Enterprise Portfolio Crediit R sk Modelling - risklab.esrisklab.es/es/jornadas/2001/DanRosen.pdf · • un der stan d the sour ces of ex posur es, how mar ket or portf oli o chnages

11

©1999 Alg o rithm ics Inc.

En t erprise Port folio Cred it Risk M od ellin gRiskLab In t ern ation al Con feren ce,

M ad rid , O ct ober 18 2001

Da n Ros enVP Res ea rch & New Solu tionsAlg orithm ics Inc.dros en@ a lg orithm ics .com


O ut lin e•Enterpris e credit ris k

•G enera l portfolio credit fra m ew ork- 2nd g enera tion credit ris k m odels - integ ra ted m a rk et & credit ris k

•BIS II a nd Enterpris e Credit ris k•Portfolio credit ris k m odelling of m inim u m ca pita l u nder IRB•Hiera rchy of m odels – reconciling reg u la tory & econom ic ca pita l

•Ca s e s tu dy - Im pa ct of correla ted m a rk et a nd credit on portfolio ris k

•Enterpris e fra m ew ork for reg u la torya nd econom ic Ca pita l

22





• Ca s e s tu dy - Im pa ct of correla ted m a rk et a nd credit on portfolio ris k•Enterpris e fra m ew ork for reg u la tory

a nd econom ic Ca pita l


Financial Institution

Tra ding BookBa nk ing Book

Reta il Reta il Com m ercia l m ediu m / s m a llCom m ercia l

m ediu m / s m a llCom m ercia l

La rg eCom m ercia l

La rg e

m ortg a g esm ortg a g es Creditca rds

Creditca rds

Lines of credit

Lines of credit

Corpora tes(Pu blic a nd

Priva te)


Priva te)

SectorsSectors SectorsSectors SectorsSectors

Priva te Firm s

Priva te Firm s

SectorsSectors

Deriva tivesCou nterpa rtiesDeriva tives

Cou nterpa rties

Sovereig n Bond Is s u ersSovereig n

Bond Is s u ers

Corpora te Bond Is s u ersCorpora te

Bond Is s u ers

Credit Deriva tives

Credit Deriva tives

En t erprise Cred it Risk

33


•Evolu tion of credit ris k m a rk ets•s trong er bond a nd loa n m a rk ets; credit deriva tives à credit tra ns fer

•Pa s s ive loa n orig ina te & holdà a ctive portfolio m a na g em ent•Integ ra tion of m a rk et a nd credit ris k : pricing a nd portfolio m odels

•u nified m a na g em ent of ris k in the ba nk ing a nd tra ding book s•credit ris k à tra ded m a rk et ris k

•Im provem ents in technolog y: effective dis tribu tion of on-line credit inform a tion a nd va lu a tion tools to a la rg e nu m ber of u s ers .

•a cces s in credit m a rk ets to non-tra ditiona l ins titu tions a nd inves tors•s ophis tica ted com pu ta tiona l tools to price a nd m a na g e credit ris k .

•Trends in reg u la tion a nd bes t pra ctices•Adva nces in credit ris k m odels : pra ctica l pricing & ris k m odels

En t erprise Cred it Risk “facilitat ors”


Obligor Creditworthiness Analysis

Instrument ValuationTransaction Management

Counterparty Exposures

Measurement & Control

PortfolioManagement

En t erprise Cred it Risk Fun ct ion s

Sovereig n

Pu blic firm s

Priva te: la rg e & m ediu m

Sm a ll bu s ines s es

Reta il cons u m ers

44


O bligor Ratin g/D efault m easurem en t m od els

Reta il(cons u m er)

Reta il(cons u m er)

s m a ll bu s ines s es


Sovereig nsSovereig nsm ediu m priva te

m ediu m priva te La rg e

Priva teLa rg e

Priva tePu blic Firm s

Pu blic Firm s

Bu rea u scores Ag ency Ra ting s

Pu blic Firm (stru ctu ra l m odels )

Priva te Firm M odels

Bu s ines s s cores

No-a rbitra g e m odels

Econom etric m odels

M a croecono-m ic M odels


O bligor Risk Qualit y An alysis

• Oblig or s coring /ra ting - cla s s ifica tion

• Defa u lt proba bilities - qu a ntifica tion

• credit m ig ra tion proba bilities (tra ns ition m a trices)

