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8/9/2019 LVA, FVA, CVA, DVA impacts on derivatives management
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LVA, FVA, CVA, DVA impacts onderivatives management
Christophe MICHELHead of RCCAD Quantitative Research
AFA!"!RMIA Apri# $th %&'%
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Contents02 Introduction to LVA
13 Introduction to CVA
19 Impact of CSA on CVA
26 A New Pricing ramewor!
31 Centra"i#ed $is! %anagement
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Introduction to LVA
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4
!ricing princip#e
Discounting Forecasted F#o(s
&o ma!e a "ong stor' s(ort) pricing is a *uestion of forecastingfuture fi+ed) f"oating or conditiona" f"ows in a
gi,en currenc' and discountingt(em consistent"' wit( a funding "e,e" in t(is currenc' -in order to a,oidar.itrage opportunities/
or a sing"e f"ow we can forma""' write
Co##atera# Impact
In case of co""atera" agreement) additiona# f#o(sare to .e ta!en into account in t(e ,a"uation process
Indeed) to .e posted a co""atera" (as to .e funded and remunerated wit( t(e funding rate) on t(e ot(er (and)t(e co""atera" posted is remunerated wit( a gi,en co##atera# ratedescri.ed wit(in t(e co""atera" agreement
&(e additiona" f"ows are a"" differentia"s of interest generated .' t(e difference )et(een funding andco##atera# ratesapp"ied to t(e co""atera" amount posted
&(ese additiona" f"ows (a,e to .e funded and t(eir price is straig(tforward as soon as we !now t(eir forecasted
,a"ue
( ) tff
t FTtBV = ,Time t value of the future flowin a given currency
Time tforecasted value of the future flow
in the given currency
Time t value of a unit of currency paid at TAccording to a funding level
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5
Va#uation of Co##atera# Impact
Co##atera# Impact Va#ue* an Imp#icit !ro)#em
Coming .ac! on t(e case of a sing"e f"ow) additiona" f"ows "in!ed to a co""atera" agreement depend upon t(e
co""atera" amount paid at eac( period
In genera") t(e co""atera" amount to .e posted is direct"' deduced from the va#ue of the co##atera#i+edderivative ie inc"uding additiona" interest f"ows) sa' Vc) w(ic( is different from the va#ue of the unsecured
derivative-Vf
/ence) t(e ,a"ue of a co""atera"i#ed deri,ati,e depends upon t(is ,a"ue were facing an imp#icit pro)#em
( ) ( ) ( )( ) 3333 trtrtC cf
Future derivative valueCollateral-linked flow paid at t4equal to
the differential of interest of collateral
Remuneration posted at t3
t0 t1 t2
t3 t4t5 t6
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6
Va#uation of Co##atera# Impact* the tandard Case
Co##atera# Impact Va#ue* the pecia# Case of -i#atera# Contracts
In case of .i"atera" co""atera" agreement) we (a,e
In t(is specia" case) under mode" assumptions) one can s(ow t(at t(e price of a co""atera"ised contract is
o.tained .' discounting wit( t(e co""atera" remuneration rate instead of t(e funding rate
or a sing"e f"ow) we can forma""' write
Note t(at in t(is case) the va#ue of the co##atera#i+ed contract doesn.t depend an/ more upon the
funding rate
Note a"so t(at if a gi,en deri,ati,e pa's f"ows in a gi,en currenc' .ut is co""atera"i#ed in anot(er currenc'
t(en its co""atera"i#ed ,a"ue wi"" depend upon F0"1erm Changes
( ) ctVtC =
( ) tcct FTtBV = ,Time t value of the future flow in a givenCurrency including collateraladditionaml flows
Time tforecasted value of the future flowin the given currency
Time t value of a unit of currency paid at T
