enterprise portfolio crediit r sk modelling - risklab.esrisklab.es/es/jornadas/2001/danrosen.pdf ·...
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©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
©1999 Alg o rithm ics Inc.
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
©1999 Alg o rithm ics Inc.
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 tory
a nd econom ic Ca pita l
©1999 Alg o rithm ics Inc.
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)
Corpora tes(Pu blic a nd
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
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©1999 Alg o rithm ics Inc.
•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”
©1999 Alg o rithm ics Inc.
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
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©1999 Alg o rithm ics Inc.
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
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
©1999 Alg o rithm ics Inc.
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
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©1999 Alg o rithm ics Inc.
Obligor Creditworthiness Analysis
Instrument ValuationTransaction Management
Counterparty Exposures
Measurement & Control
PortfolioManagement
En t erprise Cred it Risk Fun ct ion s
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
©1999 Alg o rithm ics Inc.
Obligor Creditworthiness Analysis
Instrument ValuationTransaction Management
Counterparty Exposures
Measurement & Control
PortfolioManagement
En t erprise Cred it Risk Fun ct ion s
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
©1999 Alg o rithm ics Inc.
Obligor Creditworthiness Analysis
Instrument ValuationTransaction Management
Counterparty Exposures
Measurement & Control
PortfolioManagement
En t erprise Cred it Risk Fun ct ion s
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
©1999 Alg o rithm ics Inc.
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
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©1999 Alg o rithm ics Inc.
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
©1999 Alg o rithm ics Inc.
M ark-to-Future Fram ework for Cred it Risk
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
+
+
_________
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©1999 Alg o rithm ics Inc.
1. Scena rios : • m a rk et fa ctors • credit drivers
M ark-to-Future Fram ework for Cred it Risk
X (0 ) X (t1) X (t2) X (t3)
©1999 Alg o rithm ics Inc.
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
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
©1999 Alg o rithm ics Inc.
J oin t D efault/M igration M od els
©1999 Alg o rithm ics Inc.
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
©1999 Alg o rithm ics Inc.
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
©1999 Alg o rithm ics Inc.
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
©1999 Alg o rithm ics Inc.
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)
M ark-to-Future Fram ework for Cred it Risk
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∑
==⋅====
©1999 Alg o rithm ics Inc.
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
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©1999 Alg o rithm ics Inc.
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}
+
+
©1999 Alg o rithm ics Inc.
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
©1999 Alg o rithm ics Inc.
Obligor Creditworthiness Analysis
Instrument ValuationTransaction Management
Counterparty Exposures
Measurement & Control
PortfolioManagement
En t erprise Cred it Risk Fun ct ion s
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
©1999 Alg o rithm ics Inc.
Port folio Cred it Risk Report s
Unexpected losses (99.5%)
Expected losses
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©1999 Alg o rithm ics Inc.
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
©1999 Alg o rithm ics Inc.
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
©1999 Alg o rithm ics Inc.
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)
©1999 Alg o rithm ics Inc.
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
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©1999 Alg o rithm ics Inc.
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
©1999 Alg o rithm ics Inc.
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
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©1999 Alg o rithm ics Inc.
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
©1999 Alg o rithm ics Inc.
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 tory
a nd econom ic Ca pita l
1818
©1999 Alg o rithm ics Inc.
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
©1999 Alg o rithm ics Inc.
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
©1999 Alg o rithm ics Inc.
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
©1999 Alg o rithm ics Inc.
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
©1999 Alg o rithm ics Inc.
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 ?
©1999 Alg o rithm ics Inc.
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
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©1999 Alg o rithm ics Inc.
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
©1999 Alg o rithm ics Inc.
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
©1999 Alg o rithm ics Inc.
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
©1999 Alg o rithm ics Inc.
Port folio Cred it Risk: econ om ic & regulat ory capital
•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
©1999 Alg o rithm ics Inc.
Port folio Cred it Risk: econ om ic & regulat ory capital
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)
Defa u lt M tM /M ig ra tion
Sys tem ic Idios yncra tic (G A)
W ithou tM itig a tion
W ithou tM itig a tion
Sys tem ic Idiosyncra tic
Defa u lt M tM /M ig ra tion
W ithou tM itig a tion
W ithou tM itig a tion
©1999 Alg o rithm ics Inc.
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 tory
a nd econom ic Ca pita l
2424
©1999 Alg o rithm ics Inc.
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
©1999 Alg o rithm ics Inc.
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
©1999 Alg o rithm ics Inc.
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 +
©1999 Alg o rithm ics Inc.
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
©1999 Alg o rithm ics Inc.
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
©1999 Alg o rithm ics Inc.
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
©1999 Alg o rithm ics Inc.
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
0% 25% 50%Credit Correlation
DESE
99.9% Losses
02000400060008000
1000012000
0% 25% 50%Credit Correlation
DESE
©1999 Alg o rithm ics Inc.
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
Credit Losses - 99.5% Quantile
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
©1999 Alg o rithm ics Inc.
Credit Losses - 99.5% Quantile
0
5
10
15
20
25
36 72 216 432 720 1500
Number of obligors
Cre
dit L
osse
s (%
)
DeterministicExposuresStoch. Exposures - Nocorrelations
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
•For la rg e portfolios Expos u res /LG D vola tility is u nim porta ntif thes e a re u ncorrela ted
©1999 Alg o rithm ics Inc.
Credit Losses - 99.5% Quantile
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
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
•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
©1999 Alg o rithm ics Inc.
Credit Losses - 99.5% Quantile
0
5
10
15
20
25
30
35
36 72 216 432 720 1500
Number of obligors
Cre
dit L
osse
s (%
)
DeterministicExposures
Stoch. Exposures - Nocorrelations
Stoch. Exposures -Market correlations
Stoch Exposures -Market-Creditcorrelations
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
•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
©1999 Alg o rithm ics Inc.
Credit Losses - 99.5% Quantile
0
5
10
15
20
25
30
35
36 72 216 432 720 1500
Number of obligors
Cre
dit L
osse
s (%
)
DeterministicExposures
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
©1999 Alg o rithm ics Inc.
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 tory
a nd econom ic Ca pita l
©1999 Alg o rithm ics Inc.
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
Corpora tes(Pu blic a nd
Priva te)
Corpora tes(Pu blic a nd
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
©1999 Alg o rithm ics Inc.
Obligor Creditworthiness Analysis
Instrument ValuationTransaction Management
Counterparty Exposures
Measurement & Control
PortfolioManagement
En t erprise Cred it Risk Fun ct ion s
©1999 Alg o rithm ics Inc.
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
©1999 Alg o rithm ics Inc.
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
©1999 Alg o rithm ics Inc.
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)