• Oblig a tion: Los s s everity – recovery ra tes , LG D

• J oint credit beha viou r

• s ys tem ic a nd idios yncra tic com ponents of credit qu a lity cha ng es

• neces s a ry for portfolio credit ris k a nd integ ra ted m a rk et-credit ris k

55






PortfolioManagement


Deriva tivesCredit Deriva tivesBondsSyndica ted loa nsLa rg e corpora te loa nsM iddle & s m a ll m a rk etReta il

- colla tera l m a na g em ent






PortfolioManagement


M ea s u rem ent a nd lim its

Ag g reg a tion of pos itions by

- oblig or/cou nterpa rty

- s ector

- cou ntry, etc.

Deriva tives :

- a ctu a l & potentia l expos u res

M itig a tion

- netting , colla tera l, etc.

66






PortfolioManagement


Portfolio credit ris k ca pita l

- econom ic & reg u la tory

Portfolio M a na g em ent tools- ris k contribu tions-m a rg ina l ris k-ca pita l a lloca tion-perform a nce-optim iza tion & efficient frontiers


En t erprise Cred it Risk Fram ework

•Enterpris e credit ris k m ea s u rem ent•m u s t recog nize the divers ity of oblig ors a cros s the enterpris e a nd, thu s,

provide a fra m ew ork tha t a llow s for the s im u lta neou s u s e of s evera l m odels

•Accu ra te Credit Va lu a tion•w ea lth of ins tru m ents : loa ns, bonds, deriva tives, credit deriva tives, CDOs

•Integ ra tion of m a rk et a nd credit ris k•vita l for va lu a tions, cou nterpa rty expos u res, m odelling colla tera l a nd

m itig a tion, a nd portfolio credit ris k•Effective ris k m a na g em ent tools

•u nders ta nd the s ou rces of expos u res, how m a rk et or portfolio cha ng es a ffect its ris k s profile, a nd optim a l ris k vs . retu rn tra de-offs

•tools ca nnot be ba s ed on the s ta nda rd norm a lity a s s u m ptions of M PT

77


M ark-to-Future Fram ework for Cred it Risk

1. Ris k fa ctor Scena rios (“s ta tes of the w orld”)•evolu tion of s ys tem ic (m a rk et & credit) ris k fa ctors over horizon

2. J oint defa u lt/ m ig ra tion m odel•econom ic conditions ---> defa u lt/ m ig ra tion •defa u lt/ m ig ra tion proba bilities a re conditioned on the s cena rio

(correla tions : joint va ria tion of oblig ors proba bilities over s cena rios)3. Oblig or expos u res, recoveries a nd los s es in a s cena rio

•M a rk -to-Fu tu re expos u res in a s cena rio (w ith netting , colla tera l, etc.)4. Conditiona l portfolio los s dis tribu tion in a s cena rio

•efficient com pu ta tion: credit events of ea ch oblig or a re independent 5. Ag g reg a tion of los s es in a ll s cena rios

•a vera g e over a ll s cena rios of conditiona l los s dis tribu tions



1. Scena rios : • m a rk et fa ctors • credit drivers

. . . . . . . . . .

2. Conditiona l oblig or defa u lt proba bilities

3. Oblig or s cena rio los s es

(expos u res X LGD)

4. Conditiona l portfolio los s es

. . . . . . . . . . . . . . . . . . . .

5. Unconditiona l Portfolio los s dis tribu tion

+

+

_________

88


1. Scena rios : • m a rk et fa ctors • credit drivers


X (0 ) X (t1) X (t2) X (t3)


Several J oin t D efault/M igration M od els

1. Scena rios 2. Conditiona l defa u lt proba bilities

. . . . . . . . . . . . A s ing le m odel does not fit a ll!

Reta ilReta il s m a ll bu s ines s es


Fina ncia l Ins titu tion

Sovereig nsSovereig nsm ediu m priva te

m ediu m priva te La rg e

Priva teLa rg e

Priva te Pu blic Firm s

Pu blic Firm s

Econometric

(e.g. Logit)sovereign

(e.g. structural)

Public firm

(e.g. Merton)

Private firm

(e.g. ratings based)

Small bus.

medium bus.