according to the collateral remuneration rate
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7
Va#uation of Co##atera# Impact* the enera# Case
enera# Co##atera#
%an' ot(er possi.i"ities e+ist in practice or instance t(e uni#atera# co##atera#agreement can .e written as
fo""ows
In t(is case) t(e co""atera" impact remains imp"icit .ut cannot )e e2p#icit#/ so#ved"i!e in t(e standard case
!ricing Method
&o treat t(e genera" case) one (as to so",e a high dimensiona#optima# contro# pro)#em
&(is is genera""' not do4a."e in practice .ut it is we"" appro+imated .' Monte Car#o simu#ationmet(od%ar!et data are diffused on simu"ated pat(s
5n eac( node of t(e simu"ation t(e %ar!4to4%ar!et of eac( product inc"uded in t(e co""atera" agreement are appro+imated
&(e co""atera" amount to .e posted on eac( node can t(en .e deducedAdditiona" f"ows resu"ting from co""atera" agreement can t(en .e e,a"uated on eac( node
&(e a,erage of t(eir present ,a"ue appro+imate t(e LVA impact
Note t(at t(e co""atera" impact crucia""' depends upon t(e g#o)a# portfo#io (ithin the co##atera# contractand cannot .e treated on a stand a"one .asis A contri)utionto t(e g"o.a" adustment can .e computed
( )
=else0
positiveisportfolioizedcollateraltheofMtMtheifctVtC
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During and post crisis
Li;uidit/ crisis
;r'ing up of "ending.orrowing .etween .an!s
Creditwort(iness of .an!s *uestioned
!re"crisis funding assumptions no #onger ho#d
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ro(ing importance of Credit upport Anne2 =CA>
Li*uidit' = credit ris! issues are more and more acti,e"' managed .' .an!s
&(e main trend is a c"ear s(ift towards gro(ing use of CA as co""atera"i#ation remains among t(e mostwide"' used met(ods to mitigate counterpart' credit ris! in t(e 5&C deri,ati,es mar!et
ro(th of co##atera# agreements
Source: ISDA Margin Survey 2011
ro(th of va#ue of tota# co##atera# =5D )i##ions>
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Credit upport Anne2 ='
Each CA determines the co##atera#i+ation terms )et(een counterparties* )i#atera# oruni#atera#, t/pe of co##atera#, currenc/, haircut, thresho#d, minimum transfer amount and a##other detai#s are stipu#ated in the CA6 1he amount of margin posted and the margin interest
@ and conse;uent#/ the va#uation of the structure @ (i## depend on the CA terms6
CSA determines t(e range of assets t(at ma' .e posted as aco""atera" > cash in different currencies) go,ernment .onds orcorporate or mortgage .ac!ed securities
&(e choice of co##atera# currenc/ (i## a#ter the e2pectedreturnas t(e cas( funding terms are tied to t(e correspondingcurrenc's o,ernig(t rate -need of cross currenc' swap if t(eco""atera" currenc' is not t(e same as t(e dea" currenc'/
For cash"on#/ CA.s, the funding curve corresponds to thespecified co##atera# interest rate
PV
"
-an3 posts co##atera# and receives interest
Counterpart/ posts co##atera# and receives interest
&(e thresho#d"e,e" wi"" determine (ow muc( of t(e e+posure isco""atera"i#ed %argin transfers wi"" .e made on"' if t(e minimum
transfer amount is e+ceeded
-i#atera# CA co##atera# profi#e
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Credit upport Anne2 =%
Margin transfer form
5ni#atera# > on"' one wa' transfers > CA CI7 posts a co""atera" .ut t(e counterpart' dos not -re*uired .' somesupranationa" entities /
-i#atera#> s'mmetric transfer terms
Margin ca## fre;uenc/
;ai"' margin ca"" is fre*uenc' re*uired -.ecoming a mar!et standard/ Longer t(an dai"' margin ca"" fre*uenc' can.e practica" for mar!ets and assets t(at are not ,o"ati"e
