Risk 1211 Brigo New

7/27/2019 Risk 1211 Brigo New

http://slidepdf.com/reader/full/risk-1211-brigo-new 1/5

74 RDecember 2011

cttingdg.cRditRisk

default event happens to one of the counterparties in a deal, it is stopped and marked-to-market: the net

present value (NPV) of the residual part of the deal is calculated.Te recovery rate is applied to this close-out value to determinethe default payment. While modelling the recovery is known tobe a dicult task, the calculation of the close-out amount hasnever been the focus of extensive research. Before the creditcrunch, and actually up to the Lehman Brothers default in 2008,the close-out amount was usual ly calculated as the expectation of the future payments discounted back to the default day by a Libor-based curve of discount factors.

oday, however, things are not so trivial. We are aware thatdiscounting a deal that is default-free and backed by a liquid col-lateral should be performed using a default-free curve of discountfactors, based on overnight quotations, whereas a deal that is notcollateralised and is thus subject to default risk should be dis-counted taking liquidity costs into account and include a creditvalue adjustment. NPV should be calculated in dierent wayseven for equal payouts, depending on the liquidity and creditconditions of the deal.

Te previous literature on counterparty risk assumes that whendefault happens the close-out amount is calculated treating theNPV of the residual deal as risk-free (risk-free close-out). Tis was

an obvious choice when one of the two parties, usually the bank, was treated as default-free, based on its generally very superiorcredit standing. Nowadays no counterparty can be consideredrisk-free. In the case that a default happens, the surviving party can still default before the maturity of the deal. In spite of this,even recent literature that assumes such a bilateral counterparty risk still adopts a risk-free close-out amount at default.

Te legal (International Swaps and Derivatives Association)documentation on the settlement of a default does not conrmthis assumption. Isda (2010) says: “Upon default close-out, valua-tions will in many circumstances reect the replacement cost of transactions calculated at the terminating party’s bid or oer side

of the market, and wil l often take into account the creditworthi-ness of the terminating party.” Analogously, Isda (2009) says thatin determining a close-out amount the information used includes“quotations (either rm or indicative) for replacement transac-tions supplied by one or more third parties that may take intoaccount the creditworthiness of the determining party at the timethe quotation is provided”.

A rea l market counterpart y replacing the defaulted one wouldnot neglect the creditworthiness of the surviving party. On theother hand, there is no binding prescription – the Isda documen-tation speaks of creditworthiness that is taken into account often,not always, and that may, not must, be included. Tis leaves roomfor a risk-free close-out, which is probably easier to calculate sinceit is independent of the features of the survived party. Te coun-

terparty risk adjustments change strongly depending on whichclose-out amount is considered. Also the eects at the moment of default of a company are very dierent under the two close-outconventions, with some dramatic consequences on default conta-gion, as we show in the following. Tese results should be consid-ered carefully by the nancial community, and in particular by Isda, which can give more certainty on this issue.

Risk-free versus replacement close-out: practical consequences

A risk-free close-out ha s implications that are very dierent from what we a re used to in the case of a default in standardised mar-kets such as the bond or loan markets. If the owner of a bonddefaults, or if the lender in a loan defaults, this means no losses tothe bond issuer or to the loan borrower. But if the risk-free defaultclose-out is applied to a derivatives transaction, when the netcreditor party in a derivative (thus in a position similar to a bondowner or loan lender) defaults, the value of the net debtor’s liabil-ity will suddenly jump up. Tis is because before default it ismarked-to-market accounting for this default risk, while after- wards this is excluded under the risk-free close-out and so thecontract is more valuable.

Tis increase grows with the debtor’s credit spread, and it mustbe paid upfront at default by the debtors to the liquidators of thedefaulted party. So obviously net debtors will prefer a replace-ment close-out, which does not imply this increase. Under a replacement close-out, if one of the two parties in the deal has nofuture obligations, just like a bond or option holder, his defaultprobability does not inuence the value of the deal at inception,consistently with market practice for bonds and options.

On the other hand, the replacement close-out has shortcom-ings opposite to the risk-free close-out. While protecting debtors,it can in some situations penalise the creditors. Consider the case when the defaulted entity is a company with high systemicimpact, like Lehman Brothers, such that when it defaults thecredit spreads of its counterparties are expected to jump high.Under a replacement close-out this jump reduces the creditwor-thiness of the debtors and therefore the market value of their lia-bilities. All the claims of the liquidators towards the debtors of the defaulted company will be deated, and the low level of therecovery may again be a dramatic surprise, but this time for thecreditors of the defaulted company.