99


J oin t D efault/M igration M od els


Mark-to-Future Values

Coun t erpart y Exposures through M ark-to-Future

Sce

nario

sS

cena

rios

Mark-to-Future

Instruments

aggregation, netting, collateral, aggregation, netting, collateral, credit mitigation, etc.credit mitigation, etc.

Mark-to-Future

Counterparty Portfolios

CounterpartiesCounterparties

Sce

nario

sS

cena

rios

SecuritiesSecurities

1010


SAPPHIRE - AA

0.0

30.0

60.0

90.0

6/4/97 6/4/01 6/4/05 6/4/09 6/4/13 6/4/17

Time

Cre

dit E

xpos

ure

(Mill

ions

)

SAPPHIRE - AA

0.0

30.0

60.0

90.0

6/4/97 6/4/01 6/4/05 6/4/09 6/4/13 6/4/17

Time

Cre

dit E

xpos

ure

(Mill

ions

)

TURQUOISE - AA

0.0

20.0

40.0

60.0

80.0

6/4/97 6/4/01 6/4/05 6/4/09 6/4/13 6/4/17

Time

Cre

dit E

xpos

ure

(Mill

ions

)

TURQUOISE - AA

0.0

20.0

40.0

60.0

80.0

6/4/97 6/4/01 6/4/05 6/4/09 6/4/13 6/4/17

Time

Cre

dit E

xpos

ure

(Mill

ions

)

Exposure Profiles & Lim it sCou nter Pa rty Expos u re Lim its


En t erprise Port folio: con d it ion al scen ario loss d ist ribut ion

Enterpris e Portfolio

Cou nter-pa rties

Cou nter-pa rtiesdivers ified

Sectorsdivers ified

Sectorsu ndivers ified

Sectorsu ndivers ified

SectorsSectorsSectors

“norm a l” (sem i-

divers ified) Sectors

“norm a l” (sem i-

divers ified) Sectors

Credit deriva tives

Credit deriva tives

+ + +

1111


1. Scena rios on: • m a rk et fa ctors • credit drivers

2. Conditiona l oblig or defa u lt/ m ig ra tion proba bilities p(X)


X=x1

X=x3

X=x2

pj(X=x1), j=1,… ,n

pj(X=x2), j=1,… ,n

pj(X=x3), j=1,… ,n

3. Oblig or s cena rio los s es l(X)à

(expos u res X LGD)

lj (X=x1), j=1,… ,n

lj (X=x2), j=1,… ,n

lj (X=x3), j=1,… ,n

4. Conditiona l portfolio los s es P(L= l|X)

P(L= l|X=x1)

P(L= l|X=x2)

P(L= l|X=x3)

5. Unconditiona l Portfolio los s dis tribu tion }{}|{}{

1i

M

ii PlLPlLP xXxX∑

==⋅====


S yst em ic an d Id iosyn cratic Port folio LossesSys tem ic los s es a re•The a ctu a l los s es of a n a s ym ptotica lly fined g ra ined portfolio. Form a lly, it is

•the portfolio w e obta in by dividing every expos u re into n identica l expos u res

•ta k ing the lim it a s ng ets very la rg e•Conditiona l on a g iven s cena rio, the los s dis tribu tion colla ps es to a s ing le

point à its expected loss; •a ll hig her m om ents va nis h

•Cons equ ence of the La w of La rg e Nu m bers (LLN) a nd the property of s cena rio conditiona l independence.

•It ca n be a g ood a pproxim a tion for la rg e, w ell divers ified, portfolios

1212


1. Scena rios 2. Conditiona l proba bilities p(X)

S yst em ic an d id iosyn cratic Port folio Losses

X=x1

X=x3

X=x2

pj(X=x1) j=1,… ,n

pj(X=x2)j=1,… ,n

pj(X=x3)j=1,… ,n

3. Oblig or los s es l(X)

lj (X=x1)j=1,… ,n

lj (X=x2)j=1,… ,n

lj (X=x3)j=1,… ,n

4. Conditiona l (tota l) portfolio los s es P(L= l|X)

5. Unconditiona l Portfolio los s dis tribu tion

4a . Conditiona l Sys tem ic los s es

E{L|X}

+

+


1. Scena rios 2. Conditiona l proba bilities p(X)

S yst em ic an d id iosyn cratic Port folio Losses

X=x1 pj(X=x1) j=1,… ,n

3. Oblig or los s es l(X)

lj (X=x1)j=1,… ,n

4. Conditiona l (tota l) portfolio los s es P(L= l|X)

P(L= l|X=x1)