1hresho#d
&(is is t(e e+posure amount .e"ow w(ic( co""atera" is not re*uired -t(e t(res(o"d represents an amount of
unco""atera"i#ed e+posure/ A thresho#d of +ero imp#ies that an/ e2posure is co##atera#i+ed
Minimum transfer amount
&(e sma""est amount of co""atera" t(at can .e transferred
It is used to a,oid t(e wor!"oad associated wit( a fre*uent transfer of insignificant amounts of co""atera"
Description of the CA
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Credit upport Anne2 =8
Bhat is a standard CA !a/ attention to the detai# (hen negotiating CA terms
-i#atera# margin transfer form* s'mmetric transferterms for .ot( parties
Dai#/ margin ca## fre;uenc/ -wee!"' can .e a"soaccepted as standard/
4o thresho#d > up to ?% t(res(o"d is considered asreasona."e
Cash and )onds -(aircuts > 0@42@ on s(ortterm maturities and ?410@ on "onger term maturities/
In E5R or in 5D, remunerated at E74IA FLA1 orFed Funds FLA1
tandard CA terms 4on standard agreements
4o CA
5ni#atera# CA -can .e uni"atera" in our fa,our oftensupranationa" institutions re*uire an uni"atera" CSA in t(eir
fa,our/
CA (ith ver/ high thresho#d> ?04100% t(res(o"d wi""
impact pricingCA (ith rating triggers -e+amp"e CA4CI7 needed topost an independent amount to BI7 due to t(e S=P rating
action/
u)"optima# CAs>negati,e spreads on cas( co""atera")securities recei,ed t(at cant .e re4('pot(ecated
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Introduction to CVA
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CVA -asics @ Definition
1o )e or not to )e paid
&(e Credit Va"ue Adustment appears in t(e pricing framewor! w(en a credit ris3is ta!en into account
orma""') one can e+p"icit t(is ris! .' mu"tip"'ing eac( pa'ment f"ow .' t(e fo""owing function
In case of a counterpart' defau"t at time T) t(e 3e/ ;uestion is to measure thee2posure
A priori) t(e e+posure is t(e sum of a## positive mar3 to mar3et of each transactionremaining at time Twit( t(is counterpart'
In case of netting agreementwit( t(e counterpart') t(e e+posure .ecomes t(e sum of a"" netted positi,emar! to mar!et of eac( set of transactions wit(in eac( netting agreement contract
A c#assica# formu#a
A c"assica" CVA formu"a can .e e+pressed as t(e amount of discounted future B+pected Losses
allatpaidtisn'flowtheif0
atpaidactuallyisflowtheif1becomesatpaidflowa
TFTF TT
= =!aturity
t
tttt "F#$#$"%&"CVA0
,1 ***
%oss &iven "efault "efault $ro'a'ility #(posure at "efault )"iscounted*
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CVA -asics @ e/ Ingredients
B+pected Positi,e B+posure -BPB/
Ca"cu"ated ,ia simu"ations process -%onte Car"o8/
Computation inc"uding netting and co""atera" agreements
In,o",es on"' t(e !ositive E2posures in case of Counterpart' ;efau"t
;efinition of B+posure "in!ed to t(e mar! to mar!etof transaction
B,a"uated Contingent on t(e defau"t of t(e counterpart'> inc"uding rig(t wa' wrong wa' ris!s
CA or )rea3 c#ause have a huge impacton BPB
;efau"t Pro.a.i"it'
Imp"ied from C;S spreads -mar!et4imp"ied/ or)
istorica" defau"t pro.a.i"ities
Loss i,en ;efau"t $eco,er' $ate%ar!et Imp"ied -w(ere possi."e/ L;%ar!et
Interna" $eco,er' measure L;Interna"
Mar3et CD Curve
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CVA -asics @ e/ Ingredients
Ris3 parameters*
!ea3 E2posure %a+imum of t(e %t% of t(e transaction o,er its "ifespan) gi,en a (ig( confidence "e,e" -Va$9?@/
Loan E;uiva#ent*A,erage BPB o,er time -measure to determine ris! e*ui,a"ent in terms of "oan for economiccapita" ca"cu"ation/
