强制密度与互惠性的银行间网络重构
Interbank network reconstruction enforcing density and reciprocity
AI总结：
本文针对银行间网络重构无法复现有向环数量的问题，提出一种仅利用聚合资产负债信息即可同时强制稀疏性与连边互惠性的重构方法，并基于 e-MID 数据验证其显著改善结构和谱性质的预测。
摘要：
金融敞口网络是银行间风险和困境传播的关键载体，但由于保密原因，其经验结构并不公开。这一局限推动了利用部分、聚合信息进行网络重构方法的发展。遗憾的是，即使现有最好的方法也无法复现有向环的数量，而有向环在决定图谱、进而决定网络稳定性和系统性风险程度方面起着至关重要的作用。本文通过利用以下假设来应对这一挑战：高阶环的统计量受到最短环统计量的强烈约束，即受到具有互惠连边的二元组数量的约束。首先，我们对意大利银行 e-MID 数据集上的连边互惠性进行了详细分析，发现互惠连边之间的相关性随着时间分辨率的提高而系统性增强，通常在最长约 50 天的时间尺度附近从负相关转变为正相关。然后，我们提出了一种新的网络重构方法，该方法能够仅从聚合的银行间资产和负债信息出发，同时强制实现期望的稀疏性和期望的连边互惠性。我们证实，加入互惠性后，对若干结构和谱网络性质的预测能力显著提升，包括最大实特征值以及复平面上其他特征值椭圆分布的偏心率。这些结果说明了在金融网络重构中正确处理时间分辨率及其所导致的互惠性水平的重要性。
英文摘要：
Networks of financial exposures are the key propagators of risk and distress among banks, but their empirical structure is not publicly available because of confidentiality. This limitation has triggered the development of methods of network reconstruction from partial, aggregate information. Unfortunately, even the best methods available fail in replicating the number of directed cycles, which on the other hand play a crucial role in determining graph spectra and hence the degree of network stability and systemic risk. Here we address this challenge by exploiting the hypothesis that the statistics of higher-order cycles is strongly constrained by that of the shortest ones, i.e. by the amount of dyads with reciprocated links. First, we provide a detailed analysis of link reciprocity on the e-MID dataset of Italian banks, finding that correlations between reciprocal links systematically increase with the temporal resolution, typically changing from negative to positive around a timescale of up to 50 days. Then, we propose a new network reconstruction method capable of enforcing, only from the knowledge of aggregate interbank assets and liabilities, both a desired sparsity and a desired link reciprocity. We confirm that the addition of reciprocity dramatically improves the prediction of several structural and spectral network properties, including the largest real eigenvalue and the eccentricity of the elliptical distribution of the other eigenvalues in the complex plane. These results illustrate the importance of correctly addressing the temporal resolution and the resulting level of reciprocity in the reconstruction of financial networks.
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