Specialized Lending Rating Model using AHP

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1 Specilized Lending Rting Model using AHP Credit Risk Modelling Edinburgh, 28th August 2013.

2 Agend IPRE model Vlidtion Conclusion AHP methodology Specilized lending 2

3 Specilized lending Specilized lending - 4 subclsses: Income Producing Rel Estte (IPRE) Project Finnce Object Finnce Commodities Finnce Bsel Commitee pproches: Stndrdized pproch Foundtion IRB Advnced IRB Slotting pproch (only for specilized lending) 3

4 AHP METHODOLOGY Credit Risk Modelling Edinburgh, 28th August 2013.

5 Anlyticl hierrchy process (methodology overview) Introduced by Thoms L. Sty Hierrchicl structure gol on top, criteri nd subcriteri in the middle, options on bottom (exmple of one criteri nd one subcriteri level): GOAL C1 C2 C3 SC1 SC2 SC3 SC4 SC5 SC6 OPTION1 OPTION2 OPTION3 5

6 Anlyticl hierrchy process (1st step) GOAL C1 C2 C3 SC1 SC2 SC3 SC4 SC5 SC6 OPTION1 OPTION2 OPTION3 For ech subcriteri construct pirwise comprison mtrices nd corresponding priority vector: e.g. SC 1 : 3 3 Option1 Option2 Option3 Option normliztion Option1 x 1 Option2 1/ clcultion Option2 y 1 x 1 +y 1 +z 1 = 1 of eigen vector 6 Option3 1/ 13 1/ 23 1 & eigen vlue Option3 z 1

7 Pirwise comprison How is pirwise comprison conducted? Using scle (1-9): 7 Intensity of Importnce Definition 1 Equl importnce 2 Wek or slight 3 Moderte importnce 4 Moderte plus 5 Strong importnce 6 Strong plus 7 Very strong or demonstrted importnce 8 Very, very strong 9 Extreme importnce Construct positive reciprocl mtrix: i1 n i 2 n2 1 j 2 j ij 1n 2n nn where: 11 = 22 =... = nn = 1, ji = ij -1

8 Consistency index nd consistency rtio How to check whether the weights in comprison mtrix consistent? We clculte eigenvlues of comprison mtrices: Condition for perfectly consistent weights: ik = ij jk Condition for perfectly consistent mtrices: λ mx = n Consistency index: Consistency rtio: CR 0,1 cceptble inconsistency Rndom consistency index (RI) by Sty: 8 n RI

9 Anlyticl hierrchy process (2nd step) GOAL C1 C2 C3 SC1 SC2 SC3 SC4 SC5 SC6 OPTION1 OPTION2 OPTION3 For ech subcriteri group construct mtrices out of eigen vectors: x x x y 1 z 1 x 1 x 2 y 1 y 2 y 3 z 3 x 3 x 4 y 3 y 4 y 5 z 5 x 5 x 6 y 5 y 6 x 2 z 1 z 2 x 4 z 3 z 4 x 6 z 5 z 6 y 2 y 4 y 6 9 z 2 z 4 z 6

10 Anlyticl hierrchy process (3rd step) GOAL C1 C2 C3 SC1 SC2 SC3 SC4 SC5 SC6 OPTION1 OPTION2 OPTION3 For ech criterion construct pirwise comprison mtrix nd corresponding priority vector: e.g. C 1 : SC1 SC2 SC1 SC2 1 b 12 1/b 12 1 normliztion clcultion of eigen vector & eigen vlue SC1 SC2 i 1 j 1 i 1 +j 1 = 1 10

11 Anlyticl hierrchy process (4th step) GOAL C1 C2 C3 SC1 SC2 SC3 SC4 SC5 SC6 OPTION1 OPTION2 OPTION3 For ech criteri clculte priority vector: 3 2 x 1 x 2 y 1 y 2 z 1 z i 1 j 1 = k 1 m 1 n x 3 x 4 y 3 y 4 z 3 z i 2 j 2 = k 2 m 2 n x 5 x 6 y 5 y 6 z 5 z 6 i 3 j 3 = 2 1 k 3 m 3 n 3 11