5. Unconditiona l Portfolio los s dis tribu tion }{}|{

}{

1i

M

ii PlLP

lLP

xx∑=

⋅=

==

4. Conditiona l Sys tem ic los s es

E{L|X}

}{}{

}|{

11

1

1

xx

xX

∑=

⋅

==n

jjj pl

LE

X=x3

X=x2 pj(X=x2)j=1,… ,n

pj(X=x3)j=1,… ,n

lj (X=x2)j=1,… ,n

lj (X=x3)j=1,… ,n

P(L= l|X=x2)

P(L= l|X=x3)

}{}{

}|{

21

2

2

xx

xX

∑=

⋅

==n

jjj pl

LE

}{}{

}|{

31

3

3

xx

xX

∑=

⋅

==n

jjj pl

LE

}{}]|[{

}{

1i

M

ii

s

PlLEP

lLP

xx∑=

⋅=

==

1313






PortfolioManagement


Portfolio credit ris k ca pita l

- econom ic & reg u la tory

Portfolio M a na g em ent tools- ris k contribu tions-m a rg ina l ris k-ca pita l a lloca tion-perform a nce-optim iza tion & efficient frontiers


Port folio Cred it Risk Report s

Unexpected losses (99.5%)

Expected losses

1414


Port folio Cred it Risk Report sIm pact of Tran sit ion s M atrices

Exa m ple• Sim ila r res u lts w ith S&P

a nd M oody’s• Res u lts differ w ith KM V

m a trix:• E(Los s es)~ 2X la rg er• s td. Dev ~ 45% la rg er• ta ils : 2%~ 17% la rg er


Port folio Cred it Risk Report s D efault vs. M igration Risk

Defa u lt a ccou nts for• S&P

• EL ~ 64%• UL ~ 74% - 85%

• KM V• EL ~ 21%• UL ~ 50 % -71%

Recovery Ra tes :• linea r rela tions hip to

defa u lt los s es(ea sy to stres s test)

1515


Port folio Cred it Risk Report s Im pact of In t erest Rat es (m arket)

•Portfolio m odel a s s u m es m a rk et level is cons ta nt (determ inis tic expos u re)

•Ca n s tres s im pa ct of level of IRs

Res u lts a s expected: •for a bond portfolio, the

level ofIRs does not im pa ct credit los s es ~ 10 % (for a 2 s ig m a m ove)


Port folio Cred it Risk Report s O ther Sources of Risk

Independent defa u lts- hig her m a s s in center tha n ba s e ca seThinner ta ils- Credit Va R 60 % low er tha n ba s e ca s e

Fa ls e perform ing a ccou nts- defa u lt a ccou nts tha t a t the end of ea ch m onth a re cla s s ified a s perform ing-hig her m ea n los s & ca pita l ≈50 %

Correla ted credit ris k drivers-s cena rios ca ptu re effect of econom ic cycle on cons u m er fina nce- hig her m ea n los s & low er vol. (σ)- Credit Va R 25% la rg er tha n ba se ca s e

1616


Cred it Risk M an agem en t Tools

“Hot Spots ” report

•s ectors w ith la rg es t contribu tion to portfolio credit risk

•ra nk ed by expected s hortfa ll

•expected los s non-divers ifia ble

•three s ectors concentra te m ore tha n 50 % of portfolio credit ris k

•hig h-ris k sectors (1 a nd 2) ha ve a rela tively low contribu tion to portfolio ris k


Cred it Risk M an agem en t

Dominant

sectors

M a rg ina l Ris k vs Exposu re s ize•dom ina nt s ectors ha ve hig her m a rg ina l ris k a nd expos u re tha n other sectors

• ca ndida tes for res tru ctu ring•m a rg ina l ris k decrea s es w ith orig ina l s core•correla tions m a tter

• s ector 3 ha s hig her m a rg ina l ris k tha n s ector 2

•s ectors w ith hig h m a rg ina l ris k• ⇒ increa s e s coring

thres holds• s ecu ritiza tion

1717


Risk-Return Efficien t Fron t iers

6.0%

7.0%

8.0%

9.0%

10.0%

11.0%

12.0%

0 200 400 600 800 1000 1200 1400 1600

CreditVaR (99.9%)(millions USD)