1ai# Credit Ris3 =CVaR>*a,erage of ?@ ma+imum potentia" "osses
10y EUR IRS CA-CIB Receives Fixed 2.3%
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CVA -asics @ Interpretation
CVA as an Accounting !rovision
%easure of B+pected Loss
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CVA is a fair mar!et adustment to t(e deri,ati,es portfo"io
CVA c(arges are t(ere to offset "osses in t(e g"o.a" CVA portfo"io due to new trades
Incrementa" impact on t(e portfo"io
CVA P=L is f"at pro,ided t(e cas( transfers ta!e p"ace
CVA (edges are initiated in order to offset future CVA P=L ,o"ati"it' for CA4CI7
;ue to portfo"io %&% mo,ements -I$) E) Credit edges/
;ue to counterpart' C;S Spread C(anges -Credit edges/
At inception CVA P=L is f"at) edge P=L is f"at
1 C;S spreads increase CVA increases -Loss/ ,ersus edge P=L -ain/
2 C;S spreads decrease CVA decrease -ain/ ,ersus edge P=L -Loss/
3 C;S spreads sta' static Negati,e carr' on edge -Loss/ is offset against positi,e carr' of CVA -ain/
CVA Credit edges a"so pro,ide
Fump to defau"t ris! management
-ase# III capita# reductions
;e.it Va"ue Adustment -DVA/ is t(e CVA seen from t(e counterpart' &o ta!e it into account a""ows s/mmetrica#vie(son t(e s(ared portfo"io
CVA -asics @ ummar/
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Impact of CA on CVA
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CVA impact of co##atera# on stand a#one transaction =IR>
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CVA impact of co##atera# on stand a#one transaction =IR>
!ea3 e2posure* 9 ?0K 01
Mar3et CVA* 13 12J -1J9 .ps pa/
Historica# CVA* 9 9J2 -011 .ps pa/
4o co##atera# agreement in p#ace Ris3 e2posure is ma2ima# for CA"CI-
CSA in p"ace
7i"atera"
re*uenc' dai"'
&(res(o"d 0
%&A 0
Currenc' B
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CVA impact of co##atera# on stand a#one transaction =IR>
!ea3 e2posure* 1 0J 9K
Mar3et CVA* 33 93K -03 .ps pa/
Historica# CVA* 2 2?2 -002 .ps pa/
CA agreement in p#ace Bee3#/ fre;uenc/* drift is computed on one wee! 10 da's co""atera" "ag
CSA in p"ace
7i"atera"
Fre;uenc/* dai#/
&(res(o"d 0
%&A 0
Currenc' B
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CVA impact of co##atera# on stand a#one transaction =IR>
!ea3 e2posure* 1 KK 3?6
Mar3et CVA* J3 3J6 -0J .ps pa/
Historica# CVA* 3 263 -002J .ps pa/
CA agreement in p#ace
CSA in p"ace
7i"atera"
re*uenc' dai"'
1hresho#d* &
%&A 0
Currenc' B
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CVA impact of co##atera# on stand a#one transaction =CR>
tart date* 10 Apr 2012
Maturit/* 10H
4otiona#* B
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CVA impact of co##atera# on stand a#one transaction =CR>
!ea3 e2posure* 9J 3K 96K
Mar3et CVA* 1 1K 22J -1K.ps pa/
Historica# CVA* 192 36 -2 .ps pa/
4o co##atera# agreement in p#ace Ris3 e2posure is ma2ima# for CA"CI-
CSA in p"ace
7i"atera"
re*uenc' dai"'
&(res(o"d 0
%&A 0
Currenc' B
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A ne( pricing frame(or3
Co##ecting Information
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Co##ecting Information
Mar3et Information
In t(e new pricing framewor!) mar3et pricesremain of coursea centra" source of information .ut one has to
interpret them consistent#/A price is at "east dependent wit( t(e CSA of t(e product priced and w(en one o.ser,e t(e price of an 5&C
product on a screen t(e *uestion of t(e imp#icit CAof t(is price (as to .e so",ed
&o fi+ t(is pro."em) a standardi+ationof mar!et practice arise
