A Two Stage Mixture Model for Predicting EAD
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1 A wo Sage Mixure Mode for Predicing EAD Credi Scoring & Credi Conro, Edinburgh 2013 Mindy Leow & Jonahan Crook Credi Research Cenre, Universiy of Edinburgh, UK 1
2 Moivaion Reguaory Capia ase II requires each bank in a compying jurisdicion o hod Reguaory Capia MRCR credi risk + MRCR marke risk + MRCR operaiona risk where MRCR credi risk EAD. LGD * 1 ( PD) 1 1 ( ) PD Represens 99.9 h %ie of expeced oss disribuion (VaR(99.9)). EAD is unknown before he ime of defau, bu known he very insan he accoun goes ino defau, so ahough defau-ime variabes coud be used in he modeing of LGD, hey canno be used for EAD. Economic Capia 2
3 Aernaive dependen variabes Common variabes esimaed in ieu of EAD in he ieraure are Loan Equivaen Exposure (LEQ) Facor, Credi Conversion Facor (CCF) Exposure A Defau Facor (EADF) 3
4 4 Dependen variabes used in ieraure 1 Noaion = ime of defau = aance a ime L = Limi a ime Dependen variabes used in he ieraure Loan Equivaen Exposure (LEQ) Facor, Empiricay imi usuay aken a ime accoun opened bu imi ikey o have changed since. ),, (, E EAD x EADF L L L E EADF * EAD for,,, 0 x
5 5 Dependen variabes used in ieraure 2 CCF EAD E CCF * if if,,, x ries o ge beer es of baance a defau by aking accoun of baance a some obsn. poin before defau. u baance a ime of observaion coud be 0 or negaive ) ( if if,, L LEQ L L L E LEQ 0 x No defined when L =- = =- Posiive LEQ coud be due o differen siuaions wih differen characerisics Negaive LEQ ikewise Credi Conversion Facor (CCF) Exposure A Defau Facor (EADF)
6 he Lieraure EAD papers in he corporae secor Araen and Jacobs (2001) Jimenez e a. (2009) Jacobs (2008) Jimenez and Mencia (2009) Reai Loans Qi (2009) 6
7 Disribuion of aances reaive o credi imi a defau 7
8 Proposed new mehodoogy wo-sep mixure mode Le = duraion ime; = even ime; = baance, L = imi Wish o predic, a ime = 0, ousanding baance a ime of defau ( = ) Esimae Surviva mode o predic, a = 0: P( i > L i ) Esimae mode o predic, a =0: L i Esimae mode o predic, a =0: i We wish E ( i ) { P( i Li ) E 0( Li i Li )} { P( i Li ) E ( i i Li )} 0 0 8
9 Daa Credi cards opened beween 2001 and 2010 Minimum paymen compued as percenage of baance end of previous monh Accoun goes ino defau sae if is 3 monhs in arrears (no necessariy consecuive monhs) Accouns removed: on books ess han 9 monhs hose wih zero credi imi a any ime 9
10 Fow char of mehodoogy Porfoio of oans Defaus Non-Defaus raining se: accouns opened up o end 2008 * used o esimae P( i L i ) es se I: accouns opened from beginning 2009 Limi raining se: Accouns ha have baance imi a any poin in he oan * used o esimae L i aance raining se accouns where baance < imi hroughou he oan * used o esimae i es se II accouns opened from beginning 2009 ha are in defau Prediced baance = { P( i {(1 P( i L ) Lˆ } i i i L )) ˆ } i 10
11 11 Mehodoogy 2: Surviva mode 6 3 6, og 0 1 i i i i i i S S L S Z Y X oherwise if Esimaed using discree ime, repeaed evens surviva esimaors accoun dependen accoun dep accoun indep ime independen ime dep ime dep (appicaion vars) (behav. vars) (macroeonomic vars)
12 Mehodoogy 3: condiiona baance and imi equaions Genera specificaion Pane esimaors wih accoun specific random effecs (SEs adjused for firs order seria corren.) y i X 1 i Y 2 Z i i i Assumpions incude 2 2 i ~ IID 0, IID0, i ~ Sampes: condiiona Limi: accouns where i L i for any gives E L L ) 0( i i i condiiona aance : accouns where for any gives E L ) i L i 0( i i i 12
13 Mehodoogy 4: uncondiiona baance equaion From surviva mode ~ i P L Lˆ 1 P L i i i i i ˆ i Prediced baance From imi From baance accoun i ime (pane) mode (pane) mode 13
14 Parameer esimaes Appicaion Variabes Age a app (10 groups) Empoymen saus (5 groups) Surviva P(>L) aance Income, og inary ind for 0 or missing income Limi Macroeconomic variabes agged 6 monhs Surviva aance Limi Average wage earngs No sig No seeced No seeced Credi card ineres rae Consumer confidence + No seeced House price index Landine (Y/N) No sig + No seeced No of cards ime a address No sig No seeced No seeced ime wih bank inary ind.,missing unk w - No seeced No seeced X (5 groups) ehavioura Variabes agged 6 monhs Average rans vaue No cash wihdrawas + No seeced No seeced Amoun of cash wihdrawa No sig No seeced No seeced Credi Limi + + Index of producion - No seeced No seeced ase ineres rae - No seeced No seeced Amoun ousanding, n + No seeced - FSE. Ln - - No seeced RPI No sig + No seeced Unempoymen index + - Mode Specific Variabes Surviva ime o nex even - No imes even has happened ime on books Rae of oa jumps + + No seeced % of monhs in arrears + - No seeced Repaymen amoun No seeced + Ousanding baance N* >800k >900k 14
15 Resus 1: Predicive performance: es ses Compare observed and prediced i Mode es se R 2 Mixure 1: defaus, a observaions Mixure 2: defaus, defau ime ony
16 Resus 2: Observed and Prediced Disribuions (a observed accs) Observed Prediced 16
17 Resus 3: Observed and Prediced Disribuions (a defau ime, defau accouns ony) Observed Prediced 17
18 Concusions Use of a wo sage mixure mode o predic he amoun ousanding, six monhs ahead for individua credi card accouns is feasibe and gives reasonaby accurae resus. Fuure work: We have now incuded macroeconomic variabes (MEVs) in predicive modes of PD, LGD and EAD. We pan o refine hese are use hem o run sress ess for RWA using MC simuaion from observed hisorica disribuions of MEVs. o ry o undersand he reaionships beween behavioura variabes and macroeconomic variabes. 18
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