Vale Re Par is 2010 Final

8/6/2019 Vale Re Par is 2010 Final

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Pricing & Hedginglf n r r Ri k

GlobalDerivativesTrading&RiskManagement

Paris

18May2010

osh Danzi er


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Contacts

JoshDanziger [email protected]

JoshDanzigerisaPrincipalofValere CapitalPartnersLLP,aspecialistfixedincomeconsultancybasedin

London. PriortothishewasHeadofStructuredProductsatRoyalBankofCanada,responsibleforstructured

rates,inflation,creditderivativesandprincipalfinance. HisPhDatCambridgeUniversityconcernedthe

computermodelingofthechemicalinteractionsbetweenproteinsanddrugsatamolecularlevel.

MuchofthisworkwasdoneincollaborationwithEdParcellofCobaltQuantware.

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3/28

BilateralCreditValueAdjustment(CVA):SelfRisk

BanksfinancialstatementsforQ12009:

... .

derivative positions, excluding monolines, mainly due to the widening

of [the banks own] CDS spreads

3


4/28

BilateralCreditValueAdjustment(CVA):SelfRisk

Questionstoconsider

oWhatisselfrisk?

oCanwehed eit?

oShouldwehedgeit?

havedifferentviews?

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5/28

CreditValueAdjustment(CVA)

Adjustsvaluationofatradeorportfolioforthepossibilityofselforcounterpartydefault.

PriortocreditcrunchCVAwast icall unilateral incor oratin onl the ossibilit of

counterpartydefault,withinstitutionsassumingthemselvestobedefaultfree.

IfthecounterpartyhaslowcreditqualitythentheCVAislarger,andtheNPVofthetradeis

CVAsthatincorporatethepossibilityofeithercounterpartydefaultingavoidthis.Bilateral

CVAsaresymmetric,soiftwocounterpartieshavethesameviewofthereferenceentitys,

, .

BilateralCVAcanbedecomposedintotwoparts:

o AssetCharge: NPVofcounterpartydefaultingwhentradeisinthemoney

o LiabilityBenefit/Selfrisk:NPVofourdefaultingwhenthetradeisoutofthemoney

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6/28

Assumptions

Riskneutral derivativesstylepricing

Thereshouldbeare licatin strate ortheCVAtoallowittobehed ed.

Modelindependentanalysis

Examples:

IRS:simplecommonplaceexample

CDS:morecomplex,moreheavilymodeldependent,introduceswrongwayrisk

Examplesarewithoutthebenefitsofnetting,CSAsorbreakclauses:theseareallcreditenhancementswhichreducebutdonteliminateCVA.

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7/28

Derivativesmarketreform&centralclearing

PushforderivativesmarketreformCredit Ratesetc

NoCSA Eg,monolines

CSAondowngrade Eg,AIG HighlyratedcounterpartiesCSA Interbankbusiness Interbankbusiness

100%collateral

Creditlinkednotes Structurednotes

Centralclearing

ICE,Eurex,Clearnet Swapclear

Uncertaintyoftakeup

o Nonstandardcontracts

o Non inancia s uysi e

MultipleCCPsmayleadtolargeCCPexposures.

7

.

SovereignsupportfordistressedCCPunclear.


8/28

CalculatingCVA

Forageneraltradeorportfolio

T+

[ ]dtttPtttVtBERR

CS

T

CSS

SCSCC

),(,|)(),0()1(risk-SelfBenefit/Liability

,,,

0

0

>=>==

===

Where

RRC

=Recoveryrateofcounterparty

RRS

=Recoveryrateofself

B(0,

t) =

Discount

factor

from

0

tot

V(t) =Valuationoftrade/portfolioattimet(excludingcounterpartyrisk)

V+(t) =max[0,V(t)], V-(t) = min[0,V(t)]

C

s

=Defaulttimeofself

CounterpartyValuationAdjustment(CVA).2009.Shahram Alavian,Jie Ding,PeterWhitehead&Leonardo

8

Laudicina.


