Bardoscia Marco, Battiston Stefano, Caccioli Fabio, Caldarelli Guido
London Institute for Mathematical Sciences, London, United Kingdom.
Department of Banking and Finance, University of Zürich, Zürich, Switzerland.
PLoS One. 2015 Jun 19;10(6):e0130406. doi: 10.1371/journal.pone.0130406. eCollection 2015.
The DebtRank algorithm has been increasingly investigated as a method to estimate the impact of shocks in financial networks, as it overcomes the limitations of the traditional default-cascade approaches. Here we formulate a dynamical "microscopic" theory of instability for financial networks by iterating balance sheet identities of individual banks and by assuming a simple rule for the transfer of shocks from borrowers to lenders. By doing so, we generalise the DebtRank formulation, both providing an interpretation of the effective dynamics in terms of basic accounting principles and preventing the underestimation of losses on certain network topologies. Depending on the structure of the interbank leverage matrix the dynamics is either stable, in which case the asymptotic state can be computed analytically, or unstable, meaning that at least one bank will default. We apply this framework to a dataset of the top listed European banks in the period 2008-2013. We find that network effects can generate an amplification of exogenous shocks of a factor ranging between three (in normal periods) and six (during the crisis) when we stress the system with a 0.5% shock on external (i.e. non-interbank) assets for all banks.
债务排名算法作为一种评估金融网络中冲击影响的方法，受到了越来越多的研究，因为它克服了传统违约级联方法的局限性。在此，我们通过迭代单个银行的资产负债表恒等式，并假设一个从借款人到贷款人的冲击转移简单规则，为金融网络构建了一个动态的“微观”不稳定性理论。通过这样做，我们推广了债务排名公式，既从基本会计原则的角度对有效动态进行了解释，又防止了在某些网络拓扑结构上对损失的低估。根据银行间杠杆矩阵的结构，动态过程要么是稳定的，在这种情况下渐近状态可以通过解析计算得出，要么是不稳定的，这意味着至少有一家银行会违约。我们将这个框架应用于2008 - 2013年期间欧洲上市顶级银行的数据集。我们发现，当我们对所有银行的外部（即非银行间）资产施加0.5%的冲击来给系统施压时，网络效应会使外部冲击放大三到六倍（正常时期为三倍，危机期间为六倍）。
