Osipenko Denis, Retail Risk Management, Raiffeisen Bank Aval JSC, Kiev, Ukraine. Credit Scoring and Credit Control XII conference August 24-26, 2011
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1 Osipenko enis Reail Risk Managemen Raiffeisen Bank Aval JSC Kiev Ukraine Credi Scoring and Credi Conrol XII conference Augus -
2
3 By he reason of risks inerpeneraion: Credi Risk => osses => Balance iquidiy Risk Banking managemen should consider all aspecs of banking aciviy in he decision making process.
4 Credi scoring sysems are he key ools of modern risk managemen paricularly in reail banking. However credi scoring in porfolio managemen should no be applied in isolaion from he enire se of bank s business processes. One of he soluions o he problem of consisen approach o Risk Managemen in reail banking is inegraion of Credi Scoring Models and Common ynamic Flow Models of he bank ha possesses he main feaures of Asses & iabiliies Managemen Sysem. As a resul he problem of opimal conrol for maximizaion of profiabiliy in a given ime period can be solved.
5 Approaches o solving opimal conrol problem for credi porfolio: opimal cu-offs in porfolio level model wih predeermined equiy capial (yn C. Thomas ); profi maximizaion decisions and defaul-based scores (yn C. Thomas ); profi-based cu-offs seing - profi modelling approach (Raymond Anderson ). The fundamenal aspecs of Asses & iabiliies Managemen Sysem: risk managemen inegraion model and liabiliies managemen are defined by Joseph F.Sinkey Jr. (); Sealy () proposed he common approach o he modelling of banking aciviies as he financial firm aciviy; This approach was reviewed and improved by N.Yegorova A.Smulov () o obain simulaion model of he commercial bank.
6 In he curren conex by he Asses and iabiliies Managemen Sysem we undersand mahemaical model of banking aciviies ha conains only such financial insrumens as credis and deposis In he curren conex by he Credi Scoring Sysem we undersand Applicaion Scoring Sysem only alhough i s possible o exend he approach o he full cycle credi scoring sysem Common ynamic Flow Models based on sysem of differenial equaions wih delays. Because of he analyical soluion for hese ypes of equaions is complicaed and possible for limied se of asks we propose o shape he problem wih menioned approach bu o use he calculus of approximaions eposi supply is sable and has marke average rae
7 Profiabiliy maximizaion problem a Credi Porfolio evel iquidiy risk: funding gap can arise in fuure periods Profiabiliy maximizaion problem a Credi and eposi Porfolio evel Credi risk: bad loans rae can increase in fuure periods
8 Profiabiliy maximizaion problem a Credi and eposi Porfolio evel using Credi Scoring Sysem Credi and eposi Porfolio Profiabiliy Maximizaion The liquidiy conrol and credi risk managemen problems are solved in complex in he framework of inegraed model
9 The key elemens which are used in he proposal for Credi Porfolio Auomaic Conrol Sysem are Accepance Rae funcion Bad Rae and Cumulaive Bad Rae funcions (Probabiliy of efaul) and Profiabiliy funcional. For example he cumulaive Bad Rae disribuion funcion is derived from he populaion disribuion funcion (PF) and he Bad Rae disribuion funcion for he applicaion flow wih cu-off score S: where BR ( S) = S max ( s) br( s) ar S S max S ar ( s) ar(s) is a populaion disribuion funcion; br(s) is a funcion of he bad loans share in he score s; S is cu-off score. ds ds
10 Cumulaive Applicaion Flow and Bad Rae disribuions by cu-off score are he core of opimizaion model % Score Bad Rae % % Cu-off Score Cumulaive Bad Rae %..... % Cu-off Score Cumulaive Applicaion Flow % f(x ) Score Applicaion Flow PF
11 ependence of Income and Expenses on cu-off score on Porfolio level Toal coss = Fixed Cos + Variable Cos + osses due o defauls Income i n u y e n o m s se n e x p Inc* e s TC* e m co In oss* VC* Profi osses VC Toal Coss FC FC* S* Score S
12 ynamic maximizaion crieria Z of he credi porfolio profiabiliy is defined by he following funcional: Z = ( S; ) AR( ; S( ) ) AF( ) APR BR Exp where sar ime end ime S cu-off score AR accepance rae defined by cumulaive populaion disribuion funcion APR Annual Percenage Rae AF Applicaion Flow funcion Avg average size of graned loan AvgBad average size of bad loan in porfolio Exps oal expenses per m.u. G oss Given efaul ( ) ( BR( S( ) ) G( ) ) Avg( ) ( S( ) ) G( ) AvgBad( ) ( ) Avg( ) ) Z (S iliy b fia ro P Zmax S* Cu-off score S d max
13 Populaion isribuion Funcion shifs and as a resul Profiabiliy Funcional biases (Bad Rae disribuion is sable by calibraed score) PF Biases PF PF PF Profiabiliy Biases Profi Profi Profi A differen period of ime he populaion disribuion funcion changes mean and sandard deviaion As resul he Profiabiliy funcion changes is shape
14 Because of he economic environmen flucuaions problem of he dynamic conrol over he credi porfolio characerisics needs o be solved. The displacemens of he poin (S* AR*) from posiion o posiions and resuls from shifs of he Cumulaive Accepance Rae curve o AR Cum and he AR Cum respecively. To sabilize he sysem performance classic conrol heory echniques can be used e.g. feedback conroller wih he gain facors. For example he cu-off score a ime + can be defined as: ( ) * * ( ) = AR( ; S( ) ) AR ( ) S + α + S Thus adjused cu-off score depends on curren Accepance Rae funcion AR(; S()) he arge Accepance Rae AR*() iniial opimal cu-off S* and gain facor α.