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CVAonIRS

0.250%

0.200%

0.150%

Pay

0.100%ec

0.050%

Unilateral CVA on IRS for different tenors u wardsslo in CDS curve 380 at 10 no

.

0 2 4 6 8 10 12

wrongwaycorrelation.

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10/28

CVAonIRS

Megabank(tightspread)entersinto10yIRSwithMicrobank (10yCDS@380)

, , ,

isverysubstantial.

Pay Receive

. .

Timevalue 8.3 8.3

Vega 0.5 0.5

Thisisbasedonriskneutralpricingapproach:CVAforeachtimesliceisproductof

probabilityofdefaultandrighttocancelswaption.

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CVAonIRS

WhatshouldMicrobank do?

o gree o , rea c auses,e c

o Refusetotradesofarawayfromscreenprices

o ra ew ega an , u mar a screenpr ces

o TradewithMegabank,butmarkusingbilateralCVA

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12/28

CVAonIRS

ShouldMicrobank hedgeselfriskcomponentofbilateralCSA?Ifso,how?

onsequenceso no e g ng:

o Losemoneyifselfspreadfalls...

o ...orvo a y a s...

o ...orratesmove.

cro an oes e gew ss ra egy ea e omone se eva ueo e

selfriskcomponentoftheCVA?

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13/28

MegabankhedgeforCVAonIRS

IRhedge 10.0000% Werec,8.0553%

5.0000%

0.0000%

5.0000%

0 1 2 3 4 5 6 7 8 9 10

15.0000%

10.0000%

20.0000% Wepay, 19.0682%

5.0000% CDShedge

2.0000%

3.0000%

4.0000%

1.0000%

0.0000%

1.0000%

0 1 2 3 4 5 6 7 8 9 10

13

3.0000%

2.0000%


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MegabankhedgeforCVAonIRS:carry

IRhedgecarry Tenor IRS PayHedge PayCarry RecHedge RecCarry0 1.0000%

1 1.0000% 1.2628% 0.0000% 0.7085% 0.0000%

2 1.9000% 2.2085% 0.0199% 0.8390% 0.0076%

3 2.7000% 2.8024% 0.0476% 0.8447% 0.0144%

4 3.4000% 3.0034% 0.0721% 0.7884% 0.0189%5 4.0000% 2.8655% 0.0860% 0.6977% 0.0209%

6 4.5000% 2.4808% 0.0868% 0.5873% 0.0206%

7 4.9000% 1.9474% 0.0759% 0.4644% 0.0181%

8 5.2000% 1.3496% 0.0567% 0.3300% 0.0139%

9 5.4000% 0.8893% 0.0391% 0.3082% 0.0136%

CDShedgecarry

. . . . .

TOTAL 2.7235% 0.2397% 1.5711% 0.1934%

Tenor CDS PayHedge PayCarry RecHedge RecCarry

. . . . .

1 1.0000% 4.0399% 0.0404% 0.2870% 0.0029%

2 1.7000% 2.2849% 0.0388% 0.1304% 0.0022%

3 2.3000% 1.0743% 0.0247% 0.1251% 0.0029%

4 2.8000% 0.0847% 0.0024% 0.1150% 0.0032%5 3.2000% 0.7477% 0.0239% 0.0751% 0.0024%

6 3.5000% 1.4259% 0.0499% 0.0151% 0.0005%

7 3.7000% 1.9083% 0.0706% 0.1855% 0.0069%

8 3.8000% 2.0965% 0.0797% 0.4898% 0.0186%

9 3.8000% 1.7390% 0.0661% 1.1385% 0.0433%

14

10 3.8000% 0.4856% 0.0185% 1.0116% 0.0384%

TOTAL 0.0000% 0.1931% 0.0000% 0.0730%

(*)ApositivenumberinthehedgepositionindicatesareceivepositioninIRSorasaleofprotectionleadingtopositivecarry


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Tenor IRS PayHedge PayCarry RecHedge RecCarry