Exp

ecte

d re

turn

( r ')

Variance

Expected Regret

Expected Shortfall







1818


BIS II Proposal for n ew capital ad equacy fram ework

Three pilla rs :•M inim u m ca pita l requ irem ents

•g ives the explicit ru les tha t define the m inim u m ra tio of ca pita l to ris k w eig hted a s s ets

•Su pervis ory review proces s•requ ires s u pervis ors to u nderta k e a qu a lita tive a s s es s m ent of

ca pita l a lloca tion techniqu es a nd com plia nce w ith s ta nda rds a ctu a lly in pla ce in a n ins titu tion

•M a rk et dis cipline•hig h dis clos u re s ta nda rds & a dequ a te ca pita l w hich fa cilita te

m a rk et dis cipline


M in im um Capital U n d er BIS II

Su m m a ry of m inim u m ca pita l requ irem ents

•Three a pproa ches to ca lcu la tion of ris k -w eig hted a s s ets : •(Revis ed) s ta nda rdized a pproa ch•Fou nda tion interna l ra ting s -ba s ed (IRB) a pproa ch•Adva nced Interna l ra ting s -ba s ed (IRB) a pproa ch

•Explicit ca pita l cha rg e for opera tiona l ris k

•M a rk et ris k ca pita l a s defined in the 1996 Am endm ent to rem a in la rg ely u ncha ng ed

1919


Port folio Cred it Risk & BIS II

Credit ris k m odels for the ba nk ing book (m inim u m ca pita l requ irem ents):

“The com m ittee indeed recog nizes tha t credit ris k m odeling m a y prove to resu lt in better interna l ris k m a na g em ent, a nd m a y ha ve the potentia lto be u sed in the s u pervision of ba nk s”...

“At this tim e, sig nifica nt hu rdles , principa lly concerning da ta a va ila bilitya nd m odel va lida tion, still need to be clea red before [portfolio m odeling a pproa ches ca n be u sed in the form a l proces s of settingreg u la tory ca pita l requ irem ents].”

“A new Ca pita l Adequ a cy Fra m ew ork ”, cos u lta tive pa per by the Ba sle Com m ittee on Ba nk ing Su pervision, J u ne 1999


Port folio Cred it Risk & BIS II

Credit ris k m odels for the ba nk ing book

- Althou g h portfolio credit ris k m odels a re not a llow ed for the ca lcu la tion of m inim u m ca pita l requ irem ents,

- The fu nctiona l form a nd coefficients of the BRW a nd G A a lrea dy em bed portfolio credit ris k m odel

- Sa tis fying Pilla r II w ill lik ely requ ire tha t ins titu tion on thea dva nced IRB a pproa ch ha ve im plem ented in pra ctice a portfolio credit ris k m a na g em ent s ys tem

2020


Port folio Cred it Risk M od ellin g in BIS II

BIS II IRB a pproa ch em beds a lrea dy a portfolio m odel

M odelling objective: to develop ris k -bu ck eting ca pita l ru les cons is tent w ith a portfolio credit ris k m odel:

•W eig hts m u s t be a dditive

•W eig hts m u s t be portfolio inva ria nt

•Under w ha t m odelling a s s u m ptions does a portfolio m odel yield portfolio-inva ria nt m a rg ina l ris k contribu tions ?


G A = G ra nu la rity Adju stm entRW j = Ris k W eig ht for a s s et/oblig or j

Ej = Expos u re a t defa u lt for a s s et/oblig or j

•RW x E x 8% repres ents the ca pita l for a “perfectly” divers ified portfolio (a s ym ptotica lly fined g ra ined; w ith only s ys tem ic ris k )

•The“g ra nu la rity a dju s tm ent” a dju s ts the ca pita l for the level of divers ifica tion of the a ctu a l portfolio

BIS II Ad van ced IRB Approach

GARWEn

jjj +×

⋅= ∑ %8Capital Regulatory

2121


Port folio Cred it Risk M od ellin g in BIS IIM odelling objective à Ans w er (G ordy) :•Portfolio-inva ria nt m a rg ina l ris k contribu tions

