XVA A New Risk Dimension for

Transcription

1 XVA A New Rsk Dmenson for Insuons and Regulaors Bevan Ferrera Senor Manager, FAS Quanave Rsk and Fnancal Engneerng Deloe LLP bferrera@deloe.ca

2 Dsclamer The vews expressed n hs presenaon are hose of he presener and do no represen he vews of he preseners' organsaon. The presener s organsaon assumes no lably n connecon wh any use of hs nformaon and make no warrany or guaranee ha he nformaon presened here s curren, accurae, or complee. The conen s owned by he presener and s nended for nformaon and dscusson purposes only.

3 CVA Wha s? CVA (cred value adjusmen) can be consdered as he premum, or provson, for poenal cred losses due o cred qualy mgraon of counerpares n OTC dervave conracs. I s no a new dea, bu pror o he crss of , was consdered oo dffcul o calculae relably. Durng he crss, approxmaely ⅔ of losses were due o cred mgraon shor of defaul (CVA) on OTC conracs. (hp:// New capal requremens (Basel III, Annex 4) were nroduced o address hs rsk dmenson, and were mplemened n Canada n January, 2014.

4 How o measure CVA Analogously o he premum on a defaul-rsky bond, he value of an OTC dervave conrac s adjused o accoun for cred qualy: V V CVA Noe here ha CVA s shown as a me-dependen quany. I s sochasc, and has non-zero volaly (we ll see more of hs shorly). The CVA s he defaul-rsk weghed expeced dscouned fuure exposure. I s mahemacally expressble as an negral of a sochasc quany (.e. as an expecaon): CVA T ( 1 R ) DF(, u) EE dq( u) u

5 Terms n he expresson: Alhough appearng complex, he expresson can be hough of as a connuous analog of LGD x EAD x PD, summed over all nermedae possble defaul mes. The pon-n-me recovery rae process (recovery swaps?) and so he LGD = 1 R hsorcal daa. s no observable n he markes s ypcally consan, a 40%, based on The dscoun facor DF(, u) from each fuure nsan u back o oday, has wo addonal erms: our (and he counerpary s) survval probably up o nsan u. We frequenly chea, and ake hese o be 1. The pon-n-me, rsk-neural * defaul probably s also problemac, bu marke-mpled spread daa can be used o back ou probables (we ll see hs soon). Noe hs s acually, n he lm, a hazard rae (gvng us a probably measure),.e. s nsananeous lkelhood parameer. I s NOT an acual PD. * Ths acually s no unque - he cred produc marke s no complee R dq(u)

6 The mos complex erm o compue, from a model rsk managemen, daa and smulaon vewpon hough, s EE u, he pon-n-me expeced fuure (posve) exposure of he conrac. Ths s needed for cred rsk (lne managemen, rsk proflng) and FVA as well. If you are a FRFI, you need for Regulaory Capal. There wll be a large smulaon engne runnng housands of scenaros per rade and rsk facor, o calculae hs number. Currenly, he oupu from hese engnes and frameworks s hghly varable beween producs, porfolos, and nsuons. We are sll learnng, and here has been progress recenly n speedng up, and approxmang hese exposures: beer capure of Wrong-Way Rsk, faser algorhms, analyc formulae for ceran producs, mprovemens n collaeral smulaon, replacemen of ad-hoc, pece-meal archecure wh end-o-end Enerprse-Wde measuremen and managemen frameworks

7 Basel III expresson The Basel III capal calculaon uses an approxmaon o he above negral: Noe he use of a md-pon rule for he negral, whch gves beer approxmaons wh exposure profles ha are changng rapdly. Noe he approxmaon o marke-mpled PD, based on cred spreads. You can readly see he dependency of he resul on choce of me-seps for smulaon! (he s), especally f he expresson for PD s changng sgn!

