CAMBRIDGE BANKING MODEL

Transcription

1 Cmridge Centre for isk Studies eserch Showcse 21 June 2015 CAMBIDGE BANKING MODEL Dr Olf Bochmnn eserch Associte, Centre for isk Studies Dr Fio Cccioli Dept of Computer Science, University College London

2 Cmridge Bnking Model Olf Bochmnn 1 Fio Cccioli 2 1 University of Cmridge Centre for isk Studies 2 University College London Deprtment of Computer Science O.Bochmnn@cm.c.uk June 21, 2015

3 Overview Stress Test Frmework Finncil Network Model Blnce Sheets Loss in Equity Su ered Loss in Equity Induced to the System Distress Propgtion Circle Asset Losses Inter-Bnk Losses Fire Sle Network reconstruction Fitness Model Exposure Volume Alloction Stress Test Scenrios Stress Test esults

4 Finncil Network Model n institutions (nks) Bnks cn invest in n 1 institutions A 0.3 B C

5 Finncil Network Model n institutions (nks) Bnks cn invest in n 1 institutions A A 0.3 B 0.2 B C C

6 Finncil Network Model n institutions (nks) m externl ssets 0.3 A Bnks cn invest in n 1 institutions or m ssets. A B 0.2 B C C

7 Finncil Network Model n institutions (nks) m externl ssets 0.3 A Bnks cn invest in n 1 institutions or m ssets. A B 0.2 B C C Assets (liilities) cn e externl or inter-nk, with totls s mÿ nÿ A e i = A e ik nd A i = 0.2 A ij k=1 j=1

8 Blnce Sheets Stte Vriles E i (t) equity of institution i t time t A i (t) totl ssets of institution i t time t D i (t) totl liilities of institution i t time t A ij A e ik mount institution i lends to institution j mount institution i invests in sset k l i (t) leverge of institution i t time t Assets Liilities A e = D =0.6 A =0.7 E Tle: Blnce Sheet of Bnk A The lnce sheet is defined s A e i (t)+a i (t) =A i (t) = D i (t)+e i (t) Leverge of nk is the rtio of ssets nd equity. l i (t) = A i(t) E i (t)

9 Blnce Sheets (cont.) Finncil System l i (t) leverge of institution i t time t lik e (t) externl leverge of institution i with respect to sset k t time t lij (t) inter-nk leverge of institution i towrds institution j t time t li e (t) totl externl leverge of institution i t time t l i (t) totl inter-nk leverge of institution i t time t Leverge (disggregted) of nk is the sum of it s externl nd inter-nk leverge. l i (t) = Ae i (t) E i (t) + A i (t) E i (t) = l e ik(t)+l ij (t) lik e cn e seen s elements of the djcency mtrix of n i-prtite externl leverge network nd lij of mono-prtite internk leverge network. The totls would e the sum long the columns: l e i = mÿ k=1 l e ik nd l i = nÿ lij j=1

10 Loss in Equity Su ered Distress or Vulnerility h i (t) cumultive reltive equity loss of institution i t time t H(t) cumultive reltive equity loss of of the finncil system t time t losses of nks reltive to it s equity nd with respect to seline t t = 0: h i (t) =min{1, E i(0) E i (t) } E i (0) with nk under distress for h i (t) œ (0, 1] t nd defult for h i (t) = 1. losses of the finncil system reltive to totl equity nd with respect to seline t t = 0 is the weighted verge cumultive reltive equity loss of ech nk: nÿ H(t) = w i h i = i=1 nÿ i=1 E i (0) q nj=1 E j (0) h i

11 Loss in Equity Induced to the System Impct D i glol reltive equity loss induced y the defult of institution i Detnk D i is the impct induced y the defult of ech nk individully on the system:. nÿ D k (t) = h i (T )E i (0) i=1 This is the exct solution for systemic risk s defined in BCBS [2013]

12 Distress Propgtion Circle Asset Losses negtive shock on the vlue of ssets cuses losses in nks, which is sored y equity. Inter-Bnk Losses Inter-Bnk Losses: distress from sset losses puts inter nk oligtions under pressure. Those losses re gin sored y equity. Fire Sle nks need to djust their leverge to meet regultory requirements y selling ssets. The price impct leds to further pressure on sset prices. This closes the virtuous circle.