0 1.0000%

IRhedgecarry

1 1.0000% 1.2628% 0.0000% 0.7085% 0.0000%

2 1.9000% 2.2085% 0.0199% 0.8390% 0.0076%

3 2.7000% 2.8024% 0.0476% 0.8447% 0.0144%

4 3.4000% 3.0034% 0.0721% 0.7884% 0.0189%5 4.0000% 2.8655% 0.0860% 0.6977% 0.0209%

IRhedgecarryis

significantand

6 4.5000% 2.4808% 0.0868% 0.5873% 0.0206%

7 4.9000% 1.9474% 0.0759% 0.4644% 0.0181%

8 5.2000% 1.3496% 0.0567% 0.3300% 0.0139%

9 5.4000% 0.8893% 0.0391% 0.3082% 0.0136%

whetherweare

hedgingpayor

receiveposition.. . . . .

TOTAL 2.7235% 0.2397% 1.5711% 0.1934%

CDShedgecarry Tenor CDS PayHedge PayCarry RecHedge RecCarry. . . . .

1 1.0000% 4.0399% 0.0404% 0.2870% 0.0029%

2 1.7000% 2.2849% 0.0388% 0.1304% 0.0022%

3 2.3000% 1.0743% 0.0247% 0.1251% 0.0029%

4 2.8000% 0.0847% 0.0024% 0.1150% 0.0032%5 3.2000% 0.7477% 0.0239% 0.0751% 0.0024%

6 3.5000% 1.4259% 0.0499% 0.0151% 0.0005%

7 3.7000% 1.9083% 0.0706% 0.1855% 0.0069%

8 3.8000% 2.0965% 0.0797% 0.4898% 0.0186%

9 3.8000% 1.7390% 0.0661% 1.1385% 0.0433%

15

10 3.8000% 0.4856% 0.0185% 1.0116% 0.0384%

TOTAL 0.0000% 0.1931% 0.0000% 0.0730%



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1 1.0000% 1.2628% 0.0000% 0.7085% 0.0000%

2 1.9000% 2.2085% 0.0199% 0.8390% 0.0076%

3 2.7000% 2.8024% 0.0476% 0.8447% 0.0144%

4 3.4000% 3.0034% 0.0721% 0.7884% 0.0189%5 4.0000% 2.8655% 0.0860% 0.6977% 0.0209%

6 4.5000% 2.4808% 0.0868% 0.5873% 0.0206%

7 4.9000% 1.9474% 0.0759% 0.4644% 0.0181%

8 5.2000% 1.3496% 0.0567% 0.3300% 0.0139%

9 5.4000% 0.8893% 0.0391% 0.3082% 0.0136%

CDShedgecarry Tenor CDS PayHedge PayCarry RecHedge RecCarry

. . . . .

TOTAL 2.7235% 0.2397% 1.5711% 0.1934%

. . . . .

1 1.0000% 4.0399% 0.0404% 0.2870% 0.0029%

2 1.7000% 2.2849% 0.0388% 0.1304% 0.0022%

3 2.3000% 1.0743% 0.0247% 0.1251% 0.0029%

4 2.8000% 0.0847% 0.0024% 0.1150% 0.0032%

Useveryshort

datedCDS

buckettohedge5 3.2000% 0.7477% 0.0239% 0.0751% 0.0024%

6 3.5000% 1.4259% 0.0499% 0.0151% 0.0005%

7 3.7000% 1.9083% 0.0706% 0.1855% 0.0069%

8 3.8000% 2.0965% 0.0797% 0.4898% 0.0186%

9 3.8000% 1.7390% 0.0661% 1.1385% 0.0433%

jumptodefault

risk.ATMIRS

willhavezero

jumptodefault.

16

10 3.8000% 0.4856% 0.0185% 1.0116% 0.0384%

TOTAL 0.0000% 0.1931% 0.0000% 0.0730%



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1 1.0000% 1.2628% 0.0000% 0.7085% 0.0000%

2 1.9000% 2.2085% 0.0199% 0.8390% 0.0076%

3 2.7000% 2.8024% 0.0476% 0.8447% 0.0144%

4 3.4000% 3.0034% 0.0721% 0.7884% 0.0189%5 4.0000% 2.8655% 0.0860% 0.6977% 0.0209%

6 4.5000% 2.4808% 0.0868% 0.5873% 0.0206%

7 4.9000% 1.9474% 0.0759% 0.4644% 0.0181%

8 5.2000% 1.3496% 0.0567% 0.3300% 0.0139%

9 5.4000% 0.8893% 0.0391% 0.3082% 0.0136%


. . . . .

