Banks on the verge of a crisis: phase transitions and hysteresis in - PowerPoint PPT Presentation

Banks on the verge of a crisis: phase transitions and hysteresis in banking systems Tomaso Aste 1 , 2 1 Department of Computer Science, University College London, 2 Systemic Risk Centre, London School of Economics and Political Sciences References: Annika Birch and TA "Systemic Losses Due to Counter Party Risk in a Stylized Banking System" Journal of Statistical Physics 156 (2014) 998 - 1024 Annika Birch, Zijun Liu & TA "A counterparty risk study for the UK banking system" ssrn.com/abstract=2599891, under submission T Aste (UCL, SRC) Phase Transitions in Banking Systems CoSyDy, QMUL, 06/07/16 1 / 24

Phase transitions Phase transition Change in the system state T Aste (UCL, SRC) Phase Transitions in Banking Systems CoSyDy, QMUL, 06/07/16 2 / 24

Phase transitions Phase transition Change in financial market structure across the banking crisis ES ( T a , T b ): NYSE data set 18/12/2000 1 0.9 24/12/2002 0.8 27/12/2004 0.7 26/12/2006 0.6 0.5 26/12/2008 0.4 28/12/2010 0.3 28/12/2012 0.2 0 4 6 8 0 2 2 0 0 0 0 1 1 0 0 0 0 0 0 0 0 2 2 2 2 2 2 2 / / / / / / 2 / 2 2 2 2 2 1 2 1 1 1 1 1 1 / / / / 8 / 7 / 6 / 6 8 8 4 1 2 2 2 2 2 2 N Musmeci, TA, Tiziana Di Matteo, arXiv:1605.08908 (2016) T Aste (UCL, SRC) Phase Transitions in Banking Systems CoSyDy, QMUL, 06/07/16 3 / 24

Phase transitions What is a phase transition? in Physics - Change in the system state (liquid to solid) as consequence of a change in the parameters (temperature, pressure) - Change in the internal energy - Change in the system entropy - Emergence of collective properties - Order parameter becomes finite (symmetry breaking) - Appearence of long-range correlations near the transition point - Appearance of “soft modes” in General - Change in the system state - ? T Aste (UCL, SRC) Phase Transitions in Banking Systems CoSyDy, QMUL, 06/07/16 4 / 24

Tipping Points Tipping Point the point at which small changes or incidents can cause large changes - An object at a point of unstable equilibrium - A rare phenomenon becoming rapidly more common - The point at which a technology becomes dominant and the “winner takes all” - A change happening as a consequence of a small cause that cannot be easly reverted T Aste (UCL, SRC) Phase Transitions in Banking Systems CoSyDy, QMUL, 06/07/16 5 / 24

Tipping Points Tipping Point the point at which small changes or incidents can cause large changes T Aste (UCL, SRC) Phase Transitions in Banking Systems CoSyDy, QMUL, 06/07/16 6 / 24

Tipping Points Tipping Point the point at which small changes or incidents can cause large changes T Aste (UCL, SRC) Phase Transitions in Banking Systems CoSyDy, QMUL, 06/07/16 7 / 24

Tipping Points Tipping Point the point at which small changes or incidents can cause large changes T Aste (UCL, SRC) Phase Transitions in Banking Systems CoSyDy, QMUL, 06/07/16 8 / 24

Simple stylized banking model UK banking system data from BoE We use form supervisory reports from Bank of England (BoE) for the years 2011, 2012 and 2013. Lending (unsecured, secured and undrawn) Holdings of equity and fixed-income securities (marketable securities) issued by banks; Credit default swaps (CDS) bought and sold Securities lending and borrowing (gross and net of collateral); Repo and reverse repo (gross and net of collateral); Derivatives exposures (with breakdown by type of derivative) UK banks have to report their 20 largest counterparties to the BoE semi-annually. If the top 20 does not have at least six UK-based counterparties, banks report exposures to up to six UK-based counterparties in addition to the top 20. Branches of foreign banking groups in the UK are not included. There are 176 UK banks reporting to BoE. T Aste (UCL, SRC) Phase Transitions in Banking Systems CoSyDy, QMUL, 06/07/16 9 / 24

Simple stylized banking model UK Banking Network T Aste (UCL, SRC) Phase Transitions in Banking Systems CoSyDy, QMUL, 06/07/16 10 / 24

Simple stylized banking model UK Banking Network (a) In-degree (b) In-weight (c) Out-degree (d) Out-weight T Aste (UCL, SRC) Phase Transitions in Banking Systems CoSyDy, QMUL, 06/07/16 11 / 24