13 Asset Losses Price Shock p k (t) unit price of sset k t time t r k (t) reltive price (shock) of sset k t time t shock r k (1) = p k(0) p k (1) p k (1) < 0 on the vlue of sset k reduces the vlue of the investment in externl ssets in nk i y ÿ r k (1)A ik = ÿ ÿ r k (1)l ik E i = E i r k (1)l ik k k k the loss needs to e compensted y reduction in equity A e ik(0) A e ik(1) = ÿ r k (1)A e ik(0) = E i (0) E i (1) k individul nd glol reltive equity loss t time t =1re: h i (1) = min{1, ÿ nÿ l ik r k (1)} nd H(1) = w i h i (1) k i=1

14 Inter-Bnk Losses Distress Propgtion V t (A ij ) mrket to mrket vlue of A ij The distress tht propgtes from j into ech of the lenders i is the reltive loss with respect to the originl fce vlue A ij V t (A ij ) A ij = f (h j (t 1)). individul reltive loss in equity: Y h i (t) = E i(t) E i (0) ] =min E i (0) [ 1, ÿ = l e i + ÿ j iœs A (t) Z ^ l ij f (h i (t 1)) \ lij lj e r(1) where S A (t) is the set of ctive 1 nodes. 1 nodes tht trnsmit distress t time t, s in Bttiston et l. [2012]

15 Fire Sle Price Impct i quntity of ssets of nk i ˆp shock price price impct fctor Bnks try to sell externl ssets in order to repy oligtions to move to the originl leverge: l i (0) = l i (t) = Ae i (t)+a i (t) E i (t) = ( i(0) + )ˆp + A i (t) E i (t) price impct is liner (proportionl to reltive chnge in demnd): reltive loss in equity: h i (t) = E i(t) E i (0) E i (0) i r(t) = i (0) = D i(0) i (0)ˆp (l i e ) 2 r(1) = l e i + ÿ j l ij l e j r(1) + D i(0) i (0)ˆp (l e i ) 2 r(1)

16 Network reconstruction Inter-Bnk Network 0.6, , 0.5 B A C 0.2 c d c d 0.5, 1.1

17 Network reconstruction Inter-Bnk Network 0.6, , 0.5 B A C 0.2 c d c d 0.5, 1.1

18 Network reconstruction Inter-Bnk Network 0.6, , 0.5 B A C 0.2 c d c d 0.5, 1.1

19 Network reconstruction Inter-Bnk Network 0.6, , 0.5 B A C 0.2 c d c d 0.5, 1.1

20 uiz Why re this two mtrices similr? c d c d

21 uiz Why re this two mtrices similr? c d c d c d c d Both mtrices hve the sme sum over rows nd columns I no unique mpping etween mrginls nd exposure I possile networks rnge from mximum entropy to minimum density (e.g. diversifiction vs. costs for reltionships)

22 Network reconstruction Fitness Model xi in xi out p ij lending propensity orrowing propensity exposure proility Lending nd orrowing propensity is the reltive exposure xi in = A i q j A j nd xi out = L i q j L j Fitness model pplied to internk network we ssume x i to e the fitness level. The proility tht nk i lends to nk j is : p ij = zx in i 1+zx in i x out j x out j, where z is free prmeter. The totl numer of links is equl to the expected vlue q q i j =i p ij [De Msi et l., 2006]

23 Network reconstruction (cont.) Exposure Volume Alloction fi ij verge reltive exposure fi ij = x in ij 2 + xij out Constrint: sum of exposures equl totl ssets of nk i 1= ÿ j fi ij Interctive prop. fitting lgorithm: estimte the reltive exposure fi ij iterting (1) nd (2). (1) ˆfi ij Õ = q ˆfi ij A i j ˆfi ij A (2) ˆfi ÕÕ ij = q ˆfiÕ ij i ˆfiÕ ij q j ˆfi ij A i A nd q j ˆfi ji L i L < 1% yes L i L no

24 Stress Test Scenrios Trigger y Asset Shock Shock on ssets cuses losses in nks; losses propgte to the inter-nk mrket, spred cross the network cuses further losses. Feedsck on sset prices. Historic exmples: I The Tulip nd Bul Crze (1637) I South Se Bule (1720) I Suprime Mortgge Crisis (2008) Trigger y Bnk Defult Bnks fil nd defult on their oligtions. Losses propgte vi inter-nk nd common sset holdings. Feedck on prises. Historic exmples: I Jy Cooke & Compny crisis (1873) I Bnker s Pnic (1907) I Gret Depression (1929)

25 Stress Test esults 1 externl ssets 0.8 Vulnerility H Yer 2 this dt is for illustrtion only, Tufte [2001] 2

26 Stress Test esults externl ssets inter nk Vulnerility H Yer 2 this dt is for illustrtion only, Tufte [2001] 2

27 Stress Test esults externl ssets inter nk fire sle Vulnerility H Yer 2 this dt is for illustrtion only, Tufte [2001] 2

28 eferences S. Bttiston, M. Pulig,. Kushik, P. Tsc, nd G. Cldrelli. Detrnk: Too centrl to fil? finncil networks, the fed nd systemic risk. Scientific eports, 2(541),2012. BCBS. Glol systemiclly importnt nks: updted ssessment methodology nd the higher loss sorency requirement. Technicl report, BIB, UL G. De Msi, G. Iori, nd G. Cldrelli. Fitness model for the itlin internk money mrket. Phys ev E Stt Nonlin Soft Mtter Phys, 74(6Pt2): , Dec E.. Tufte. The visul disply of quntittive informtion. Grphics Press, Cheshire, Conn., 2nd ed edition, ISBN

29 The End