A multi-layer network perspective on systemic risk

Transcription

1 A multi-layer network perspective on systemic risk Frank Schweitzer In collaboration with: R. Burkholz, A. Garas

2 Chair of Systems Design Multi-layer network perspective on systemic risk Introduction Frank Schweitzer MFM Winter 26 Meeting Stern School, NYU Jan 26 2 / 24 Chair of Systems Design at ETH Zurich Main Research Areas Economic Networks & Social Organizations e.g. ownership networks, R&D networks, financial networks,... e.g. online communities, OSS projects, animal societies,... Methodological Approach: Data Driven Modeling economic databases: ORBIS, Bloomberg, patent databases online data: user interaction, communication records, blogs

3 What is the problem? Data: FDIC (Federal Deposit Insurance Corporation), 2 Chair of Systems Design Multi-layer network perspective on systemic risk Introduction Frank Schweitzer MFM Winter 26 Meeting Stern School, NYU Jan 26 3 / 24

4 What is the problem? Possible explanations: Cascades: spreading failure domino direct interaction: failure affects connected agents Macroeconomic feedback: indirect coupling popcorn no interaction, but externally driven toward critical state Data: FDIC (Federal Deposit Insurance Corporation), 2 Chair of Systems Design Multi-layer network perspective on systemic risk Introduction Frank Schweitzer MFM Winter 26 Meeting Stern School, NYU Jan 26 3 / 24

5 Chair of Systems Design Multi-layer network perspective on systemic risk Systemic risk Frank Schweitzer MFM Winter 26 Meeting Stern School, NYU Jan 26 4 / 24 Risk as endogeneous to the system Systemic risk risk that a whole system comprised of many agents fails macroscopic property that emerges from the nonlinear interactions of agents and is amplified through macroscopic feedback complements exogeneous risk systems generate the conditions of their failure themselves failure of the few gets amplified interaction

6 Chair of Systems Design Multi-layer network perspective on systemic risk Systemic risk Frank Schweitzer MFM Winter 26 Meeting Stern School, NYU Jan 26 5 / 24 Bottom-up Approach Internal agent dynamics s i (t + ) = Θ[φ i (t, s, A) θ i ] fragility φ i (t) > : depends on neighbors (interaction matrix A) threshold θ i : individual conditions (heterogeneity) dynamics of φ i (t) depends on degree distribution p(k), distribution of load to neighbors probabilistic approach: prediction of systemic risk ϱ(t)

7 Chair of Systems Design Multi-layer network perspective on systemic risk Systemic risk Frank Schweitzer MFM Winter 26 Meeting Stern School, NYU Jan 26 6 / 24 Predicting systemic risk σ µ Phase diagram of systemic risk Mathematical network model various degree distributions p(k) different threshold distributions p(θ) finite/infinite networks different load distribution mechanisms Heterogeneity of agents matters! µ : increasing global instability σ: measure of initial heterogeneity in θ i small variations in initial conditions lead to complete failure non-monotonous behavior: intermediate σ most dangerous

8 The need to combine two perspectives Micro: Socioeconomic perspective strategic behaviour of single agents network architecture Macro: Physics/Computer science perspective statistical regularities of the network as a whole Data-driven modeling: infer interaction rules of agents more details in: F. Schweitzer, G. Fagiolo, D. Sornette, F. Vega-Redondo, D. R. White (29). Economic Networks: What Do We Know And What Do We Need To Know?, Advances in Complex Systems 2 (29) 47 Chair of Systems Design Multi-layer network perspective on systemic risk Network approach Frank Schweitzer MFM Winter 26 Meeting Stern School, NYU Jan 26 7 / 24

9 Networks are constructed aggregation over time network density depends on time window importance of nodes changes temporal ordering cannot be preserved Chair of Systems Design collaboration event sliding window t t+3d time Multi-layer network perspective on systemic risk Network approach Frank Schweitzer MFM Winter 26 Meeting Stern School, NYU Jan 26 8 / 24

10 Networks are reconstructed aggregation over activity direct interactions are often unknown aggregation at institutional level decomposition heuristics co-appearence temporal network, ranked activities weights for links core-periphery structure Data: US Office of the Comptroller of the Currency, 998/Q4-22/Q4 Chair of Systems Design Multi-layer network perspective on systemic risk Network approach Frank Schweitzer MFM Winter 26 Meeting Stern School, NYU Jan 26 9 / 24