Close-out convention tensionsThere is an ambiguity in the market about the

convention or establishing a derivative’s close-out

value to be settled at deault – in particular whether

or not to include adjustments or the credit risk o the

surviving party. Damiano Brigo and Massimo Morini

show how to include these adjustments and take

seriously the dierences in the convention choice – and

fnd that while the risk-ree close-out can exacerbate

contagion by increasing debtors’ liabilities, in highly

correlated environments the risky close-out candramatically lower the recovery received by creditors

When a



risk.net/risk-magazine 75

Unilateral and bilateral valuation adjustments

Consider two parties entering a deal with nal maturity T , aninvestor I and a counterparty C . Assume the deal’s discountedtotal cashows at time t , in the absence of default risk of eitherparty, are valued by I at P

I (t , T ). Te analogous cashows seen

from C are denoted with PC (t , T ) = –P I (t , T ). In a ‘unilateral’situation where only the counterparty risk of name C is consid-ered, one can write the value of the deal to either party including this counterparty risk. Tis will be the value when this defaultdoes not occur before maturity, plus a credit value adjustment (for I ) or debit value adjustment (for C ) term consisting of theexpected value at default plus terms reecting the recovery pay-ments. From the point of view of C this is:

NPV C

C t ( ) = Et

1 τC >T

ΠC

t ,T ( ){ }+Et 1

t < τC ≤T Π

C t , τ

C ( )⎡⎣{

+ D t , τC ( ) NPV

C τ

C ( )( )+

− REC C

− NPV C

τC ( )( )

+( )⎤⎦⎥} where REC and LGD = 1 – REC denote recoveries and loss givendefaults, D(t , T ) is the discount factor between times t and T , and

the expected exposure NPV C (t ) = Et [PC (t , T )] is the default risk-free value of the residual deal at time t , seen by C . Te corre-sponding formula for I is the classical result from Brigo & Masett i(2005) and can be seen by changing the lower index – which rep-resents who is doing the valuation – to I , and switching the orderof the recovery and positive exposure terms in the dierence part,remembering that the sign of the exposure changes.

In the situation where both I and C may default, we have a bilateral valuation adjustment (see, for example, Brigo & Cap-poni, 2008, or Gregory, 2009, for the general framework, andBrigo, Pallavicini & Papatheodorou, 2011, for the application tointerest rate instrument portfolios with netting and wrong-way risk). We dene t1 to be the rst-to-default time, t1 = min( t

I , t

C ).

Inclusion of bilateral default risk leads to the risk-free close-out adjustment:

NPV I

Freet ,T ( ) = Et

1 τ1>T { }

Π I

t ,T ( ){ }+E

t 1

τ1= τC <T { }

Π I

t , τC ( )+ D t , τ

C ( )⎡⎣{ REC

C NPV

I τ

C ( )( )+ − − NPV I

τC ( )( )+( )⎤⎦⎥}

+Et 1

τ1= τ I <T { }

Π I

t , τ I ( )+ D t , τ

I ( )⎡⎣{− NPV

C τ

I ( )( )+ − REC I

NPV C

τ I ( )( )+( )⎤⎦⎥}

(1)

where we use the risk-free NPV upon the rst default to close the

deal, in keeping with a risk-free close-out. But, as we saw in theintroduction, this choice is not obvious in a bilateral setting because the surviving party is not default risk-free, and even Isda documentation considers a replacement close-out taking intoaccount the credit quality of the surviving party. So we considerthe substitutions:

NPV I τC ( ) → NPV

I

I τC ( )

NPV C

τ I ( ) → NPV

C

C τ I ( )

with the counterparties va luing the NPV account for the r isk of their own default, as denoted by the superscript. Te nal for-

mula for the adjustment under a replacement close-out is thesame as equation (1) but with this substitution. We denote therelated NPV by NPV

I Repl(t , T ). For more details, see Brigo &

Morini (2010) and Morini (2010).

