key standard provisions of the master agreement,
the latter allows any two counterparties to agree to make certain choices
speci¬ed in the printed form and/or to amend any provisions.
We could go on at length in a discussion of master agreements and
other legal issues involving credit derivatives, but that would go beyond
the intent of this book. Those interested in learning more about the ISDA
documentation framework may want to visit ISDA™s website, www.isda.org.


24.1.1 Essential Terms of a CDS Transaction
In addition to the names of the two parties in the contract”the buyer
and seller of default protection”essential terms that need to be speci¬ed
front and center in the con¬rmation letter include, obviously, the identity
of the reference entity, the types of obligations of that entity that are
covered by the contract, the speci¬c events that will trigger a payment by
the protection seller, and the procedures for settling the contract in the
event of default by the reference entity. As basic and self-evident as some
of these terms may seem, they need to be carefully de¬ned in the text
of the agreement. Any ambiguity regarding these key terms can result in
signi¬cant legal and ¬nancial headaches down the road.


24.1.1.1 The Reference Entity
With regard to the reference entity, if all that the contract did were to
name it, one might reasonably ask whether a default by a fully owned sub-
sidiary of that entity is enough to trigger payments by protection sellers,
or whether following the merger or demerger of the reference entity, the
successor entity or entities become the new reference entity in the CDS.
These questions, and other related issues, have been addressed in the Def-
initions and in various Supplements over the years. For instance, a default
by a subsidiary generally does not trigger a contract written on the parent
company, provided that company itself has not defaulted. Only contracts
referencing the subsidiary are triggered. On the second question, the doc-
umentation determines that if an entity assumes 75 percent or more of the
24.1 Standardization of CDS Documentation 289

bonds and loans of the original reference entity, then the assuming entity
becomes the new reference entity.4

24.1.1.2 Reference and Deliverable Obligations
The reference obligation is a debt instrument issued by the reference entity
that is designated in the CDS contract. The characteristics of the reference
obligation are important for several reasons. First, it dictates the level of
the reference entity™s capital structure at which default protection is being
bought and sold. Typically, the reference obligation is a senior unsecured
debt instrument of the reference entity, although some contracts are writ-
ten with reference to subordinated debt. Second, in the case of physically
settled CDSs, the reference obligation is always a deliverable obligation
(see Section 24.2.2), but a deliverable obligation need not be a reference
obligation. For instance, most contracts in the United States accept obli-
gations that have the same rank in the reference entity™s capital structure
as the reference obligation, generally subject to certain restrictions such as
the currency in which the instrument is denominated and, in the case of
bank loans, the ability to transfer the obligations to someone else.
The con¬rmation letter generally also speci¬es the range of obligations
in which a default must occur in order for a credit event to take place.
Most contracts simply specify the catch-all category “borrowed money,”
although, as we shall see below, there are some safeguards to prevent the
contract from being triggered prematurely, for instance, because of certain
events involving small dollar amounts or short delays in repayment.

24.1.1.3 Settlement Method
As we saw in Chapter 6, upon default by the reference entity, a CDS can
be either physically or cash settled. The choice of settlement method is
speci¬ed in the con¬rmation letter, which, as noted above, also determines
the types of debt securities that can be delivered in the case of physically
settled contracts.
Cash-settled CDS contracts are more common in Europe than in the
United States, where physical settlement is the method of choice. We
discuss settlement procedures in greater detail in Section 24.2.

24.1.1.4 Credit Events
One of the most important de¬nitions in a credit default swap contract is
that of “default.” Which event, or events, must take place for the protection

4
If no single entity assumes 75 percent of the bonds and loans of the original reference
entity, then the notional amount of the CDS contract is split pro rata among all entities
assuming at least 25 percent of the bonds and loans of the original entity.
290 24. Anatomy of a CDS Transaction