11 Interdependent Networks inter-layer plus intra-layer interactions restricted access: use layer to control layer use peripherial nodes to control central nodes cost-efficient strategy to influence the whole network Y. Zhang, A. Garas, F. Schweitzer: The value of peripheral nodes in controlling multilayer networks, Physical Review E (26) Chair of Systems Design Multi-layer network perspective on systemic risk Network approach Frank Schweitzer MFM Winter 26 Meeting Stern School, NYU Jan 26 / 24

12 Chair of Systems Design Multi-layer network perspective on systemic risk Network approach Frank Schweitzer MFM Winter 26 Meeting Stern School, NYU Jan 26 / 24 Economics: A Multi-Layer Network a a3 a2 Knowledge Risk b b3 b2 c c3 c2 Ownership a5 a4 b5 b4 c5 c4 a6 b6 c6 a7 b7 c7 a8 b8 c8 multiple interactions ownership/control risk diversification knowledge transfer feedback within layers investments/participation credit relations, OTC derivatives R&D collaborations feedback between layers ownership failure risk ownership knowledge transfer failure risk knowledge transfer

13 Multi-layer structure of financial networks Banking network of Mexico 3 September 23 (a) exposures from derivatives (b) securities, cross-holdings (c) foreign exchange exposures (d) deposits and loans (e) combined banking network Banks colored according to their systemic impact Ri Node-size represents banks total assets Link-width is the exposure size between banks S. Poledna, J.L. Molina-Borboa, M. van der Leij, S. Martinez-Jaramillo, S. Thurner: Multi-layer network nature of systemic risk in financial networks and its implications, Journal of Financial Stability 2, 7-8, (25) Chair of Systems Design Multi-layer network perspective on systemic risk Network approach Frank Schweitzer MFM Winter 26 Meeting Stern School, NYU Jan 26 2 / 24

14 Chair of Systems Design Multi-layer network perspective on systemic risk Network approach Frank Schweitzer MFM Winter 26 Meeting Stern School, NYU Jan 26 3 / 24

15 Systemic risk in a network of firms dynamic state: healthy: s i (t) =, or failed: s i (t) = s i (t + ) = Θ[φ i (t, s, A) θ i ] threshold: θ i = C i /L i ratio between capital buffer C i and liabilities L i fragility: depends on the fraction of failed neighbors diversification mitigates the impact of a single neighbor j nb(i) sj w i φ i (k i ) = k i s j = ni k i = L i j nb(i) loss from failing neighbors divided by total liability firm s liability: L i = j nb(i) w i financial obligation to each neighbor: w i = L i /k i Watts (22), Gleeson&Cahalane (27), Gai&Kapadia (2), Amini, Cont & Minca (2), Battiston et al. (22), Roukney et al. (23) Chair of Systems Design Multi-layer network perspective on systemic risk A Two-Layer Model of Firms Frank Schweitzer MFM Winter 26 Meeting Stern School, NYU Jan 26 4 / 24

16 Chair of Systems Design Multi-layer network perspective on systemic risk A Two-Layer Model of Firms Frank Schweitzer MFM Winter 26 Meeting Stern School, NYU Jan 26 5 / 24 When is it beneficial to have two layers? Strategic decision of firms to operate in two different layers core business: layer () subsidiary business: layer () different risk profiles F (θ () ), F (θ () ) 2 to merge businesses compare systemic risk risk in separate layers vs aggregated measure final cascade size in layer () ϱ () = N i s () i

17 Chair of Systems Design Multi-layer network perspective on systemic risk A Two-Layer Model of Firms Frank Schweitzer MFM Winter 26 Meeting Stern School, NYU Jan 26 6 / 24 Asymmetric feedback between layers failure propagation () () leads to a failure in () s () i = s () i = failed nodes cannot recover

18 Chair of Systems Design Multi-layer network perspective on systemic risk A Two-Layer Model of Firms Frank Schweitzer MFM Winter 26 Meeting Stern School, NYU Jan 26 6 / 24 Asymmetric feedback between layers failure propagation () () leads to a failure in () s () i = s () i = failed nodes cannot recover 2 failure propagation () () leads to a threshold reduction in () θ () i ( r ) θ () i may lead to subsequent failure in () vary coupling strength r