A quantitative analysis and a numerical exampleHere we choose quite simple payouts and modelling assumptions.Tis is done to show the eects of the close-out conventions by dinsentangling them from complex modelling and payoutassumptions that would obscure patterns. We consider a simpleT -maturity call option on stock S , with the risk-free price for I ,the option holder, given by:

NPV I

0,K ,T ( ) = P 0,T ( )E0 S T −K ( )

+⎡⎣

⎤⎦

where we assume deterministic interest rates and P(0, T ) is thedeterministic discount factor (risk-free bond price), and an evensimpler deal where C promises to pay an amount K to I at matu-rity T . In this case the risk-free price to the bondholder I is:

NPV I 0,

K ,T

( )= P

0,T

( )K

Notice that in the above deals I is the option or bondholder,so it is the lender in the deal, with no further obligation afterthe payment of the premium at inception, while C is in theposition of the borrower, the party that commits to executepayments at a future time. We will often refer to I as the lenderand to C as the borrower. Te second payout is an establishedmarket standard to compare the consistency of each close-outassumption. Here the comparison with a bond-style payout isinteresting for a further reason: when bilateral counterparty risk was introduced for derivatives, it was pointed out in themarket that this approach, involving a bank including its ownrisk of default in valuation, already existed for bonds throughthe fair-value option, and this analogy dominated the discus-sion on its appropriateness.

We now introduce risk of default for both parties. If we con-sider an underlying stock independent of the risk of default of theparties, the above formulas for the risky price under the two pos-sible close-out assumptions reduce to:

PV I Repl

0,K ,T ( )

NPV I 0,K ,T ( ) Q τC >T ( )+ REC C Q τC ≤ T ( )⎡⎣ ⎤⎦

PV I Free

0,K ,T ( )

NPV I 0,K ,T ( )

Q τC >T ( )+Q τ I < τC <T ( )+ REC C Q τC ≤min τ I ,T ( )( )⎡⎣ ⎤⎦

NPV I 0,K ,T ( )

Q τC >

T ( )+

REC C Q τC ≤ T ( )+

LGDC Q τ I <

τC <

T ( )⎤⎦ whereQ is the risk-neutral probability measure. We see an impor-tant oddity of the risk-free close-out in this case. Te adjustedprice of the bond or of the option depends on the credit risk of thelender I (bondholder or option holder) if we use the risk-freeclose-out. Tis is counter-intuitive since the lender has no obliga-tions in the deal, and it is not consistent with market practice forloans or bonds. From this point of view, the replacement close-out is preferable.

Tis bizarre dependence of the risk-free close-out price on therisk of default of the party with no obligations in a deal can be



76 RDecember 2011

cttingdg.cRditRisk

properly appreciated in the following numerical example, where we consider the option-style payout with S

0= 2.5, K = 2 and a

stock volatility equal to 40% in a standard lognormal Black-Scholes framework. Set the risk-free rate and the dividend yield atr = q = 3%, and consider a maturity of ve years. Te price of anoption varies with the default risk of the option writer, as usual,and here also with the default risk of the option holder, due to therisk-free close-out. In gure 1, we show the price of the option fordefault intensities l

I , l

C going from zero to 100%. We consider

RC = 0 so that the level of the intensity approximately coincides with the market credit default swap spread on the ve-year matu-rity. We also assume that default of the entities I and C are inde-pendent of each other.

We see that the eect of the holder’s risk of default is not negli-gible, and is particularly decisive when the writer’s risk is high.Similar patterns are shown for a bond payout in Brigo & Morini(2010): with a risk-free close-out there is a strong eect of thedefault risk of the bondholder, an eect that is higher the higherthe risk of default of the bond issuer. Te results of gure 1 can becompared with those of gure 2, where we apply the formula thatassumes a replacement close-out. Tis is the pattern one wouldexpect from standard nancial principles: independence of theprice of the deal from the risk of default of the counterparty thathas no future obligations in the deal.

We can also consider a specia l case where, at rst sight, thepicture appears dierent – when we assume maximal dependencebetween the defaults. We assume the default of I and C to be co-monotonic, and the spread of the lender I to be larger, so itdefaults rst in all scenarios (for example, C is a subsidiary of I , ora company whose wellbeing is completely driven by I : C is a tyrefactory whose only client is car producer I ). In this case, the two

formulas become:

NPV I Repl

0,K ,T ( )

= NPV I 0,K ,T ( ) Q τC >T ( )+ REC C Q τC ≤ T ( )⎡⎣ ⎤⎦

NPV I Free

0,K ,T ( )

= NPV I 0,K ,T ( ) Q τC >T ( )+Q τC <T ( )⎡⎣ ⎤⎦= NPV I 0,K ,T ( )

Now the results we obtain with a risk-free close-out appear some-how more logical. Either I does not default, and then C does notdefault either, or when I defaults C is still solvent, and so I recov-ers the whole payment. Te credit risk of C should not aect the

deal. Tis happens with the risk-free close-out but not with thereplacement close-out. However, one may argue that this result is

obtained under a hypothesis that is totally unrealistic: thehypothesis of perfect default dependency with heterogeneousdeterministic spreads (co-monotonicity), which can imply thatcompany C will go on paying its obligations, maybe for years, inspite of being doomed to default at a fully predictable time. For a discussion on the problems that can arise when assuming perfectdefault dependency with deterministic spreads, see Brigo &Chourdakis (2009) and Morini (2009) and (2011).