8 A shor approxmaon Bu who wans o negrae sochasc quanes all day? (Well, some of us propeller heads, maybe ). In addon, he above negral (based on Fundamenal Asse Prcng Theorems, Feynman-Kac, and he law of one prce ) s an dealsaon. We can approxmae he CVA by geng around he negraon / summaon process as follows (whch s an asse-sde expresson!) CVA asse EPE EPE s Expeced Posve Exposure,.e. a sor of loan equvalen amoun (or EAD) ha crysallses all possble exposure scenaros no a sngle value. s C s he spread of he counerpary. We have approxmaed nsananeous PD (acually he hazard rae, no he PD) wh s LGD s C

9 Regulaory Capal (Basel II and III) The reamen of regulaory adjusmens for Counerpary Rsk s wo-fold: A cred rsk componen (reflecng for capal reserve agans cred losses) A marke rsk componen (reflecng capal reserve agans losses due o CVA volaly) The cred rsk componen was n place under Basel II Basel III added he marke rsk vol charge, called CVA VaR (acually CVA DSR VaR and GMR VaR n Canada) as well as a CRM o reflec volaly n he correlaon radng porfolo. Cred rsk capal used he expresson EAD EEPE and calculaed RWA as RWA EAD K The erm EEPE reflecs a conservave, non-decreasng average of he exposure profle, ou o he one-year horzon, n order o accoun for rollover of rade bookngs.

10 The marke rsk equvalen vol charge s based on he Basel III formula: The CVA VaR s compued by shockng he above expresson (or equvalen) only on he cred spread leval.e., a sngle profle for EE s assumed. Dscoun facors, and marke rsk facors (EQ, FX, IR, CO) are lef fxed. Ths avods double-counng marke rsk effecs n he radng book. However, as compensaon, Basel only allows CDS hedges (or equvalen) specfcally held and managed for mgaon of CVA, o offse CVA capal Marke rsk hedges wll be consdered n he upcomng FRTB framework.

11 The wo sdes o CVA As alluded o prevously, here s an asse-sde, and a lably sde o CVA: CVA, or CVA asse DVA, or CVA lably Unless our spread and our counerpares spreads are very well algned, hese wll NOT n general provde perfec offse. Recall, we hough of CVA as approxmaely EPE s C. We can hnk of DVA as ENE s O n an analogous way, usng our own spread. Then oal CVA for a counerpary s bcva EPE s ENE C s O

12 Here, we ake N EPE EE (0, DF 1 ) and for low spread counerpares (e.g. large fnancals) we may use rsk-neural dscounng, df 0, ): DF(0, ( ) df (0, )e Noe ha usng LIBOR nsead of OIS we njec addonal premums no he dscoun curve. For ENE, we d make use of he negave sde of he exposure scenaros, and average hose values a each me sep, o ge he correspondng N neg ENE (0, ) EE 1 DF Noe due o he dfferen spreads, CVA asse and DVA do no necessarly offse. So should we even have DVA? How s he far prce of anyhng? Bookng DVA as par of he oal CVA prevens a sudden mraculous prof n he even of our own cred deeroraon! CVA desks are gong o charge he oal poson o he dealng desks, a leas a fracon of DVA, so hs pracce should be refleced. s c LGD e s o LGD

13 Oher own-cred-ssue adjusmens OCA s no he same as DVA: DVA s based on a blaeral exposure relaonshp as we ve seen, CVA and DVA don make src sense for valuaon as sand-alone ems, snce he exposure profles are arfcal and deal-specfc. DVA s conngen, and based on mulple sochasc rsk facors, whereas he exposures for own-ssued deb end no o aler. However, boh are clearly cred-sensve quanes. Basel III (for regulaed nsuons) does no recognze DVA offse for marke rsk capal. There s no secondary marke for blaeral OTC dervaves, however, our radng desk could fnd hemselves holdng ownssued deb nsrumens n nvenory.

14 Typcal IR swap exposure profle: EPE EE ENE T Noe, he profles may noe be symmerc, due o possble drf of MM, (e.g. a non-par swap) and of course, our spreads could dffer from our counerpary, so ha DVA s no jus he negave of CVA.