TOTAL 2.7235% 0.2397% 1.5711% 0.1934%

. . . . .

1 1.0000% 4.0399% 0.0404% 0.2870% 0.0029%

2 1.7000% 2.2849% 0.0388% 0.1304% 0.0022%

3 2.3000% 1.0743% 0.0247% 0.1251% 0.0029%

4 2.8000% 0.0847% 0.0024% 0.1150% 0.0032%

Sellingvery

shortdated

protection5 3.2000% 0.7477% 0.0239% 0.0751% 0.0024%

6 3.5000% 1.4259% 0.0499% 0.0151% 0.0005%

7 3.7000% 1.9083% 0.0706% 0.1855% 0.0069%

8 3.8000% 2.0965% 0.0797% 0.4898% 0.0186%

9 3.8000% 1.7390% 0.0661% 1.1385% 0.0433%

makesanon

trivial

contributionto

carry.

17

10 3.8000% 0.4856% 0.0185% 1.0116% 0.0384%

TOTAL 0.0000% 0.1931% 0.0000% 0.0730%



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1 1.0000% 1.2628% 0.0000% 0.7085% 0.0000%

2 1.9000% 2.2085% 0.0199% 0.8390% 0.0076%

3 2.7000% 2.8024% 0.0476% 0.8447% 0.0144%

4 3.4000% 3.0034% 0.0721% 0.7884% 0.0189%5 4.0000% 2.8655% 0.0860% 0.6977% 0.0209%

6 4.5000% 2.4808% 0.0868% 0.5873% 0.0206%

7 4.9000% 1.9474% 0.0759% 0.4644% 0.0181%

8 5.2000% 1.3496% 0.0567% 0.3300% 0.0139%

9 5.4000% 0.8893% 0.0391% 0.3082% 0.0136%


. . . . .

TOTAL 2.7235% 0.2397% 1.5711% 0.1934%

. . . . .

1 1.0000% 4.0399% 0.0404% 0.2870% 0.0029%

2 1.7000% 2.2849% 0.0388% 0.1304% 0.0022%

3 2.3000% 1.0743% 0.0247% 0.1251% 0.0029%

4 2.8000% 0.0847% 0.0024% 0.1150% 0.0032%

CDShedgecarry

issimilarinthis

instancetoCVA.5 3.2000% 0.7477% 0.0239% 0.0751% 0.0024%

6 3.5000% 1.4259% 0.0499% 0.0151% 0.0005%

7 3.7000% 1.9083% 0.0706% 0.1855% 0.0069%

8 3.8000% 2.0965% 0.0797% 0.4898% 0.0186%

9 3.8000% 1.7390% 0.0661% 1.1385% 0.0433%

18

10 3.8000% 0.4856% 0.0185% 1.0116% 0.0384%

TOTAL 0.0000% 0.1931% 0.0000% 0.0730%



19/28

CVAonIRS

Totheextentthat Megabankhasawellchosenmodeladoptsanappropriatehedging

strategy,thenonaveragewewouldexpectittoincurhedgecostsequaltotheCVA

whilstprotectingitselffromthedefaultofMicrobank.

CanMicrobank simplyreverseMegabanksstrategytorecoupselfrisk?

o o ey aveaccess o e u se o e g ng oo s

o Isthereadifferenceincarrycosts?