15 e s se he A&M Sysem as differenial equaions wih delays. The loans debi urnover is he demands funcion and is defined by applicaion flow as ( U F ; ) = AF( U ( ) F ( ) ) The loans credi urnover is defined as Cr ( U ) F S; = ( ( U F ; τ ) ( τ ) m i ( ) + BR dτ rl τ where i (-τ) is credi ineres raes a he momen of ime -τ; m is maximum erm of credi; τ is ime lag (delay) which reflecs he erm of he loan; The loans credi urnover funcion includes he risk componen which is defined as (-BR) and corresponds o he payback credi amoun.
16 Hereinafer we consider one of he approaches o Asses & iabiliies Managemen Sysem modelling. The dynamic of he sysem saus X (curren funds of he bank) based on he accouning balance is defined by differenial equaion wih ime delay τ a he momen of ime : ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) C IB F U F U d rd i F U F U X Cr Cr n Cr ; ; ; ; = τ τ τ τ &
17 e s inroduce new conrol ino he differenial equaion cu-off S. The volume of graning loans depends on accepance rae as well as on pricing and adverising conrols. ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) C IB F U F U d rd i F U F U X Cr Cr n Cr ; ; ; ; ; = S S τ τ τ τ &
18 The demand funcion is changed by new conrol inroducion. The loans debi urnover is he demands funcion and is defined as The loans credi urnover is defined as S max ( U F S; ) = AF( U ( ) F ( ) ) ar( s) S max ( ) ( ) ( ) ( ( ) ( ) ar s br s ds m i ( ) τ S Cr U F S; = U F S; τ + S dτ max rl τ ar( s) ds S ( ) where i (-τ) i (-τ) are deposi and credi ineres raes a he momen of ime -τ; S is cu-off score; m is maximum erm of credi; τ is ime lag (delay) which reflecs he erm of he loan. S ( ) ds The Expeced osses are included ino he Cr funcion.
19 As a resul of he research he inegral Credi Porfolio ynamic Model and Asses & iabiliies Managemen Sysem Model were developed and he gross profi funcional was inroduced which is defined as ( ) P = m n ( ( U F S; τ )) Cr ( U F ; τ ) i ( τ ) i rlτ ( τ ) rd dτ dτ + IB ( ) r ( ) C( ( ) ( ) ) where Cr and are he loans credi urnover and deposis debi urnover i and i are he loans and deposis ineres raes respecively τ is a lag (delay) equal o he erm of he loan; S is a cu-off score; C(()()) is a cos funcion; U U are he conrols; τ IB d max F F are he exernal facors. Solving he maximizaion problem based on his funcional is he maer of variaions calculus hough he funcional is oo complicaed for he analyical echniques.
20 Wha is he bes sraegy o increase porfolio profiabiliy? Increase ineres rae margin growh (if demand is inelasic) ecrease ineres rae applicaion flow growh (if demand is elasic) Adverising campaign/acions applicaion flow growh All his sraegies can bias he populaion disribuion. Wha is he decision and consequences? Increase accepance rae increase/fixed bad rae; Fixed accepance rae increase/decrease bad rae (i depends on disribuion shif) Scenario analysis and simulaion can help o answer his quesion and find he mos opimal sraegy of conrols. If you se cu-offs hen review he fuure funds availabiliy. oss now gain in fuure!
21 The AM sysem based on he dynamic models in his paricular case employing delayed differenial equaions for he bank s aciviies simulaion is one of he mos suiable approaches o effecive risk-based managemen. There are hree main direcions for applicaion and furher research: Invesigaion of he macroeconomics facors impac on he reail banking and developmen of appropriae conrol sraegy for he porfolio on decision making process level; credi porfolio and bank liquidiy sress-esing esing and he anicrisis sraegies developmen (conrols and decisions); Opimal dynamic conrol modelling based on full cycle scoring sysems and dynamic flow models for he muli-arge managemen problems of: profi maximizaion in he shor- and long-erm period reenion of he marke share and/or porfolio qualiy on he defined level; challenger sraegy esing Theoreical and concepual approach o he inegraion of: credi porfolio conrol model based on full cycle scoring sysems (response applicaion behavioural collecion ariion ec.) AM sysem based on dynamic flow model a he eniy level. Simulaion process is a producive way o find he opimal soluion o complex maximizaion problem wih sysem of limiaions.
22 Osipenko enis Reail Risk Managemen Raiffeisen Bank Aval JSC Kiev Ukraine
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