payment to be triggered? There are several “credit events” that constitute
default in the ISDA documentation framework for credit derivatives and
each are detailed in the Credit Derivatives De¬nitions. The following is a
brief description of each event:
• Bankruptcy constitutes a situation where the reference entity
becomes insolvent or unable to repay its debts. This credit event does
not apply to CDS written on sovereign reference entities.
• Obligation Acceleration occurs when an obligation has become due
and payable earlier than it would have otherwise been.
• Failure to Pay means essentially what it says. It occurs when the
reference entities fails to make due payments.
• Repudiation/Moratorium is deemed to have occurred when the
reference entity rejects or challenges the validity of its obligations.
• Restructuring is a change in the terms of a debt obligation that is
adverse to creditors, such as a lengthening of the maturity of debt.
We discuss restructuring in greater detail later in this chapter.
Not all of the above events apply to all contracts. The parties to the
contract can agree to exclude certain events. For instance, the market
consensus has moved towards excluding obligation acceleration as a credit
event in newly entered CDS contracts in the US. In addition, as we shall see
in Section 24.3, there is a certain degree of bifurcation in the marketplace,
where some contracts allow for restructuring to be included in the list of
credit events, whereas others do not.

24.1.2 Other Important Details of a CDS Transaction
Other important terms and provisions included in the con¬rmation letter
and accompanying documentation include:
• The maturity of the contract, also referred to as the “scheduled
termination date” of the contract.
• The notional amount of the contract, called the “¬xed rate payer
calculation amount” in the language of the con¬rmation letter.
• the CDS premium, which the contract calls the “price” or “¬xed rate,”
normally expressed in terms of basis points per annum.5

5
The protection payment and the protection seller are often referred to as the ¬‚oating-
rate payment and ¬‚oating-rate payer, respectively, borrowing on language commonly
used in the interest rate swap market. One interpretation of the use of this terminology
24.2 When a Credit Event Takes Place... 291

• The day-count conventions that should be applied, for instance, to
the calculation of accrued premiums in the event of default by the
reference entity while the contract is in force.
• The frequency with which CDS premium payments are made”
payments are typically made on a quarterly basis on dates speci¬ed in
the con¬rmation letter.

24.1.3 A Few Words of Caution
The standardization of CDS documentation has worked to reduce, but
not eliminate, the legal risks associated with CDS transactions. Nonethe-
less, standardized documents are no guarantee of universal agreement as
to the interpretation of those documents. Indeed, the e¬ort to improve
on the existing documentation framework is an ongoing one, especially as
unanticipated market developments have come to expose de¬ciencies and
limitations of earlier contracts, an issue that we discuss in Section 24.3.
Moreover, given that the CDS market is, as discussed in Chapter 2, still
a relatively young marketplace, there is potentially much to be learned
regarding how CDS documentation will be interpreted by the parties
involved and by the courts. For instance some market observers have
expressed concerns about the eventual enforceability of the language in
ISDA contracts in national courts, especially in cases involving non-OECD
parties.


24.2 When a Credit Event Takes Place...
The contract speci¬es in detail all the procedures that must be followed
in the event of default by the reference entity while the CDS is in place.
But before the settlement phase of the contract goes fully into gear, the
ISDA documentation provides for some safeguards to ensure that a bona
¬de credit event has indeed taken place.

24.2.1 Credit Event Noti¬cation and Veri¬cation
A credit event is not a credit event until it meets certain minimum pay-
ment and default requirements under the terms of the CDS contract. For
instance, a qualifying failure-to-pay event must take into account any appli-
cable grace periods and must involve a minimum dollar threshold”e.g., a

is that, unlike the protection buyer who knows exactly when and how much to pay for
as long as the contract is in force and the reference entity is solvent, uncertainty about
the recovery rate means the seller does not know in advance the timing or size of the
protection payment, if any, that it will have to make to the buyer.
292 24. Anatomy of a CDS Transaction

loss of at least $1 million. Repudiation, moratorium, and restructuring
events also are subject to minimum dollar thresholds. In addition to meet-
ing the minimum payment and default requirements, a credit event has to
be veri¬able through at least two sources of public information, such as
Bloomberg, Reuters, or similar services. The event noti¬cation and veri¬-
cation process is generally formalized via the delivery of the Credit Event
Notice and the Notice of Public Information by the party triggering the
contract.6
These pre-settlement requirements are designed to protect the interests
of both sellers and buyers of protection. From the seller™s perspective, a
premature triggering of the contract involving an otherwise solvent refer-
ence entity may mean that the seller will end up making a payment in a
situation where no bona ¬de credit event ever takes place during the life
of the CDS. From the buyer™s perspective, the seller may end up receiving
a small protection payment now while foregoing valuable protection down
the road when a bona ¬de event takes place.