Simple stylized banking model Phase transition in a Stylized Banking System We propose a model combing the balance sheet based model 12 , with the contagion model 3 creating a stylized banking system 4 . We distinguish between normally operating banks and distressed banks: I 1 if bank i is operating normally S i ( t ) = . 0 if bank i is distressed We consider a system of N banks that borrow and deposit money into each-other though an interbank network 1 P. Gai et al. (2007). In: Journal of Risk Finance 8.2, pp. 156–165. 2 E. Nier et al. (2007). In: Journal of Economic Dynamics and Control 31.6, pp. 2033–2060. 3 J. P. Solorzano-Margain et al. (2013). In: Computational Management Science , pp. 1–31. 4 S. Heise et al. (2012). In: The European Physical Journal B 85.4, pp. 1–19. T Aste (UCL, SRC) Phase Transitions in Banking Systems CoSyDy, QMUL, 06/07/16 12 / 24

Simple stylized banking model Balance Sheet Liabilities: L i ( t ) = sum of the bank’s customer Capital : E i (t)=A i (t)-L i (t) Interbank Lending deposits, ˆ L i ( t ) , and interbank bor- rowings q N j g j , i . ∑ g i , j ( t ) S j ( t ) a σ b σ p(t) Deposits j = 1 ˆ L i ( t ) Assets: A i ( t ) = sum of non-interbank assets, Non Interbank Assets (stocks + external assets) ˆ A i ( t ) , interbank lending to non Interbank Borrowing ˆ A i ( t ) distressed banks q N j g i , j ( t ) S j ( t )  L i ( t ) = ∑ g j , i ( t ) j = 1 Bank’s capital: Liabili&es L i (t) Assets A i (t) E i ( t ) = A i ( t ) − L i ( t ) ( > 0) T Aste (UCL, SRC) Phase Transitions in Banking Systems CoSyDy, QMUL, 06/07/16 13 / 24

Simple stylized banking model Systemic risk S j Capital : E i (t)=A i (t)-L i (t) Interbank Lending N ∑ g i , j ( t ) S j ( t ) a σ b σ p(t) g i , j S j Deposits j = 1 ˆ L i ( t ) S i Non Interbank Assets (stocks + external assets) Interbank Borrowing ˆ A i ( t ) N  L i ( t ) = ∑ g j , i ( t ) j = 1 Liabili&es L i (t) Assets A i (t) Annika Birch and TA "Systemic Losses Due to Counter Party Risk in a Stylized Banking System" Journal of Statistical Physics 156 (2014) 998 - 1024 Annika Birch, Zijun Liu & TA "A counterparty risk study for the UK banking system" ssrn.com/abstract=2599891, under submission T Aste (UCL, SRC) Phase Transitions in Banking Systems CoSyDy, QMUL, 06/07/16 14 / 24

Simple stylized banking model Dynamics Balance Sheet Equation: a bank operate normally if A i ( t ) ≥ L i ( t ) , it is in distress otherwise. The state of a bank at time t + 1 is I 1 if A i ( t ) − L i ( t ) ≥ 0 S i ( t + 1 ) = if A i ( t ) − L i ( t ) < 0 . 0 The state of the system is associated with two main quantities: randomly distributed with balance sheet quantities are all banks same size and Homogeneous system: Non-Counterparty-dependent balance sheet mean: a σ ; ˆ L i ( t ) A i ( t ) − Variance: σ 2 ¸ ˚˙ ˝ ¸ ˚˙ ˝ Liabilities Non-Counterparty-dependent assets Counterparty-dependent assets: q j g i , j S j ( t ) mean: b σ p t T Aste (UCL, SRC) Phase Transitions in Banking Systems CoSyDy, QMUL, 06/07/16 15 / 24

Simple stylized banking model Dynamics Balance Sheet Equation: a bank operate normally if A i ( t ) ≥ L i ( t ) , it is in distress otherwise. The state of a bank at time t + 1 is I 1 if A i ( t ) − L i ( t ) ≥ 0 S i ( t + 1 ) = if A i ( t ) − L i ( t ) < 0 . 0 The state of the system is associated with two main quantities: randomly distributed with balance sheet quantities are all banks same size and Homogeneous system: Non-Counterparty-dependent balance sheet mean: a σ ; ˆ L i ( t ) A i ( t ) − Variance: σ 2 ¸ ˚˙ ˝ ¸ ˚˙ ˝ Liabilities Non-Counterparty-dependent assets Counterparty-dependent assets: q j g i , j S j ( t ) mean: b σ p t T Aste (UCL, SRC) Phase Transitions in Banking Systems CoSyDy, QMUL, 06/07/16 15 / 24

Onset of a fragile state with irreversible dynamics Fixed Point Solutions (Normal distribution) p = Φ ( bp − a ) p t + 1 = Φ ( bp t − a ) 1 Small a (large non-interbank assets): b= 7 0.9 only one solution p = 1 0.8 0.7 - all banks functioning normally Φ ( bp − a ) a 2 = 1.96 0.6 Large a (small non-interbank assets): 0.5 only one solution p = 0 0.4 a 1 = 5.04 0.3 - all banks in distress 0.2 Intermediate a: three solutions 0.1 - one unstable and 2 stable solutions 0 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 p The central fixed point is unstable and forms a barrier. The dynamics becomes irreversible. T Aste (UCL, SRC) Phase Transitions in Banking Systems CoSyDy, QMUL, 06/07/16 16 / 24