In an example such as the one described above, where the bor-rower is so linked to the lender, the realistic scenario is that thedefault of the borrower will not happen simultaneously with thedefault of the lender, but before the settlement of the lender’sdefault, so that the borrower will be in a default state and will pay only a recovery fraction of the risk-free present value of the deriv-ative. Tis makes the payout exactly the same as in a replacementclose-out, so this assumption also appears more logical in the spe-cial case of co-monotonic companies. Standard formulas forcounterparty risk cannot capture this reality because they makethe simplication that default is settled exactly at default time, a spointed out above.

We now analyse contagion issues. We write the price at a generictime t < T , and then assume the lender defaults between t and t +

Dt , t < t I

< t + Dt , checking the consequences in both formulas:

NPV I Repl

t ,T ( )

= NPV I t ,T ( ) Qt τC >T ( )+ REC C Qt t < τC ≤ T ( )⎡⎣ ⎤⎦

NPV I Free

t ,T ( )

= NPV I Repl

t ,T ( )+ NPV I t ,T ( ) LGDC Qt t < τ I < τC <T ( )

(2)

Here the subscript t on the probabilities means we are condition-ing on the market information at time t . Tis conditioning will becrucial in the co-monotonic case. Indeed, we focus on two cases:n t

I and t

C are independent. In this case, the default event t

I

alters only one quantity: we move from:

Q

t τ I < τ

C <T ( ) <Qt

τC <T ( )

to:

Q

t +Δt τ I < τC <T ( ) =Qt +Δt

τC <T ( ) ≈ Qt

τC <T ( )

for small Dt so that from NPV I

Free(t , T ) given in (2) we move to:

Writer (borrower)five-year spread λC (%)

Buyer (lender)five-year spread λI (%)

100

80

60

40

20

0 0

1 0

2 0

3 0

4 0

5 0

6 0

7 0

8 0

9 0

1 0 0

1 0 0

9 0

8 0

7 0

6 0

5 0

4 0

3 0

2 0

1 0

0

%

2Valueofaopowhubuoloe-ou

Writer (borrower)five-year spread λC (%)

Buyer (lender)five-year spread λI (%)

100

80

60

40

20

0 0

1 0

2 0

3 0

4 0

5 0

6 0

7 0

8 0

9 0

1 0 0

1 0 0

9 0

8 0

7 0

6 0

5 0

4 0

3 0

2 0

1 0

0

%

1Valueofaopowhr-freeloe-ou



risk.net/risk-magazine 77

NPV I Free

t +Δt ,T ( ) = NPV I t +Δt ,T ( )

whereas the replacement close-out price does not change.n t

I and t

C are co-monotonic. ake an example where t < t

I < t +

Dt implies that t + Dt < tC

< T. Ten, using A ⎥→ B with the mean-ing of ‘we go from A to B’, we have with t < t

I < t + Dt :

Qt τC >T ( ) > 0aQ

t +Δt τC >T ( ) = 0

Qt τC ≤ T ( ) <1aQt +Δt

τC ≤ T ( ) =1

Qt τ I < τ

C <T ( ) <1aQt +Δt

τ I < τ

C <T ( ) =1

Tis means that from NPV I

Repl(t , T ) given in (2) we move to:

NPV I Repl

t +Δt ,T ( ) = REC C NPV I t +Δt ,T ( )

Under a risk-free close-out and independent defaults, a previ-ously risky derivative turns suddenly into a risk-free one atdefault of the lender, suddenly raising the liability of the bor-rower. Tis jump will be greater the higher the default risk of the borrower. As we said above, it is a form of contagion thataects debtors of a defaulted entity and adds to the standardcontagion aecting creditors. Under a replacement close-out we have no discontinuit y and no contagion of the debtors.