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20/28

MicrobankhedgeforCVAonIRS:IRcarry

Megabank IR

hedgecarryTenor IRS PayHedge PayCarry RecHedge RecCarry

0 1.0000%

1 1.0000% 1.2628% 0.0000% 0.7085% 0.0000%

2 1.9000% 2.2085% 0.0199% 0.8390% 0.0076%

3 2.7000% 2.8024% 0.0476% 0.8447% 0.0144%

4 3.4000% 3.0034% 0.0721%

0.7884%

0.0189%5 4.0000% 2.8655% 0.0860% 0.6977% 0.0209%

6 4.5000% 2.4808% 0.0868% 0.5873% 0.0206%

7 4.9000% 1.9474% 0.0759% 0.4644% 0.0181%

8 5.2000% 1.3496% 0.0567% 0.3300% 0.0139%

9 5.4000% 0.8893% 0.0391% 0.3082% 0.0136%

Microbank IR

. . . . .

TOTAL 2.7235% 0.2397% 1.5711% 0.1934%

Tenor IRS RecHedge RecCarry PayHedge PayCarry

. .

1 1.004% 1.000% 1.3788% 0.0001% 0.7055% 0.0000%

2 1.909% 1.897% 2.5183% 0.0229% 0.8200% 0.0074%

3 2.714% 2.687% 3.2751% 0.0561% 0.8394% 0.0142%

4 3.421% 3.368% 3.5787% 0.0866% 0.8146% 0.0193%5 4.029% 3.940% 3.4736% 0.1052% 0.7581% 0.0223%

6 4.538% 4.407% 3.0544% 0.1081% 0.6721% 0.0229%

7 4.949% 4.774% 2.4307% 0.0960% 0.5563% 0.0210%

8 5.261% 5.044% 1.7041% 0.0726% 0.4095% 0.0166%

9 5.472% 5.222% 1.1335% 0.0507% 0.3927% 0.0166%

20(*)ApositivenumberinthehedgepositionindicatesareceivepositioninIRSorasaleofprotectionleadingtopositivecarry

10 5.308% 5.585% 19.1699% 0.8258% 7.6883% 0.3525%

TOTAL 3.3774% 0.2275% 1.7200% 0.2124%


21/28

MicrobankhedgeforCVAonIRS:credithedge

StrategiesforhedgingselfcreditriskcomponentofCVA

o Nohedge

Creditcomponentmonetisedonlybyselfdefault

o Proxyhedge

Se CDSonanot ernameoronan n ex

Needstobesimilarspreadtoself

o Bu ownbonds

ExposuretoCDS/bondbasisFundingrequirement(mustbeshortterm)

Limitedcapacity

o UsefullcollateralCSAorSPVtosellownnameprotection

NoexposuretoCDS/bondbasis

Nofundingrequirementprovidedcollateralavailable

21

Limitedcapacity


22/28

MicrobankhedgeforCVAonIRS:credithedge

Buyownbonds

o ParbondmaturityTproducesassetswapspreadofsT+b

TwhereasCDSyieldss

T;

hencebondpurchaseinvolvesexposuretoCDS/bondbasisaswellasCDSspread.

o CarryonassetswappedbondfundedtotimetissT+b

T-s

t-b

t.

o Bon purc ase un e tomaturitycreatesnoexposuretosT

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23/28

CalculatingCVAonCDS

WebeginbyignoringtheeffectofnettingandCSAs.Wewilllookatwaystorelaxthese

assumptionslater.

[ ] dtttPtttVEtBRRT

SC

T

SCC),(,|)(),0()1(ChargeAsset

0

>=>== +

Inthiscase:

Thereisnostaticreplicatingportfolioofstandardtrades.CVAcontainsoptionality itdepend

onthevolatilit oftheunderl in ,sonot ossibletore licatewithfirsttodefaultsand

dtttPtttVEtBRRCSCSS

),(,|)(),0()1(risk-SelfBenefit/Liability0

>=>==

secondtodefaults.

Asusualforcreditproducts,weassumerecoveryandinterestratesaredeterministic.

NeedtomodeltherelationshipbetweenvaluationoftheCDSanddefaulttimesofselfand

counterparty.Thisisdifficultasitrequiresmodellingspreadsanddefaulttimes/probabilities.

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24/28

Markovchainmodel

Self,then'U

Selfdefaulted

defaulted(SU)

UnderlyingNodefaults

Counterparty,

then'

Counterparty

e au te

underlying

defaulted(CU)

e au te C

Calibratebysetting'U=

U(choose basedonhistoricaldata),andsolvingfor

Usothat

thedefaultfreeCDSontheunderlyingreprices themarket.

o UnderlyingdefaultintensitydifferentinSorC(e.g.ifcounterpartylesssystemically

important).