24.2.2 Settling the Contract
Once the occurrence of a credit event is veri¬ed, usually via acceptance of
the Credit Event Notice and Notice of Publicly Available Information, the
contract goes into its settlement phase.
For cash-settled contracts, upon default by the reference entity the pro-
tection buyer is entitled to receive from the seller the di¬erence between
the par and market values of the reference obligation. The latter tends to
be a bond issued by the reference entity as bond prices are typically easier
to determine in the marketplace than those of loans. The market value of
the reference obligation is commonly determined by a dealer poll typically
conducted a few days after the credit event. The contract generally allows
the settlement price to be determined on the basis of a similar obligation
of the reference entity if the original reference obligation is no longer avail-
able, which could be the case if, for instance, it was prepaid by the reference
entity.
For physically settled contracts, the protection buyer has the right to
decide which of the eligible obligations of the reference entity will be deliv-
ered to the seller. Once that decision is made, the buyer delivers a Notice
of Intended Physical Settlement to the seller and then commits to deliver-
ing the designated obligations. The physical settlement period is capped at
30 business days. If delivery is not successful during that period because,


6
Commonly, the Credit Event Notice and the Notice of Publicly Available Informa-
tion can be delivered up to 14 days after the maturity date of the contract, provided the
event itself took place while the contract was still in place.
24.3 The Restructuring Debate 293

say, the buyer was not able to buy the obligations in the marketplace,
the contract usually allows for “fallback” settlement procedures, which are
described in ISDA™s 2003 Credit Derivatives De¬nitions.


24.3 The Restructuring Debate
One of the most prominent documentation issues in the history of the
credit derivatives market has evolved around the de¬nition of restructuring
as a credit event. The scope of the issues debated by market participants
over the years has ranged from the very de¬nition of restructuring to the
question of whether restructuring should be included in the list of allowable
credit events in the ¬rst place.
In the early days of the marketplace, restructuring was de¬ned only in
very broad terms in ISDA™s standard CDS documentation. Indeed, the
then-prevailing de¬nition, which had been adopted by ISDA back in 1991,
characterized restructuring essentially as any change in the terms of the
obligations of a reference entity that was “materially less favorable” to its
creditors. The Asian crisis of 1997 and the Russian default of 1998 brought
to light some of the problems with the subjectivity of the 1991 de¬nition,
and, in 1999, market participants adopted a new de¬nition of structuring.7
That de¬nition basically provided a narrower characterization of which
circumstances would trigger the restructuring clause in CDS contracts. In
particular, the 1999 ISDA de¬nition characterized restructuring as:
• a reduction in the rate or amount of interest payable;
• a reduction in the amount of principal;
• a postponement of interest or principal payment;
• a change in the seniority of the debt instrument;
• a change in the currency composition of any payment.

In addition, market participants, through ISDA, adopted the condition
that, for any of the above to constitute a restructuring event for the pur-
poses of a CDS contract, they must result “directly or indirectly from a
deterioration in the creditworthiness or ¬nancial condition of the reference
entity.”

7
Rule (2001)[68] discusses the events that led up to the adoption of the 1999 de¬nition
of restructuring, as well as other important cases in the history of the marketplace, such
as the Conseco restructuring episode in the United States, summarized below, and the
National Power demerger case in the United Kingdom, which helped shape the successor
provisions outlined in Section 24.1.1.1 of this book.
294 24. Anatomy of a CDS Transaction