(a dditive a nd portfolio inva ria ntw eig hts) only if tw o conditions hold:

•As ym ptotica lly fined g ra ined portfolio (system ic los s es)

•Sing le s ys tem ic ris k fa ctor

•Ana lys is of ra tes of converg ence à s im ple a pproxim a tion for “portfolio level” a dd-on cha rg e for u ndivers ified, idios yncra tic, ris k

•AFG P a s s u m ption is thu s g enera lly not a pra ctica l problem

•Sing le fa ctor a s s u m ption is recog nized to ca u s e a n im porta nt lim ita tion


BIS II Port folio M od el

Cons ider a Va s icek (tw o-s ta te form of CreditM etrics ) M odel

•Defa u lt driven by M erton M odel

•Sing le s tep portfolio credit los s es over 1 yea r

•Ca pita l to cover 99.5% of the los s dis tribu tion

•Determ inis tic oblig or expos u res & LG D (holds a ls o if EAD, LG D a re independent of ea ch other a nd of the s ys tem ic fa ctor)

•Sing le s ys tem ic ris k fa ctor – s ta nda rd Norm a l

X (t) ~ N(0, 1)

2222


Port folio Cred it Risk: econ om ic & regulat ory capital

Reg u la tory Ca pita l

Defa u lt M tM /M ig ra tion

W ithou t M itig a tion

Sys tem ic(u nsca led)

( )]/)1(0470.01[

288.1)(118.15.976)(44.0

1

PDPD

PDNNPDBRW

−⋅+⋅+⋅= −

GARWEn

jjj +×

⋅= ∑ %8Capital Reg

}5.12, adj. Mat.%)50/min{( LGDBRWLGDRW ×⋅⋅=

Sys tem ic %8×

⋅= ∑

n

jjj RWE

Idios yncra tic (G A)

GA = (1/n*) x (1.5/0.08) X (0.4 + 1.2 LGD)

x (0.76 + 1.1 PD / F )

W ithou t M itig a tion



•Look ing a t ca pita l throu g h the eyes of the g enera l portfolio fra m ew ork s u g g es ts a na tu ra l portfolio m odel hiera rchy to reconcile econom ic a nd reg u la tory ca pita l

•Is s u es to reconcile

•Sys tem ic Fa ctors, X(inclu des m a rk et a nd credit drivers : Xm , Xc)

•Defa u lt vs M tM Los s es

•Correla ted M a rk et&Credit: s tocha s tic a nd correla ted expos u res /LG D s

•Sys tem ic vs . idios yncra tic (g ra nu la rity)

•Ba s e ca libra tion

2323



Reg u la tory Ca pita l Econom ic Ca pita l

Reg u la tory M odel s ing le fa ctor

Integ ra ted m a rk et- credit

M u lti-Fa ctor, X(best) Sing le-

Fa ctor, XSta nda rd

M u lti-Fa ctor, X

Sys tem ic(u nsca led)


Sys tem ic Idios yncra tic (G A)

W ithou tM itig a tion


Sys tem ic Idiosyncra tic










2424


Port folio Cred it Risk M od els

•“Fou r m odels ” - Firs t g enera tion •ca n be s een a s va ria tions of s tru ctu ra lor redu ced form credit m odels

Firs t g enera tion m odels a ppea r qu ite different on the s u rfa ce, bu t…

•G enera lly, they a re “m a them a tica lly equ iva lent”

•i.e. they ca n be m a pped one to a nother

•differences in s om e m odeling a s s u m ptions a nd s olu tion m ethod

•Em pirica l s tu dies : u s ing cons is tent da ta , m odels yield s im ila r res u lts

•Som e ca n ha ndle rea dily only defa u lt los s es

They ca n a ll be s een a s s pecific ins ta nces of a g enera l fra m ew ork


Port folio Cred it RiskFirs t g enera tion PCR m odels a re s pecific ins ta nces of a g enera l fra m ew ork

One lim ita tion tha t a ll s ha re:

• As s u m e, in g enera l, determ inis tic m a rk et fa ctors : IRs , s prea ds, FX, etc.• Expos u res a re not s tocha s tic & LG D s a re a ls o g enera lly not s tocha s tic or

not correla ted• m a y be OK for s om e loa ns & bonds (specia lly floa ting ra te)• not a ppropria te for deriva tives (e.g . s w a p), loa ns w ith optiona lity,

portfolios w ith colla tera l• Als o does not ca ptu re properly ris k from s prea d m oves / vola tility

A com prehens ive fra m ew ork requ ires fu ll integ ra tion of m a rk et a nd credit• portfolio credit ris k , expos u res (w rong w a y), s pecific ris k for bonds ...