15 Managng and hedgng CVA There are many vews of CVA. Some nclude: as he marke prce of counerpary rsk,.e. as he cos of a CCDS, as an opon prce (an opon on he neng se, wh a srke of 0), as a capal reserve amoun (Basel III currenly akes hs vew), as he cos of clearng an OTC hrough a CCP. CVA s managed by rsk mgaon, hrough hedgng of exposures, collaeral, and cred proecon. If we look a CVA sensves, urns ou we can approxmae a change n CVA ( CVA) n a smlar fashon: bcva EPE s ENE C s O Ths gves suppor o he sensvy of CVA prmarly o spreads. Accordngly, CVA can be hedged boh by mgang defaul rsk ( s C ), as well as hedgng exposure o marke rsk facors ha drve he exposure self.

16 In case our spreads and he counerpary s DO move n andem, and rades are even (refleced profles), hen CVA s low (DVA gves full, or nearly full offse) showng DVA as a naural hedge. Noe hs s no he same as PnL due o DVA, bu s smply reflecng he rue value of he rade and canno effecvely be monezed excep f we defaul! We can drecly hedge he marke rsk exposure IR, FX, EQ, CO and CR sensves, whch wll produce dampened exposure profles. Noe, exac hedges are ofen no possble (OTC, non-sandardsed conracs). Collaeral can be used o reduce our exposure n he even of defaul. However, for cred mgraon shor of defaul, collaeral s no usable o offse agans MM losses n he even ha we novae he rade - s by no means unversal pracce o package he counerpary s collaeral along wh he rade a novaon. Fnally, we can hedge CVA volaly, and of course acual defaul rsk, wh CDSs (or equvalen). Ths s he only hedge recognzed under Basel III (he FRTB wll address hs, and nclude marke-rsk hedges also).

17 Term srucure of CDS hedges Noe possble maury and noonal msmaches.

18 FVA he cos of fundng our radng acves FVA mus be hough of as he cos of dong busness. I s a real cos, based on fundng our desks n he managemen of counerpary rsk. Thnk of us as a facory producng cars: DVA can represen he rsk ha our sandards wll slp (bad news abou arbags, maybe?), and people wll demand dscouns for our vehcles. FVA can be hough of as our cos of componens. They are clearly dfferen. Furher, FVA s defned a porfolo (or desk) level, whle CVA s ypcally a neng se or counerpary level. CTPTY CSA coll. OIS Dealer Xchg coll. OIS - spread Exchange deal Coll. Shorfall Marke rsk OIS hedges + fundng spread Fundng Ins.

19 Confuson sll exss beween DVA and FVA. In a perfec world, wh perfec lqudy, complee markes, and he law of one prce, DVA s ndeed he cos of fundng CVA lably or DVA. Tha s, our CDS spread wll be our fundng spread. I s hen he cos of nsurng our counerpary agans our defaul. In he real world, n whch deals are prced and sold, collaeral s no passed on a connuous bass, prcng nformaon s pachy a bes, we need o adjus for FVA, he acual cos we pay for dealng wh hedgng and collaeral msmaches. In addon, f we have llqud CDS spread quoes on ourselves, we can mmedaely see an ssue wh usng DVA as s as our cos of fundng. We now fnd he cred-rsky value of our OTC deal s V V CVA FVA We are no sang ha hs s wha we would receve for unwndng he rade!

20 FVA he wo sdes As can be seen n prevous sldes, here s a poenal fundng cos o me (o make up a collaeral posed/shorfall on ITM rades) as well as a poenal benef o me pad for collaeral posed o OTM rades: FVA FCA FBA These can be broken down accordng o expeced cash needs as follows: FCA N $ borrowng EPE DF( s 0, 0 ) FBA N $ lendng ENE DF( s 0, 0 ) $ $ We ake EPE max( C,0) and where s he ENE mn( C,0) C borrowng excess cash requremen a me-sep, and s and s are our spreads for borrowng / lendng. lendng