24.3.1 A Case in Point: Conseco
Conseco Inc. is an insurance and ¬nancial services company based in the
United States. The company was facing a deteriorating ¬nancial outlook in
the late 1990s and eventually lost access to the commercial paper market,
a situation that led it to rely on its back-up lines of bank credit to repay
maturing debt. In 2000, even though its business condition was showing
some signs of improvement, Conseco™s lines of credit were fully utilized
and about to become due. Conseco™s bankers agreed that it would not
be able to repay the maturing bank loans and decided to restructure the
loans, extending their maturity while charging a higher interest rate and
obtaining some collateralization.
The loan restructuring helped Conseco remain solvent in 2000.8 More-
over, given the higher coupon and degree of collateralization on the
restructured debt, the a¬ected lenders were thought to have been at least
partially compensated for the maturity extension. Yet, according to the
1999 de¬nition of restructuring a qualifying restructuring event had taken
place, and CDS contracts written on Conseco were consequently triggered.
The Conseco case helped expose one shortcoming associated with the
1999 de¬nition of restructuring. Unlike an outright default or bankruptcy,
where the market prices of the bonds and loans of the reference entity
broadly converge regardless of their maturity, restructurings often a¬ect the
prices of bonds and loans of the reference entity di¬erently. For instance,
in Conseco™s case, the restructured loans were trading at a substantially
smaller discount from their face value shortly after the triggering of the cor-
responding CDS contracts than were longer-dated senior unsecured bonds
previously issued by Conseco. Yet, both the long-dated bonds and the loans
were deliverable obligations under the terms of the contract!
As a result, some protection buyers in the CDS market that had made
loans to Conseco were more than compensated for their restructuring-
related losses regarding Conseco. They su¬ered a relatively small marked-
to-market loss in the restructured loans, but that loss was more than o¬set
by gains derived from their CDS positions, where they could deliver the
cheaper longer-dated bonds, as opposed to the loans, and receive their full
face value from their CDS counterparties.
To sum up, the 1999 de¬nition of restructuring had the e¬ect of giving
protection buyers a potentially valuable cheapest-to-deliver option in their
CDS positions. While protection sellers honored the letter of the CDS
contracts written on Conseco and made good on their commitments under
the contracts, many wondered whether the Conseco episode was consistent

8
The company™s troubles were not fully resolved by the 2000 restructuring of its
bank debt, however. In late 2002, Conseco ¬led for Chapter 11 bankruptcy protection.
It emerged from its Chapter 11 reorganization process in September 2003.
24.3 The Restructuring Debate 295

with the spirit of a CDS agreement. Indeed, most market participants
point to the Conseco case, as we do in this book, as a major catalyst of
the debate that culminated with the adoption of a new set of provisions
regarding restructuring in CDS contracts.


24.3.2 Modi¬ed Restructuring
The main thrust of the so-called modi¬ed restructuring provision of CDS
contracts”which was introduced in the standard CDS documentation in
an ISDA Restructuring Supplement adopted in 2001 and later incorporated
into the 2003 Credit Derivatives De¬nitions”was to mitigate the cheapest-
to-deliver problem that was at the heart of the Conseco case. Thus, without
substantially changing the 1999 de¬nition of restructuring as a credit event,
the new provisions had mostly the e¬ect of limiting the range of obliga-
tions that would become deliverable when a contract is triggered by a
restructuring event. The new provisions also disallowed the applicability of
the restructuring clause in cases where restructuring is limited to bilateral
loans.
The motivation for the ¬rst set of main changes associated with modi¬ed
restructuring”limiting the basket of deliverables in contracts triggered by
restructuring”is very straightforward in light of the Conseco case. Indeed,
modi¬ed restructuring works primarily by capping the maturity of obliga-
tions that are eligible to be delivered in the event of restructuring. As for
the second main innovation brought about by modi¬ed restructuring”the
bilateral-loan exclusion”its primary intent was to address potential “moral
hazard” problems, whereby a lender may force the restructuring of a loan
on which it bought protection and then attempt to gain from “exercising”
any remaining cheapest-to-deliver option embedded in a CDS contract.
Remaining provisions of the modi¬ed restructuring clause sought to ¬ne
tune other issues related to restructuring as a credit event, including the
transferability of any deliverable obligations and the treatment of changes
in the seniority of an obligation in the reference entity™s capital structure.