In the co-monotonic case, under a replacement close-out thedefault of the lender sends the value of the contract to its mini-mum value, the value of a defaulted contract. Te borrower willsee a strong decrease of its liabilities to the lender. Tis is a posi-tive fact for debtors, but it is an increase of the contagion of thecreditors of the defaulted company, which will see the recovery reduced. Tis does not happen in case of a risk-free close-out.Tis example is under the extreme hypothesis of co-monotonicity,but in this case the main conclusions do not hinge on the unreal-

istic elements of this hypothesis. We can see it as the extreme of a realistic scenario: the case when the defaulted company has a strong systemic impact, leading the spreads of the counterpartiesto very high values, deating the liabilities of the debtors under a replacement close-out. We cannot deny this is realistic: it is what we saw in the Lehman case.

Let us now consider the loan/bond/deposit payout, withcounterparty C (borrower) promising to pay K = 1 to I (lender). We start from the above r = 3% and maturity of ve years, for a 1 billion notional. Now we take RC = 0% and two risky parties. We suppose the borrower has a very low credit qualit y, asexpressed by l

C = 0.2, which means a probability to default

before maturity of 63.2%, while l I

= 0.04, which means a default probability of 18.1%. An analogous risk-free ‘bond’

would have a price:

P 0,5 y( ) = 860.7million

while taking into account the default probability of the two par-ties, which are assumed to be independent, we have:

NPV I Free

0,5 y( ) = 359.5million, NPV I Repl

= 316.6million

Te dierence of the two valuations is not negligible but not dra-matic. More relevant is the dierence in case of a default. Wehave the following risk-adjusted probabilities of the occurrence of a default event:

min 5 y, τ I , τC ( ) = τC

withprob58%

τ I withprob12%

5 ywithprob30%

⎧

⎨⎪⎪

⎩⎪⎪

Te two formulas disagree only when the lender defaults rst. Letus analyse in detail what happens in this case. Suppose the exactday when default happens is t I = 2.5y. Just before default, at 2.5years less one day, we have for the borrower C the following book value of the liability produced by the above deal, depending onthe assumed close-out:

NPV C Free

τ I −1d ,5 y( ) =−578.9million

NPV C Repl

τ I −1d ,5 y( ) =−562.7million

Now default of the lender happens. In case of a risk-free close-out, the book value of the bond becomes simply the value of a

risk-free bond: NPV C

Free τ I +1d ,5 y( ) = −927.7million

Te borrower, which has not defaulted, must pay this amountentirely – and soon. He has a sudden loss of 348.8 million dueto default of the lender. With the substitution close-out, wehave instead:

NPV C Repl

τ I +1d ,5 y( ) = −578.9million

Tere is no discontinuity and no loss for the borrower in case of default of the lender. Tis is true, however, only in case of inde-pendence. If the default of the lender leads to an increase of the

DEFAUL

T

τLen

Replacement close-out

when lender and borrower

have strong links


Risk-free close-out

Risk-free close-out

–Pr ( τBor > T )e–rT


–Pr ( τLen < τBor < T )e–rT

–e–r (T – τLen)

0

4Lowerreoveryforreoruerreplaeme

loe-ou

DEFAUL T


Risk-free close-outReplacement close-out

Risk-free close-out

0

τLen



–Pr ( τLen < τBor < T )e–rT

–e–r (T – τLen)

– Pr ( τBor > T )e–r (T – τLen)

τLen

3Loforheborroweraefaulofheleeruer

r-freeloe-ou



78 RDecember 2011

cttingdg.cRditRisk

spreads of the borrower, the liability can jump to lower in abso-lute value, also lowering the expected recovery for the liquidatorsof the defaulted lender (see gures 3 and 4, and table A).

In Brigo & Morini (2010), we also cover the issue of how totreat the two close-out conventions for the case of collateralised

deals, when the nal outcome should always be that, irrespectiveof close-out, collateral and exposure match at default.

Conclusion

We have analysed the eect of the assumptions about the computa-tion of the close-out amount on the counterparty risk adjustmentsof derivatives. We have compared the risk-free close-out assumed inthe earlier literature with the replacement close-out we introducehere, inspired by the recent Isda documentation on the subject.

We have provided a formula for bilateral counterpar ty risk when a replacement close-out is used at defau lt. We reckon thatthe replacement close-out is consistent with counterparty risk adjustments for standard and consolidated nancial productssuch as bonds and loans. On the contrary, the risk-free close-outintroduces at time zero a dependence on the risk of default of the

party with no future obligations. We have also shown that in case of the risk-free close-out, a

party that is a net debtor of a company will have a sudden loss atthe default of the latter, and this loss is higher the higher the debt-or’s credit spreads. Tis does not happen when a replacementclose-out is considered.