21 Noe, we have already bul he CVA engne o calculae expeced exposures, so we can leverage hs o oban our expeced posve or negave cashflow needs: We have rsk facor dynamcs, prcng and neng, and CDS curves bul, We have (by now, hopefully) a fully negraed collaeral smulaon, We now need o add n neng of collaeral requremens, o aggregae collaeral effecs up o porfolo level, and esmae scenaros of collaeral surplus or shorfall. We noe collaeral placed and receved wh counerpary j s Col and f a neng se s uncollaeralzed, s conrbuon s 0. Collaeral hrough he exchanges s where we hedgng our marke rsk, s hedge hedge hedge Col IM VM Col CSA CSA, k j, j, neng ses

22 Pung ogeher: l Consder smulang scenaros for rades, and le n be he prce of he l-h rade, n scenaro n, a me, n excess of he nal margn already held. hedge l Then VM s smulaed as he smple sum of he erms over V n, each rade. IM s harder o esmae, whou knowng how he exchange arrves a he requremens. Also, as of Sepember 2016, OSFI wll requre mos OTC rades beween FRFI s o pos Inal Margn, whch may be modeled by nsuons nernally, or, hese wll be se by regulaory gudance. In case we assume a 99% VaR ype merc, we would esmae IM (wh h usually = 10 days ) of roughly 2.33 h 252 porfolo V,

23 If we esmae a dependence beween IM and VM (and sugges a scalng facor see Ruz) we oban: Col hedge l F Vn, rades where F > 1. In hs case, we d oban EPE $ Emax F l CSA, k V Col, 0 n, j, neng ses rades and we have as before. FCA FBA N $ borrowng EPE DF( s 0, 0 ) N $ lendng ENE DF( s 0, 0 )

24 Capal Impac KVA? The jury s ou on wheher here should be a capal cos adjusmen. Remember, valuaon s no he same as prcng we may consder accounng for our ncremenal capal coss n enerng a new rade. Model rsk and governance concerns have frequenly led o unexpeced capal ncreases for Canadan regulaed nsuons. I would seem ha some consderaon for he possble (however remoe) effecs on capal should be ake no accoun. We can defne KVA as KVA T DF r Kˆ u s he expeced capal o be se asde a me u, DF u s he rsky dscoun curve, and r k s he cos rae of capal on he nerval ( u, u d). Kˆ u u k du

25 Now we need o ge a handle on Kˆ u. We know capal s expressble as (why?) C UL EL Also, many regulaed FI s have capal requremen Le us use Regulaory Capal as our capal requremen (hs s no all ha unusual pos 2008 crss, bu remans debaable pracce, especally n he case of sandardsed charges!) In hs case, we can esmae Kˆ usng Reg Cap charges: u VaR IRC CCR CVA Kˆ u Ku Ku Ku In he Canadan conex, IRC s a large componen of marke rsk capal. The sub-componens are K VaR IRC u K max( EC, RC) ( 3)( VaR %,10d svar 99%,10d ) 1.0 max( IRCu, IRC12 99 wk avg where s se by he regulaor, based on performance of he marke rsk model. ).

26 And also, and K K CCR u CVA u EAD ( LGD MA nengses, u ( PD,,0.999) PDavg ), u ( 3)( CVA VaR %,10d CVA svar 99%, d ), u Here, ( ( PD,,0.999) PD avg ), u s he ASRF Vascek copula erm for he UL for AIRB, calculaed on a rollng bass, and he CVA VaR calculaon wll make use of spread delas (CS01 s) o generae spread-based PnL shocks for CVA. I s hus possble (perhaps n he nex generaon of capal frameworks?) o assgn ncremenal capal mpacs ΔKVA o rades and neng ses, for OTC dervaves. The elephan n he room s.. why sop here?

27 Thank you s I would lke o hank Ignaco Ruz (Ruz Consulng), Vcor Chen (JPM), Jean-Paul Haddad and Parck Tobn (OSFI), for her nsghs, suppor and nspraon durng many hours of nvaluable dscusson and debae on he subjec. And hank you all for aendng! Quesons?