2525


Exposures M easurem en t &Cred it risk of swap port folio

Sim ple idea

Portfolio: Tw o cou nterpa rties- CP1: 1 s w a p - pa ys fix- CP2: 1 s w a p - pa ys floa t- s im ila r m a tu rities

• A pos itive M tM w ith both is not pos s ible in a ny s ta te of the w orld:

•Portfolio m odels g enera lly ta k e a s ing le expos u re nu m ber for ea ch CP ---> ca nnot es tim a te econom ic ca pita l correctly

•Qu es tion: by how m u ch?

IRs S1 S2

+ 0

0 +


Port folio Cred it Risk an d S tochastic Exposures/LG D

The contribu tion of s tocha s tic Expos u re/LG D depends m a inly on fou r fa ctors

• Rela tive vola tility/dis pers ion of individu a l expos u res /LG D

• Portfolio g ra nu la rity – level of divers ifica tion

• M a rk et correla tions : codependence of expos u res /LG D s

• M a rk et-Credit correla tions

2626


Exam ple: Swap port folio 1

•M ea s u rem ent of one yea r los s es du e to defa u ltPortfolio: 72 cou nterpa rties

- 1 IR s w a p (USD) - pa ys fix (m a tu rity: 3 yea rs)

Swap Profile: Receive Fix

0

50

100

150

200

250

300

350

400

450

1/26

/99

3/26

/99

5/26

/99

7/26

/99

9/26

/99

11/2

6/99

1/26

/00

3/26

/00

5/26

/00

7/26

/00

9/26

/00

11/2

6/00

1/26

/01

3/26

/01

5/26

/01

7/26

/01

9/26

/01

11/2

6/01

1/26

/02

3/26

/02

Mean

95% right tail

Mean+SD Pay FixAverage 85StdDev 139

95% 37299% 560

99.90% 813

One Yea r expos u res


Exam ple: Swap port folio(M arket -Cred it D river Correlat ion = 25%)

Expected Losses

020406080

100120

0% 25% 50%

Credit Correlation

DESE

Standard Deviation of Losses

0

200

400

600

800

0% 25% 50%

Credit Correlation

DESE

2727


Exam ple: Swap port folio(M arket -Cred it D river Correlat ion = 25%)

99% Losses

0500

10001500200025003000

0% 25% 50%Credit Correlation

DESE

99% Short Fall Losses

01000200030004000500060007000


DESE

99.9% Losses

02000400060008000

1000012000


DESE


G en eral Loss con t ribut ion s

•Portfolio g ra nu la rity a nd s tocha s tic expos u res /LG D

Credit Losses - 99.5% Quantile

02468

1012141618

36 72 216 432 720 1500

Number of obligors

Cre

dit L

osse

s (%

)

Deterministic Exposures


02468

1012141618

36 72 216 432 720 1500

Number of obligors

Cre

dit L

osse

s (%

)

DeterministicExposures

•La w of La rg e Nu m bers : Infinitely g ra nu la r portfoliodis tribu tion of Los s es à dis tribu tion of expected los s es

2828



0

5

10

15

20

25

36 72 216 432 720 1500

Number of obligors

Cre

dit L

osse

s (%

)

DeterministicExposuresStoch. Exposures - Nocorrelations



•For la rg e portfolios Expos u res /LG D vola tility is u nim porta ntif thes e a re u ncorrela ted



0

5

10

15

20

25

36 72 216 432 720 1500

Number of obligors

Cre

dit L

osse

s (%

)

DeterministicExposuresStoch. Exposures - NocorrelationsStoch. Exposures -Market correlations



•Expos u re/LG D Correla tions m a y contribu te s u bs ta ntia lly to Los s es even for la rg e portfolios

2929



0

5

10

15

20

25

30

35

36 72 216 432 720 1500

Number of obligors

Cre

dit L

osse

s (%

)


