Enhanced capital-asset pricing model for the reconstruction of bipartite financial networks

A fundamental problem in studying and modeling economic and financial systems is represented by privacy issues, which put severe limitations on the amount of accessible information. Here we introduce a novel, highly nontrivial method to reconstruct the structural properties of complex weighted networks of this kind using only partial information: the total number of nodes and links, and the values of the strength for all nodes. The latter are used as fitness to estimate the u...

Systemic risk arises as a multi-layer network phenomenon. Layers represent direct financial exposures of various types, including interbank liabilities, derivative- or foreign exchange exposures. Another network layer of systemic risk emerges through common asset holdings of financial institutions. Strongly overlapping portfolios lead to similar exposures that are caused by price movements of the underlying financial assets. Based on the knowledge of portfolio holdings of fin...

We present a novel method to reconstruct complex network from partial information. We assume to know the links only for a subset of the nodes and to know some non-topological quantity (fitness) characterising every node. The missing links are generated on the basis of the latter quan- tity according to a fitness model calibrated on the subset of nodes for which links are known. We measure the quality of the reconstruction of several topological properties, such as the network...

Common asset holding by financial institutions, namely portfolio overlap, is nowadays regarded as an important channel for financial contagion with the potential to trigger fire sales and thus severe losses at the systemic level. In this paper we propose a method to assess the statistical significance of the overlap between pairs of heterogeneously diversified portfolios, which then allows us to build a validated network of financial institutions where links indicate potentia...

Scale invariance, collective behaviours and structural reorganization are crucial for portfolio management (portfolio composition, hedging, alternative definition of risk, etc.). This lack of any characteristic scale and such elaborated behaviours find their origin in the theory of complex systems. There are several mechanisms which generate scale invariance but maximum entropy models are able to explain both scale invariance and collective behaviours. The study of the struct...

In this paper we estimate the propagation of liquidity shocks through interbank markets when the information about the underlying credit network is incomplete. We show that techniques such as Maximum Entropy currently used to reconstruct credit networks severely underestimate the risk of contagion by assuming a trivial (fully connected) topology, a type of network structure which can be very different from the one empirically observed. We propose an efficient message-passing ...

Network (or matrix) reconstruction is a general problem which occurs if the margins of a matrix are given and the matrix entries need to be predicted. In this paper we show that the predictions obtained from the iterative proportional fitting procedure (IPFP) or equivalently maximum entropy (ME) can be obtained by restricted maximum likelihood estimation relying on augmented Lagrangian optimization. Based on the equivalence we extend the framework of network reconstruction to...

Within network analysis, the analytical maximum entropy framework has been very successful for different tasks as network reconstruction and filtering. In a recent paper, the same framework was used for link-prediction for monopartite networks: link probabilities for all unobserved links in a graph are provided and the most probable links are selected. Here we propose the extension of such an approach to bipartite graphs. We test our method on two real world networks with dif...

A major problem in the study of complex socioeconomic systems is represented by privacy issues$-$that can put severe limitations on the amount of accessible information, forcing to build models on the basis of incomplete knowledge. In this paper we investigate a novel method to reconstruct global topological properties of a complex network starting from limited information. This method uses the knowledge of an intrinsic property of the nodes (indicated as fitness), and the nu...

Financial markets are exposed to systemic risk, the risk that a substantial fraction of the system ceases to function and collapses. Systemic risk can propagate through different mechanisms and channels of contagion. One important form of financial contagion arises from indirect interconnections between financial institutions mediated by financial markets. This indirect interconnection occurs when financial institutions invest in common assets and is referred to as overlappin...