19 How cascades propagate Chair of Systems Design Multi-layer network perspective on systemic risk A Two-Layer Model of Firms Frank Schweitzer MFM Winter 26 Meeting Stern School, NYU Jan 26 7 / 24

20 How cascades propagate Chair of Systems Design Multi-layer network perspective on systemic risk A Two-Layer Model of Firms Frank Schweitzer MFM Winter 26 Meeting Stern School, NYU Jan 26 7 / 24

21 How cascades propagate Chair of Systems Design Multi-layer network perspective on systemic risk A Two-Layer Model of Firms Frank Schweitzer MFM Winter 26 Meeting Stern School, NYU Jan 26 7 / 24

22 How cascades propagate Chair of Systems Design Multi-layer network perspective on systemic risk A Two-Layer Model of Firms Frank Schweitzer MFM Winter 26 Meeting Stern School, NYU Jan 26 7 / 24

23 How cascades propagate Chair of Systems Design Multi-layer network perspective on systemic risk A Two-Layer Model of Firms Frank Schweitzer MFM Winter 26 Meeting Stern School, NYU Jan 26 7 / 24

24 How cascades propagate Chair of Systems Design Multi-layer network perspective on systemic risk A Two-Layer Model of Firms Frank Schweitzer MFM Winter 26 Meeting Stern School, NYU Jan 26 7 / 24

25 How cascades propagate Chair of Systems Design Multi-layer network perspective on systemic risk A Two-Layer Model of Firms Frank Schweitzer MFM Winter 26 Meeting Stern School, NYU Jan 26 7 / 24

26 How cascades propagate Chair of Systems Design Multi-layer network perspective on systemic risk A Two-Layer Model of Firms Frank Schweitzer MFM Winter 26 Meeting Stern School, NYU Jan 26 7 / 24

27 How cascades propagate Chair of Systems Design Multi-layer network perspective on systemic risk A Two-Layer Model of Firms Frank Schweitzer MFM Winter 26 Meeting Stern School, NYU Jan 26 7 / 24

28 Mathematical Model Assumptions: each layer: random graph (ER network) network size N, C node i: independently at random: degrees k () i, k () i from p (k () i ), p (k () ) thresholds θ () i, θ () i from F (θ () ), F (θ () ) Goal: calculate final cascade size ϱ R. Burkholz, M. Leduc, A. Garas, F. Schweitzer: Systemic risk in multiplex networks with asymmetric coupling and threshold feedback, Physica D (26) Chair of Systems Design Multi-layer network perspective on systemic risk A Two-Layer Model of Firms Frank Schweitzer MFM Winter 26 Meeting Stern School, NYU Jan 26 8 / 24

29 Chair of Systems Design Multi-layer network perspective on systemic risk A Two-Layer Model of Firms Frank Schweitzer MFM Winter 26 Meeting Stern School, NYU Jan 26 9 / 24 Analytic Approach: Local tree approximation Average fraction of failed nodes: ϱ = k p (k )P(s = k ) Prob. to fail because of neighb. failures in layer (l): ϱ s,l = k l p l (k l ) ( k l n l = B(n l, k l, πl )F nl l k l ). Failure prob. in (l) given node s degree: P(s l = k l ) = ) kl n l = B(n l, k l, πl (s )P l = k l, n l, ϱ s, l. Ability ( to withstand shocks: ) P s l = k l, n l, ϱ s, l = (( ϱ s, l ) F l ( nl k l ) + ϱ s, l F l ( )) nl k l /( r l,l ). Fail. Prob. Neighb.: πl = L (πl ) := p l (k l )k l ) kl k l z l n l = B(n l, k l, πl (s )P l = k l, n l, ϱ s, l where z l = k l p l (k l ) k l.