12 Anlyticl hierrchy process (5th step) GOAL C1 C2 C3 SC1 SC2 SC3 SC4 SC5 SC6 OPTION1 OPTION2 OPTION3 Construct mtrix out of eigen vectors nd construct pirwise comprison mtrix,corresponding priority vector nd eigen vlue: k 1 k 2 k 3 C1 3 3 C2 C3 m 1 n 1 m 2 n 2 m 3 n 3 C1 1 c 12 c 13 normliztion C1 d k 1 k 2 k 3 m 1 m 2 m 3 n 1 n 2 n 3 C2 C3 1/c 12 1 c 23 1/c 13 1/c 23 1 clcultion of eigen vector & eigen vlue C2 C3 f g = 1

13 Anlyticl hierrchy process (finl step) GOAL C1 C2 C3 SC1 SC2 SC3 SC4 SC5 SC6 OPTION1 OPTION2 OPTION3 Clculte finl priority vector on which decision will be mde: 3 3 k 1 k 2 k 3 d Option1 q m 1 m 2 m 3 f = Option2 r mx {q,r,t} choice n 1 n 2 n 3 g Option3 t 13

14 IPRE MODEL Credit Risk Modelling Edinburgh, 28th August 2013.

15 Model segmenttion Four sub models: 1) Constructed rel estte for sle 2) Rel estte under construction for sle 3) Constructed rel estte for lese 4) Rel estte under construction for lese Five top level criteri common to ll four sub models: 1) Finncil strength 2) Politicl nd legl environment 3) Project nd/or sset chrcteristics 4) Strength of the sponsor nd developer 5) Security pckge Subcriteri nd their weights differ cross sub models 15

16 Model overview Exmple of rting criteri for one of the submodels: Rting Finncil strength Politicl & legl enviroment Asset chrcteristics Strength of sponsor nd developer Security pckge Brek even Politicl enviroment Competition Shre in equity Collterl Price sensitivity Legl frmework Loction Cost overrun Income control LTV Design Reputtion SPV Pre-sles Asset condition Network strength... 16

17 IPRE model vs stndrd AHP methodology Usully in AHP options re crdinl vribles, while in IPRE they re on ordinl scle (4 slotting grdes: from 1 strong to 4 wek) This hs impct on the first step: RATING C1 C2 C3 SC1 SC2 SC3 SC4 SC5 SC6 SLOT1 SLOT2 SLOT3 SLOT4 17

18 IPRE model vs stndrd AHP methodology RATING C1 C2 C3 SC1 SC2 SC3 SC4 SC5 SC6 SLOT1 SLOT2 SLOT3 SLOT4 Pirwise mtrix for ech subcriterion is not constructed (it is meningless to compre one slot to the other) Alterntive pproch: for every subcriterion we construct vector tht clssifies tht subcriterion to certin slot, e.g. one subcriterion clssified to 3rd slot: Slot 1 Slot 2 Slot 3 Slot After tht process is the sme s in stndrd AHP methodology

19 Vlidtion Low defult portfolio usul bcktesting not fesible Entire IPRE portfolio of the bnk ws rted by 3 deprtments: Sles Underwriting Monitoring Consistency of rting distribution mong these deprtments indicte model qulity Consistency ws clculted using rtings mtrix nd slots drift, e.g: Credit Risk Underwriting Totl Slots drift % 19 Sles Totl or 1 29% +2 or -2 2% +3 or -3 0%

20 Conclusion Strengths: Simple Interpretble Usge of domin experts knowledge Weknesses: Time consuming Decision ftigue (drop of concentrtion) Correltion between subcriteri (treshold for correltion?) 20

21 References T.L. Sty, The Anlytic Hierrchy Process: Plnning, Priority Setting, Resource Alloction, McGrw Hill, T.L. Sty, Decision mking with the nlytic hierrchy process, Int. J. Services Sciences, vol. 1, no. 1, BIS Bsel Committee on Bnking Supervision, Bsel II: Interntionl Convergence of Cpitl Mesurement nd Cpitl Stndrds: A Revised Frmework Comprehensive Version, 200 Directive 2006/48/EC of the Europen Prliment nd of the Council, Bsel Committee on Bnking Supervision, Working Pper on the Internl Rtings- Bsed Approch to Specilised Lending Exposures, N. Srdchom, The vlidtion of nlytic hierrchy process (AHP) scoring model, Interntionl Journl of Libility nd Scientific Enquiry, vol. 4, no. 2, pp ,

22 Contcts Igor Kluđer Ivn Augustin Mlden Drgičević 22

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Chapter URL: This PDF is selection from n out-of-print volume from the Ntionl Bureu of Economic Reserch Volume Title: Price nd Quntity Trends in the Foreign Trde of the United Sttes Volume Author/Editor: Robert E.