Standard swap are assumed c"eared wit( a co""atera" in t(e currenc' of t(e swap wit( a co""atera" remuneration at
5IS rate
%u"ti4currenc' products are often assumed co""atera"i#ed in
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g
Diffusion Data
In addition to mar!et data and c"ient data) we (a,e seen t(at most of +VA are "in!ed to g#o)a# portfo#io
measures )ased on Monte Car#o simu#ations5nce t(e diffusion mode" is defined) its ca#i)rationcan part"' .e imp"icit -ca"i.ration on a set of mar!etprices/ .ut wi"" main"' "in!ed to (istorica" mar!et .e(a,iour
Li!e for an' diffusion mode" design for structured deri,ati,es pricing) t(e ca"i.ration process is dependent
wit( t(e sop(istication of t(e diffusion process-from a t(eoretica" point of ,iew/ and a,ai"a.i"it' of imp#icitand historica# information
A !e' point to focus on is t(eoint )ehaviour )et(een a## c#ass of mar3et ris3s-"ets sa' corre"ation to
simp"if'/ imp"icit"' defined in t(e diffusion process It is indeed we"" !nown t(at t(is point wi"" dri,e mar!et ris!netting from t(e g"o.a" portfo"io point of ,iew
Missing Credit Data
or a great num.er of counterparties t(ere is no ;uoted CD
&(e CVA needs information on defau"t pro.a.i"ities and L; for an' counterpart' &(is information is to .e
forecasted
7ased on a"" interna# (or3s on counterpart/ ris3management -sector c"assification) interna" ratings)(istorica" reco,er' rates) 8/) it .ecomes possi."e to map an' counterpart' on mar!et information
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A)out !ortfo#io"Lin3ed Adustments
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A 4on Linear Adustment
enera""' spea!ing) portfo"io4"in!ed adustments arent "inear ie t(e va#ue adustment of a given dea#depends upon the portfo#io-and mar!et data/ at t(e moment t(e ,a"uation
ame tradewit( two counterparties) wit( different credit profi"es or portfo"io ,is4O4,is t(e .an!) wi"" (a,edifferent mar3et prices
B+amp"e C"ient recei,es i+ed on 10' Swap
%id %ar!et 10' Swap $ate 231@> C"ient 1 $ated A4 recei,es 22@ J.p CVA c(arge
> C"ient 2 $ated 7 recei,es 223@ K.p CVA c(arge
In practice) an incrementa# portfo#io va#ue adustmentre"ating to t(e new trade is used It corresponds to t(edifferentia" of portfo"io ,a"ue adustment wit( and wit(out t(e dea"
&(is incrementa" ,a"ue can eit(er .e positive or negativeand a pricing po#ic/ is to )e defined
Adustment -rea3do(n
&(e g"o.a" portfo"io ,a"ue adustment is made wit( severa# sources of ris3s-credit) "i*uidit') funding/ and wit(severa# mar3et data ;ua#ities-pure mar!et data ,ersus forecasted data/
&o "oo! into t(ese) it is meaningfu" to e,a"uate t(e g#o)a# portfo#io va#ue adustment )rea3do(n.ased ont(ose different sources of ris! and data *ua"ities
Simi"ar"') t(is )rea3do(ncan .e computed for incrementa" portfo"io ,a"ue adustments at t(e dea# #eve#
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Hedging Ris3s
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tand"a#one Va#ue Ris3 Management
A priori) t(e stand"a#one product va#uecan .e (edged trading des! per trading des! wit(out particu"ar need
of centra"isationNe,ert(e"ess) t(e mu"tip"icit' of CSA ma' induce Mnot so materia" additiona" sources of ris!s for trading
des!s -"i!e cross4currenc' .asis swap margin ris!s/ w(ic( can po##utetrading des! ris! management andw(ic( cou"d .e centra"ised
Ge (a,e to !eep in mind t(at an' transaction (as) from ,a"uation and ris! management point of ,iew) astand"a#one part anda portfo#io part &(e imp"icit CSA of t(e stand4a"one part of t(e dea" isnt necessari"'t(e actua" CSA of t(e dea"
