Big Data & (Financal) Networks

Transcription

1 Big Data & (Financal) Networks Daniele Tantari Scuola Normale Superiore, Pisa October 11, /19

2 Motivations I Big data: big opportunities together with technological, methodological and conceptual new challenges. I Extract informations in a sea of noise. I Complex Networks representation of data: the role of the interactions, beyond individuality I From macro to micro: Classification and Prediction. 2/19

3 Financial networks: general tasks I Finance provides a large set of situations where networks are present or can be constructed from data. I Examples: interbank networks, trading networks, payment networks, shareholder networks, control networks, etc, I Many other examples comes from time series: Correlation networks, Partial correlation networks, Granger causality networks, etc. I Prediction on Nodes: signal propagation (risk/default), central nodes, network vulnerability I Prediction on Links: network formation/evolution, reconstruction from partial observations, recommendation systems. 3/19

4 Financial networks: outline of the talk In this presentation I will discuss some financial applications to: I Local risk vs Global network properties with an application to the study of Unicredit payments network. Prediction on nodes I Temporal networks and link forecasting with an application to preferential trading in interbank networks Prediction on links 4/19

5 Payment Network and Credit Risk Rating (E. Letizia and F. Lillo) 5/19

6 THE CORPORATE PAYMENT NETWORK Source: Unicredit Large proprietary dataset of payments between Italian firms: 2.4M companies, 47M payments in Includes information on risk rating for a large fraction of companies. 6 / 19

7 Is the position of a company in the payment network informative on its riskiness beyond its local properties? Company B Company D Company A Company C Low Risk Medium Risk High Risk Company E Company I Company H Company G Company F I How much are your neighbours informative on your risk? I What is the relation between the macro organization of the network and the risk distribution? 7/19

8 Degree Strong relation between degree and risk. Assortativity Using the three risk classes P i B = e ii a i b P i 1 i a ib i where e ij is the fraction of edges connecting vertices of type i and j, a i = P j e ij and b j = P i e ij. Homophily of risk. B > 0: neighbours of firms in the payment network tend to have similar risk profile. 8/19

9 Ranking hierarchical organization I Strong hierarchical structure of the payment network: data driven supply chains identification. I A high risk concentration in low class nodes (top of the hierarchy) could trigger a cascade of distress in the higher rank classes. Machine Learning risk classifier! I Evaluation of new clients from partial informations. I New measure of risk based on network properties. 9/19

10 Random models for temporal networks and link forecasting (with P. Mazzarisi, P. Barucca, and F. Lillo) 10 / 19

11 Research question Many networks are inherently dynamic as links are created and destroyed through time. I Preferential relations between nodes tend to preserve past links (If we were friends yesterday we will be friend today). I Node specific properties can drive the evolution of the network topology (Two social persons are more likely to be friend). We propose a novel methodology for modelling temporal networks subject to link persistence and time-varying node characteristics and disentangling their role. I How the node characteristic and the preferential trading shape a financial network and how to account for the two linking mechanisms in a statistical model of temporal networks? I A proper modeling of network dynamics allows performing short term link prediction. 11 / 19

12 Link persistence I We model the tendency of a link that does (or does not) exist at time t 1 to continue existing (or not existing) at time t. I Discrete AutoRegressive DAR(1) model P(A t A t 1,, )= Y i,j>i ij I A t ij A t 1 +(1 ij ) At ij ij (1 ij) 1 At ij ij I The larger is ij,themorepersistentisthelinkbetweeni and j. 12 / 19

13 Fitness dynamics I The dynamic parameter i t (fitness) of node i is latent and describes its tendency in creating links. I We extend the fitness model to the dynamic case. I We model it as a hidden Markov chain 13 / 19

14 Fitness dynamics (2) I Each node i is characterized by a quantity i t,i.e.thenode fitness. We assume that it follows an AR(1) process, t i = 0,i + 1,i t 1 i + t i 0,i 2 R, 1,i < 1and t i NID(0, i) with i > 0. I We define the link probability at time t as: P(A t ij =1 t i, t j )= e( t i + t j ) 1+e ( t i + t j ) I The larger i t node i. is, the larger is the probability for all links incident to 14 / 19

15 Dynamic fitness + link persistence We combine the hidden dynamics of (fitness) with the mechanism of copying from the past (link persistence). 15 / 19

16 Empirical results We investigate two aspects: I How strong is preferential trading between two banks, when their propensity to trade is accounted for (using fitness)? I Link prediction. The investigated database is the electronic Market of Interbank Deposit (e-mid), an electronic segment of Italian interbank market. We focus on the time series of weekly aggregated, unweighted, and directed adjacency matrix A t : A t ij =1ifbanki lends money at least once to bank j during the week t. 16 / 19

17 What is fitness measuring? EURO (mln) Bank exposure for lender '3' bank exposure δ e θ 3,t 0 Aug 2012 Feb 2013 Aug 2013 Feb 2014 Aug 2014 Feb 2015 I Correlations between x t i e t i and the bank s exposure in the weighted network; I We obtain information on the weighted e-mid network having only the binary information. Disentangle random and preferential trading I The DAR(1) model that does not account for time evolving network topology (fitness), tends to overestimate link stability. I Statistical validation of preferential trading against the null (only fitness) DAR-TGRG DAR(1) α ij 17 / 19

18 Out-of-sample link prediction for e-mid Sensitivity TGRG (AUC 0.83) DAR-TGRG (AUC 0.85) DAR(1) (AUC 0.80) Specificity AUC TGRG DAR-TGRG DAR(1) threshold value for α ij I Out of sample analysis for the e-mid interbank market. I DAR-TGRG outperforms TGRG and DAR(1) network models. I In average, network topology is more important than link stability for link prediction in e-mid. 18 / 19

19 Conclusions I Financial networks are a powerful tool to study the (dynamic) interaction of a large set of financial agent. I Financial networks are the channels of propagation of risk. Interesting interplays between idiosyncratic risk and local or global network topology I Random network models are a powerful tool for I I Modeling temporal networks and forecasting links Inference of large scale network structures 19 / 19