30 Chair of Systems Design Multi-layer network perspective on systemic risk A Two-Layer Model of Firms Frank Schweitzer MFM Winter 26 Meeting Stern School, NYU Jan 26 9 / 24 Analytic Approach: Local tree approximation Average fraction of failed nodes: ϱ = k p (k )P(s = k ) Prob. to fail because of neighb. failures in layer (l): ϱ s,l = k l p l (k l ) ( k l n l = B(n l, k l, πl )F nl l k l ). Failure prob. in (l) given node s degree: P(s l = k l ) = ) kl n l = B(n l, k l, πl (s )P l = k l, n l, ϱ s, l. Ability ( to withstand shocks: ) P s l = k l, n l, ϱ s, l = ( ( ϱ s, l ) F l ( nl k l ) + ϱ s, l F l ( )) nl k l /( r l,l ). Fail. Prob. Neighb.: πl = L (πl ) := p l (k l )k l ) kl k l z l n l = B(n l, k l, πl (s )P l = k l, n l, ϱ s, l where z l = k l p l (k l ) k l.

31 Chair of Systems Design Multi-layer network perspective on systemic risk A Two-Layer Model of Firms Frank Schweitzer MFM Winter 26 Meeting Stern School, NYU Jan 26 2 / 24 Result: Sharp regime shift.8.6 ρ *.4.2 µ =.6 σ =. µ =.5 σ =.5 µ =.2 σ = r Computer simulations/ analytical results initial condition: core business is safe vary: threshold distribution of subsidiary layer: µ, σ Emergence of large cascades core business collapses below a critical µ : coupling leads to complete failure

32 Chair of Systems Design Multi-layer network perspective on systemic risk A Two-Layer Model of Firms Frank Schweitzer MFM Winter 26 Meeting Stern School, NYU Jan 26 2 / 24 Reference case: merged layers nodes in aggregated layer degree: k agg = k () + k () better diversified, but higher connectivity amplification of cascades threshold: θ agg = θ() k () + θ () k () k () + k () θ = C/L shared capital buffers

33 Chair of Systems Design Multi-layer network perspective on systemic risk A Two-Layer Model of Firms Frank Schweitzer MFM Winter 26 Meeting Stern School, NYU Jan / 24 Is merging of businesses safer? Layer (): ϱ Layer (): ϱ Aggregated: ϱ agg r =. σ σ σ µ µ µ r =.2 σ σ σ µ µ µ No for small coupling r.

34 Chair of Systems Design Multi-layer network perspective on systemic risk A Two-Layer Model of Firms Frank Schweitzer MFM Winter 26 Meeting Stern School, NYU Jan / 24 Is merging of businesses safer? Layer (): ϱ Layer (): ϱ Aggregated: ϱ agg r =.4 σ σ σ µ µ µ r =.8 σ σ σ µ µ µ Yes for stronger coupling r.

35 Chair of Systems Design Multi-layer network perspective on systemic risk A Two-Layer Model of Firms Frank Schweitzer MFM Winter 26 Meeting Stern School, NYU Jan / 24 Mergers not always decrease risk Layer (): ϱ Layer (): ϱ Aggregated: ϱ agg r r r µ µ µ Influence of coupling r and µ (small σ ) r.2 : Disaggregation blocks cascade amplification! increased systemic risk above critical coupling

36 Chair of Systems Design Multi-layer network perspective on systemic risk Conclusions Frank Schweitzer MFM Winter 26 Meeting Stern School, NYU Jan / 24 Conclusions Systemic risk emerges bottom-up approach, mathematical framework ϱ(t) ϱ 2 Multi-layer network approach networks are (re)constructed several pitfalls interdependent networks more pitfalls (intra/inter-layer links) 3 Systemic risk in multi-layer networks split into core/subsidiary business amplification of failure critical coupling strength r, critical risk profile µ sharp transition between no/full collapse

37 Chair of Systems Design Multi-layer network perspective on systemic risk Conclusions Frank Schweitzer MFM Winter 26 Meeting Stern School, NYU Jan / 24 Conclusions Systemic risk emerges bottom-up approach, mathematical framework ϱ(t) ϱ 2 Multi-layer network approach networks are (re)constructed several pitfalls interdependent networks more pitfalls (intra/inter-layer links) 3 Systemic risk in multi-layer networks split into core/subsidiary business amplification of failure critical coupling strength r, critical risk profile µ sharp transition between no/full collapse Advice for risk managers Understand the role of couplings between businesses! 2 Did you draw risk scenarios for split businesses from an aggregated model? Then you have underestimated your real risk!