24.3.3 A Bifurcated Market
Modi¬ed restructuring went a long way towards meeting the interests of
both buyers and sellers in the CDS market. Many sellers, especially banks
who count on the credit derivatives market to obtain regulatory capital
relief, wanted the broadest possible default protection and thus preferred
to keep restructuring in the list of allowable credit events. Protection sellers,
on the other hand, wanted to minimize the cheapest-to-delivery problem,
which, as we discuss below, introduces some tough valuation issues. The
modi¬ed restructuring clause thus emerged as a compromise between these
two positions.
296 24. Anatomy of a CDS Transaction

Still, the restructuring debate is most likely not over. Indeed, some degree
of bifurcation persists in the marketplace, with some contracts being nego-
tiated with restructuring and some without. In addition, there are some
variations in the standard contracts used in North American, Europe, and
Asia when it comes to restructuring. For instance, in Europe, contracts
typically allow for less stringent maturity limitations than in the United
States.


24.4 Valuing the Restructuring Clause
A contract that provides protection, for instance, against restructuring,
bankruptcy, and failure-to-pay events ought to cost more than one that
provides protection only against the latter two. How much extra should a
protection buyer have to pay to have restructuring added to the list of credit
events? Drawing an analogy with the vast default risk literature, theory
would suggest that the value of the restructuring clause should depend
on the probability of a restructuring taking place. Unfortunately, however,
there are no well-known models of restructuring probabilities so the analogy
between modeling default and restructuring risks does not take us very far
in terms of valuing the restructuring clause.
One simple approach to gauging the value of the restructuring clause is to
compare premiums actually charged in CDS contracts that include restruc-
turing to those that do not. Based on the limited amount of data generated
since the modi¬ed structuring clause became part of the standard CDS doc-
umentation, some market participants have estimated that premiums that
correspond to contracts with the modi¬ed restructuring clause are about
5 to 10 percent higher than premiums for contracts without restructuring.

24.4.1 Implications for Implied Survival Probabilities
In Chapter 16 we discussed a simple method for inferring risk-neutral prob-
abilities of default from CDS premiums quoted in the marketplace. Suppose
now that all that we have are premiums that correspond to contracts that
include the modi¬ed restructuring clause, but that we are interested in
the risk-neutral probabilities of an outright default over various horizons”
where by outright default we mean events like bankruptcy and failure to
pay. The discussion in the previous section suggests a simple two-step
approach to computing those probabilities. First, we reduce the observed
premiums by 5 to 10 percent in order to obtain a rough estimate of premi-
ums that would prevail in the absence of the modi¬ed restructuring clause.
Second, we follow the same method described in Section 16.1.
Table 24.1 shows the results of the two-step approach when applied
to AZZ Bank, one of the hypothetical reference entities examined in
24.4 Valuing the Restructuring Clause 297

TABLE 24.1
CDS-implied Survival Probabilities and Modi¬ed Restructuring

Horizon/ CDS Survival Probabilities Bias
Maturity premium Raw quotes Adjusted quotes
(3) ’(4)
(basis points) (percent) (percent)

(1) (2) (3) (4) (5)

One year 29 99.42 99.48 0.06

Two years 39 98.45 98.60 0.15

Three years 46 97.26 97.53 0.27

Four years 52 95.88 96.29 0.40

Five years 57 94.37 94.92 0.55

Note. Assumed recovery rate: 50 percent. All probabilities shown are risk-neutral. All
other assumptions are as in Table 16.1.



Chapter 16. Column 2 shows the CDS premiums quoted in the market
place, which we are now assuming to be for contracts that include the
modi¬ed restructuring clause. Column 3 shows CDS-implied survival prob-
abilities based on the unadjusted (raw) quotes shown in column 2”these
are the same probabilities shown in Table 16.2. Column 4 shows survival
probabilities obtained from the two-step approach, where we reduced the
premiums shown in column 2 by 10 percent. The results suggest that, at
least for highly rated reference entities such as the one examined in this
exercise, the survival probabilities based on the adjusted premiums di¬er
very little from those based on the raw market quotes.
The di¬erences between results derived from raw and restructuring-
adjusted premiums”shown in the column labeled “bias””would be bigger
for lower-rated entities such as XYZ Corp., the other entity examined in
Chapter 16. Still, the maximum absolute value of the bias for XYZ Corp.
would amount to only minus 2.75 percentage points. We should also note
that it is often the case that CDS contracts written on lower-rated entities
tend not to include restructuring in the list of allowable credit events so the
“restructuring bias” in derived survival probabilities is often not an issue
for these reference entities.
25
A Primer on Bank Regulatory Issues



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