Stoch. Exposures - Nocorrelations

Stoch. Exposures -Market correlations

Stoch Exposures -Market-Creditcorrelations



•M a rk et a nd credit correla tions m a y contribu te s u bs ta ntia lly to Credit Los s es



0

5

10

15

20

25

30

35

36 72 216 432 720 1500

Number of obligors

Cre

dit L

osse

s (%

)


Stoch. Exposures - Nocorrelations

Stoch. Exposures -Market correlations

Stoch Exposures -Market-Creditcorrelations

Im plication s for Syst em ic risk an d gran ularit y ad just m en t

•This im plies tha t there s hou ld be a s ys tem ic ris k “a dju s tm ent” for correla tions a nd w rong w a y expos u res

•G A s hou ld a ls o correct for vola tility a nd correla tions

3030








m ortg a g esm ortg a g es

SectorsSectors

Financial Institution

Tra ding BookBa nk ing Book

Deriva tivesCou nterpa rtiesDeriva tives

Cou nterpa rties

Reta il Reta il Com m ercia l m ediu m / s m a llCom m ercia l

m ediu m / s m a llCom m ercia l

La rg eCom m ercia l

La rg e


Priva te)


Priva te)

Creditca rds

Creditca rds

Lines of credit

Lines of credit

SectorsSectors SectorsSectors

Priva te Firm s

Priva te Firm s

SectorsSectors

Sovereig n Bond Is s u ersSovereig n

Bond Is s u ers

Corpora te Bond Is s u ersCorpora te

Bond Is s u ers

Credit Deriva tives

Credit Deriva tives

En t erprise Cred it Risk

3131






PortfolioManagement



BIS II IRB & Port folio Cred itBuild in g blocks

The m inim u m ca pita l ca lcu la tion requ ires•Proba bilities of defa u lt for ea ch oblig or (PD)•Expos u re a t defa u lt for ea ch tra ns a ction (EAD)•Los s g iven defa u lt for ea ch tra ns a ction (LG D )•M a tu rity of ea ch tra ns a ction (M )•Corpora te/reta il benchm a rk ris k w eig hts (BRW )

Fu ll portfolio credit ris k m odelling fu rther requ ires•Oblig or correla tion m odel•Fu ll M tM for ea ch tra ns a ction (for M tM m odels)

3232


En t erprise Cred it Solut ion : Econ om ic an d Regulatory (BIS-II) Capital

Oblig or Creditw orthiness D a ta

Ra ting s PD/TM LG D Credit

correla tions

Interna l Sys tem s Externa l Sys tem sOblig or

rela tions hips

Market

Data

Credit Drivers(fa ctors)

IRs . FX, EQ., etc.

Bonds :Prices /

s prea ds

Loa ns :Prices /s prea ds

CreditDerivs .

Inte

rnal

Syst

emsEx

tern

al Sy

stems

Colla tera lG u a ra ntees M itig a tion

Term s & Conditions

Exposu res

Pos itionsInternal Systems

Transaction Data

M a pping Interfa ce (extra ct, m a p, loa d)

Mappi

ng I

nter

face Mapping Interface

Da ta Sta g ing , Res u lts M a na g em ent Da ta ba se

Oblig orTra ns a ctionColla tera lM a rk et

Inpu t DB

Sta nda rd Reg u la toryCa pita l

Report DB

Exposu re/M tMBIS PCR Lim its

Fina ncia l Eng ines

Colla tera l M a na g em ent


Con clud in g Rem arks •Enterpris e credit ris k fra m ew ork•integ ra te credit ris k•integ ra te m a rk et a nd credit•va lu a tion a nd M tM•portfolio credit ris k m a na g em ent

• M odelling expos u res /LG D a ccu ra telyis k ey for a ccu ra te PCR m ea s u rm ent

•ECR Fra m ew ork à s olid ba s is for •m a na g ing a nd reconciling reg u la tory a nd econom ic ca pita l•pilla r II •providing tra ns pa rency (Pilla r III)

3333


www.algorithm ics.comwww.m ark-to-future.com

See alsoAlgo Research Quart erly

Enterprise Portfolio Crediit R sk Modelling - risklab.esrisklab.es/es/jornadas/2001/DanRosen.pdf · • un der stan d the sour ces of ex posur es, how mar ket or portf oli o chnages

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