Tus, the risk-free close-out increases the number of operatorssubject to contagion from a default, including parties that cur-rently seem to think they are not exposed, and this is certainly a negative fact. On the other hand, it spreads the default losses toa higher number of parties and reduces the classic contagionchannel aecting creditors. For the creditors, this is a positivefact because it brings more money to the liquidators of thedefaulted company.

We think the close-out issue should be considered carefully by market operators and Isda. For example, if the risk-free close-outintroduced in the previous literature had to be recognised as a

standard, banks should understand the consequences of this asexplained above. In fact, banks usually perform stress tests andset aside reserves for the risk of default of their net borrowers, butdo not consider any risk related to the default of net lenders. Teabove calculations and the numerical examples show that underrisk-free close-out banks should set aside important reservesagainst this risk. On the other hand, under replacement close-out, banks can expect the recovery to be lowered when their netborrowers default, compared with the case when a risk free close-out applies. In the case of a replacement close-out, the money collected by liquidators from the counterparties will be lower,since it will be deated by the default probability of the counter-

parties themselves, especially if they are strongly correlated to thedefaulted entity. n

damaoBroglbarprofeoraheaofheaalmahema

reearhroupak’colleeLoo.MamoMorheaofre

moelao-oraorofmoelreearhaBaaiMi.theywoulleo

hagoroFahe,MaroBahe,Luce,MarBaxer,Area

Bu,Vlamrchory,Johdazer,iorsmrovaoherparpa

aheicBi2010globaldervaveaRMaaemecofereefor

helpfuluo.theywoulaloleovepealhaoArea

PallavaAreaPrampolforhorouhlyaeeplyuhe

reearhueoereharle.theremaerrorareherow.

tharleexpreehevewofauhoraoeorepreehe

uowhereheauhorarewororhaveworehepa.suh

uo,luBaaiMi,areorepobleforayuehamaybe

maeofharle’oe.mal:[email protected],mamo.

[email protected]

Brigo D and I Bakkar, 2009

Accurate counterparty risk valuation for

energy-commodities swaps

Energy Risk, March, pages 106–111

Brigo D and A Capponi, 2008

Bilateral counterparty risk valuation

with stochastic dynamical models and

application to credit default swaps

Working paper available at http://arxiv.

org/abs/0812.3705. Short updated

version in Risk March 2010, pages 85–90

Brigo D and K Chourdakis, 2009

Counterparty risk for credit default

swaps: impact of spread volatility and

default correlation

International Journal of Theoretical

and Applied Finance 12(7), pages

1,007–1,026

Brigo D and M Masetti, 2005

Risk neutral pricing of counterparty risk

In Counterparty Credit Risk Modeling:

Risk Management, Pricing and

Regulation, edited by M Pykhtin, Risk

Books, London

Brigo D and M Morini, 2010

Dangers of bilateral counterparty risk:

the fundamental impact of closeout

conventions

Available at http://arxiv.org, http:// deaultrisk.com and http://ssrn.com/

abstract=1709370. Summary appeared

as Rethinking Counterparty Default in

Creditux 114, pages 18–19, 2011

Brigo D, A Pallavicini and

V Papatheodorou, 2011

Arbitrage-free valuation of bilateral

counterparty risk for interest-rate

products: impact of volatilities and

correlations

International Journal of Theoretical and

Applied Finance 14(6), pages 773–802

Gregory J, 2009

Being two faced over counterparty

credit risk

Risk February, pages 86–90

International Swaps and Derivatives

Association, 2009

Isda close-out amount protocol

Available at www.isda.

org/isdacloseoutamtprot/

isdacloseoutamtprot.html

International Swaps and Derivatives

Association, 2010

Market review of OTC derivative

bilateral collateralization practices

March 1

Morini M, 2009

One more model risk when using

Gaussian copula for risk management

April, available at http://ssrn.com/

abstract=1520670

Morini M, 2010

Can the default of a bank cause the

default of its debtors? The destabilizing

consequences of the standard denition

of bilateral counterparty risk

Working paper, March

Morini M, 2011

Understanding and managing model

risk. A practical guide for quants, traders

and validators

Wiley

Morini M and A Prampolini, 2011

Risky funding with counterparty and

liquidity charges

Risk March, pages 70–75

Referee

A.impaofheleerefauloouerparea

oao–ryar-freeloe-ou

depeee→ iepeee co-moooy

cloe-ou↓

R-free Negatively aects borrower No contagion

subuo No contagion Further negatively aects lender

Documents

Risk 1211 Brigo New