Abstract
This paper points out a methodological lacuna in the recent stream of numerical analyses of contagion in financial networks, and presents a solution to amend it. Under some conditions, the intercyclical obligations that connect the agents in a financial network cause the indeterminacy of the vector of payments that clears such obligations. This problem, first pointed out by Eisenberg and Noe (Manage Sci 47:236–249, 2001), has received little or no attention by authors who investigate payment flows and domino effects in networks using numerical simulations. Here we present an original result that establishes necessary and sufficient conditions for the uniqueness of the clearing payment vector for any financial network, and we demonstrate this result to control for the occurrence of the above-mentioned indeterminacy while performing numerical exercises on financial networks.
I wish to thank Raffaele Mosca, Paola Cellini and two anonymous referees for their generous advice.
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Notes
- 1.
A directed path is a sequence of nodes, with a start node and an end node, such that for any two consecutive nodes, i and i + 1, there is a link going from i to i + 1. A cycle in a directed graph is a directed path where the start node and the end node are the same.
- 2.
For ease of comparison, we use the same terminology and notation used by Eisenberg and Noe [7].
- 3.
See Eisenberg and Noe [7, Theorem 1, p. 240].
- 4.
The set of descendants of a node \(i \in \mathcal{N}\) consists of all nodes \(j \in \mathcal{N}\) such that there exists a directed path starting at i and ending at j.
- 5.
I am indebted to Paola Cellini for her generous help in characterising the singularity conditions of this matrix.
- 6.
This means that, for every risk orbit, there is at least one agent i with strictly positive operating cash flows: e i > 0.
- 7.
Note that all closed SCCs with positive operating cash flows are surplus sets, whereas the converse is not true because surplus sets need not be strongly connected.
- 8.
See the proof of Theorem 5.2.
- 9.
See, inter alia, the fictitious default algorithm in EN and the algorithm proposed in Eboli [6].
References
Allen F, Gale D (1998) Optimal financial crises. J Finance 53:1245–1248
Allen F, Gale D (2000) Financial contagion. J Polit Econ 108(1):1–34
Blavarg M, Nimander B (2002) Interbank exposures and systemic risk. Sveriges Riksbank Econ Rev 2:19–45
Cifuentes R (2003) Banking concentration: implications for systemic risk and safety net design, Volume 231 di Documentos de trabajo, Banco Central de Chile
Degryse H, Nguyen G (2007) Interbank exposures: an empirical examination of contagion risk in the Belgian banking system. Int J Cent Bank 3:123–172
Eboli M (2013) A flow network analysis of direct balance-sheet contagion in financial networks, working paper n∘ 1862. Kiel Institute for the World Economy
Eisenberg L, Noe TH (2001) Systemic risk in financial systems. Manag Sci 47(2):236–249
Elsinger H, Lehar A, Summer M (2006) Risk assessment of banking system. Manag Sci 52(9):1301–1314
Freixas J, Parigi BM, Rochet JC (2000) Systemic risk, interbank relations, and liquidity provision by the central bank. J Money Credit Bank 32(3):611–638
Furfine C (2003) Interbank exposures: quantifying the risk of contagion. J Money Credit Bank 35:111–128
Mistrulli PE (2011) Assessing financial contagion in the interbank market: maximum entropy versus observed interbank lending patterns. J Bank Finance 35(5):1114–1127
Nier E, Yang J, Yorulmazer T, Alerton A (2007) Network models and financial stability. J Econ Dyn Control 31(6):2033–2060
Pokutta S, Schmaltz C, Stiller S (2011) Measuring systemic risk and contagion in financial networks. Available at SSRN: http://papers.ssrn.com/sol3/papers.cfm?abstract_id=1773089
Rochet J-C, Tirole J (1996) Interbank lending and systemic risk. J Money Credit Bank 28: 733–762
Shin HS (2008) Risk and liquidity in a system context. J Financ Intermed 17(3):315–329
Sheldon G, Maurer M (1998) Interbank lending and systemic risk: an empirical analysis of Switzerland. Swiss J Econ Stat 134:685–704
Upper C (2007) Using counterfactual simulations to assess the danger of contagion in interbank markets. BIS Working Paper No. 234, August
Upper C, Worms A (2001) Estimating bilateral exposure in the German interbank market: is there a danger of contagion? BIS, Basel
Van Lelyveld I, Liedorp F (2006) Interbank contagion in the Dutch banking sector: a sensitivity analysis. Int J Cent Bank 2(2):99–133
Wells S (2002) U.K. interbank exposure: systemic risk implications. Financial Stability Review, 13. Bank of England, pp 175–182
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Eboli, M. (2014). On the Indeterminacy of the Clearing Payment Vectors in Numerical Simulations on Financial Networks. In: Chen, SH., Terano, T., Yamamoto, R., Tai, CC. (eds) Advances in Computational Social Science. Agent-Based Social Systems, vol 11. Springer, Tokyo. https://doi.org/10.1007/978-4-431-54847-8_5
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