Funding Ris3Funding ris3cou"d in t(eor' .e managed on a stand4a"one .asis since t(is ris! isnt e+p"icit"' "in!ed to t(eportfo"io ,iew
7ut t(is ris! can.t )e direct#/ ris3 managed in the mar3et
ence) t(is ris! (as to .e ris3 managed oint#/ (ith ALM Indeed) t(e sta!e is t(e remuneration or t(ec(arge of t(is adustment &(is (as to .e made consistent"' wit( t(e wa' t(ese remunerationc(arge are
monetised )/ ALM"o.a" simu"ation too"s can of course .e ,er' used to o.tain a comp"ete ,iew of t(e distri)ution of fundingneeds at an/ future maturit/-e+pectation) standard de,iations) 8 of funding needs inc"uding co""atera"simu"ation/
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Capita# re;uirements for Counterpart/ Credit Ris3 =CCR>
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Capita# CCR on#/ covers defau#t ris3*%t% standardi#ed add4on .ased on issuer t'pe) under"'ing and maturit'
No capita" re*uirement for %&% "oss due to c(ange in counterpart' credit spread
Capita# CCR on#/ covers defau#t ris3
Interna" $atings47ased approac( Interna" assessment of defau"t ris! ,ia interna# pro)a)i#it/ of defau#t and LD
No capita" re*uirement for %&% "oss due to c(ange in counterpart' credit spread
BPB counterpart' e+posure estimated using non4stressed mar!et data) on a 1H (ori#on
-ase# III Capita# CCR Capita" ;efau"t -7ase" II/ Capita# CVA
Capita# CVA*additiona" Capita" re*uirement for %t% "oss due to c(ange in counterpart' credit spread
Capita" CVA*%ar!et $is! capita" c(arge estimated using stressed Va$ on credit instruments
BPB counterpart' e+posure estimated under stressed parameters on t(e fu"" maturit'
CVA Va$ is ca"cu"ated Net of B"igi."e edges
5t(er adustments
> Assuming a (ig(er corre"ation .etween financia" institutions in t(e super,isor' formu"a
> B+tending t(e co""atera" "ag period from 10 da's to 20 da's
-ase# I
-ase# III
-ase# II
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Centra# Des3 Mandate
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Centra"ise and ris! manage 5 deri,ati,es counterpart' and portfo"io4"in!ed ris!
%inimise +VA P=L impact for 5 t(roug(
S'stematic %acro (edging of t(e o,era"" +VA P=L impact
Sing"e Name defau"t (edging -w(ere practica"/
Acti,e participation in $GA management
&arget .usiness mode" is to incenti,ise Sa"es orce not on"' on re,enue generation .ut a"so on $GA and "i*uidit' consumption
Sa"es recognition met(odo"og' (as to .e consistent"' defined
Bsta."is( a Pricing Po"ic' a"igned wit( t(e interna" +VA met(odo"og'
Bducate and train sa"es and support functions in +VA re"ated issues
In,o",ement in $egu"ator' ;iscussions ;ecisions affecting +VA
In,o",ement in IS;A CSA discussions affecting +VA
Need to remain Competiti,e in Pricing 8
%ust remain .usiness4focused and incenti,ise t(e rig(t t'pes of trades
> Gai,er B+emption for &arget C"ients 7usinesses
> Additiona" C(arge for Grong Ga' trades
> 7enefits for $ig(t Ga' &rades
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Centra# Des3 is there to upport the -usiness*In accurate"' pricing Credit and Li*uidit' into new trades) and
&o manage t(e credit ris! of deri,ati,es portfo"io t(roug( d'namic CVA (edging
1o achieve this Centra# Des3 needs*Active Dia#oguewit( &rading Sa"es Structuring on new trades) and e+isting portfo"io -ris! reduction opportunities/
Invo#vement in Comp#e2 1rades) especia""' w(ere rep"acement costs in defau"t are (ard to define
C"ear
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