24

. . .


25/28

CVAonCDS

120

CVA(bps)vs Deltavs (Counterpartyspread=180bps)

60

80

100

15.0%

20.0%

25.0%

0

20

40

5.0%

10.0%

0% 100% 200% 300% 400%

Counterpartyspread=180bps

Counterpartyspread=450bps

0.0%

0% 100% 200% 300% 400%

Delta(Counterparty)

CDSisanexampleofaproductwithclearwrongwayrisk.

HighcorrelationbetweenprotectionsellerandreferenceentityproduceslargeCVAs.

oun erpar ycre r s e a ncreasesasre erenceen yw ens:crossgamma.

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26/28

Counterparty andselfriskCVAhedging

CounterpartyCVAhedging Self riskCVAhedging

Megabankwishestobuyprotectionon Microbank wishestosellprotectionon

RefCo (tradingat600)fromMicrobank

(tradingat300).

RefCo (tradingat600);theythemselvesare

tradingat300.

Megabankmodeldeterminesthat Microbank modeldeterminesthat

correlationbetweenRefCo andMicrobank

meansweagreetopayonly350for

protectionratherthan600.

correlationbetweenRefCo andthemselves

meanstheyagreetoacceptonly350for

protectionratherthan600.

TohedgecounterpartyriskMegabankwill

havetoincurtheexpenseofbuying

protectiononadeltaamountofMicrobank.

TohedgeselfriskMicrobank willsell

protectiononadeltaamountofits own

name(perhapsthroughaCSAorSPV,or

bu in its own bonds .

Megabankshouldalsobeawarethatthey

havelessthan100%deltaonRefCo.

Microbank shouldalsobeawarethatthey

havelessthan100%deltaonRefCo.

Failuretobuyprotection onMicrobank may

makeprotectionlookcheap(350ratherthan

600),butMegabankisrunningtheriskof

Failuretosellprotection onthemselves

leavesMicrobank exposedtotheirown

name:ifittightenedintodoubledigitsthey

26

Microbank wideningout,andperhapsfailing. mightfindthemselves~250basispoints

underwater,withoutanychangeinRefCo.


27/28

Impactofcounterparty orselfhedging

Hedgingcounterpartyriskenhances

correlationbetweenprotectionsellerand

reference entit e monolines . 7080

90

100

2000

2500

30

40

50

60

1000

1500

MBIA(LHaxis)

ABX062(RHaxis)

0

10

20

0

500

Sep05 Mar06 Sep06 Mar07 Sep07 Mar0 8 Aug08 Mar0 9 Aug09 Mar10

Hedgingselfriskmayinvolveovercomingfundinghurdlesand/orregulatory/accountancy/investor concerns:

uy ngown on s requ res un ng ;or

Sellingownprotectioneg,throughCSAorSPV.

whichprotectionsold...

....Butmakespoortradesmuchmorepainful!

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28/28

Selfrisk:tohedgeornottohedge?

Donthedgeselfrisk Hedge self risk

GeneratespositiveMTM changewhen When companyisindifficulty,difficulties

company isindifficulty,therebysmoothing

revenue.

exacerbatedbynegativeMTMonselfrisk

hedge,accentuatingP+Lvolatility.

Newbusinessseenasprofitableat

inceptionatatimeofwidespreadsmay

become lossmakingifcompanysspread

Attempts topreserveprofitabilityofnew

businessinceptedatatimeofwidespreads.

.

Unhedged marketriskcomponentofself

riskmayleadtounexpectedP+L.

UnexpectedP+Lfrommarketrisk

componentofselfriskeliminatedbyhedging.

Wrongway risk(eg,credit)amplifies

spreadvolatility.

Intheory,ascreditspreads widen,company

shouldbesellingprotection.

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Vale Re Par is 2010 Final

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Transcript of Vale Re Par is 2010 Final