CSH Talk by Christian Diem: “Optimal financial networks and measuring systemic risk in multilayer networks”

Nov 29, 2019 | 15:0016:00

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The lecture by Christian Diem, CSH Vienna/IIASA will take place at the Complexity Science Hub Vienna.

Room: Salon


If you are interested in participating, please email to office@csh.ac.at.




Management of systemic risk in financial markets is traditionally associated with setting (higher) capital requirements for market participants. There are indications that while equity ratios have been increased massively since the financial crisis, systemic risk levels might not have lowered, but even increased (see ECB data1; SRISK time series2). It has been shown that systemic risk is to a large extent related to the underlying network topology of financial exposures. A natural question arising is how much systemic risk can be eliminated by optimally rearranging these networks and without increasing capital requirements. Overlapping portfolios with minimized systemic risk which provide the same market functionality as empirical ones have been studied by Pichler et al. (2018). Here, a similar method for direct exposure networks is proposed, and applied to cross-sectional interbank loan networks, consisting of 10 quarterly observations of the Austrian interbank market. We show that the suggested framework rearranges the network topology, such that systemic risk is reduced by a factor of approximately 3.5 (70%), and leaves the relevant economic features of the optimized network and its agents unchanged. The presented optimization procedure is not intended to actually re-configure interbank markets, but to demonstrate the huge potential for systemic risk management through rearranging exposure networks, in contrast to increasing capital requirements that were shown to have only marginal effects on systemic risk (Poledna et al., 2017). We compute that on average bank equity needs to be increased by a around 230% to achieve the same reduction in DebtRank as our optimization procedure. Ways to actually incentivize a self-organized formation toward optimal network configurations were introduced in Thurner and Poledna (2013) and Poledna and Thurner (2016). For regulatory policies concerning financial market stability the knowledge of minimal systemic risk for a given economic environment can serve as a benchmark for monitoring actual systemic risk in markets.


Systemic risk in financial networks has been extensively investigated for different types of contractual networks. Examples are interbank loan networks, derivative exposure networks, equity cross holding networks or exposure networks arising from asset crossholdings of agents. More recently the paradigm of multi-layer networks has been used to model systemic risk for multiple financial networks jointly. [1] aggregated different direct exposure networks and showed that looking at single layers in isolation can underestimate systemic risk drastically. [2] take a different approach using extensions of classical centrality measures, like eigenvector centrality or page rank to multiplex networks. However, these algorithms cannot provide a monetary quantification of banks systemic riskiness in case of defaults. DebtRank, which aggregates the losses occurring in asset valuation cascades does not suffer this problem, but is only defined on a single layer [3,4]. Thus, we suggest to extend the valuation shock transmission mechanism of DebtRank into the multilayer framework when considering networks layers, which cannot be aggregated by summation. We establish such an extension of DebtRank by incorporating the funding liquidity contagion layer into the algorithm. Thus, this allows us to quantify the costs for the financial system in case of bank defaults in a more complete way. It also allows us to simulate different combinations of funding liquidity shocks and valuation shocks jointly. Since, valuation and funding liquidity cascades are interacting on most bi-layer network specifications we expect higher systemic risk impacts of bank defaults, than if the two contagion mechanisms are modelled separately. In a related study [5] modelled these contagion channels as supraadjacency matrix in order to analyse network stability properties for small simultaneous macro shocks.
Considering multiple networks simultaneously can change the structure of higher order connection of agents. In financial transaction networks this means that second and higher order risks agents are facing when creating a link, can look dramatically different in comparison to a single layer perspective. The multilayer extension of DebtRank can take such higher order connections arising from different layers into account.


1. Poledna, Sebastian, et al. “The multi-layer network nature of systemic risk and its implications for the costs of financial crises.” Journal of Financial Stability 20 (2015): pp 70-81.
2. Bardoscia, Marco, Ginestra Bianconi, and Gerardo Ferrara. “Multiplex network analysis of the UK OTC derivatives market.” (2018).
3. Battiston, Stefano, et al. “DebtRank: Too Central to Fail? Financial Networks, the FED and
Systemic Risk.” Scientific reports 2 (2012): 541.
4. Bardoscia, Marco, et al. “DebtRank: A Microscopic Foundation for Shock Propagation.” PloS one 10.6 (2015): e0130406.
5. Wiersema, Garbrand, et al. “Inherent Instability: Scenario-Free Analysis of Financial Systems with Interacting Contagion Channels.” (2019)



Nov 29, 2019


Complexity Science Hub Vienna
+43 1 59991 600
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CSH Vienna
Josefstaedter Straße 39
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+43 1 59991 600
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