lva, fva, cva, dva impacts on derivatives management

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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10

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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11

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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16

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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!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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!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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!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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