A simple data—driven financial network model for contagion analysis

[Abstract] This paper develops a data-driven financial model. Contagion analysis can be used to test the stability of a financial system and detect the systemically important and risk-vulnerable financial entities.

1 Introduction

Macro-prudential regulations neglected the negative systemic consequences （Markose 2013）. Moreover， little exploration Following the research of Furfine （2003）， Markose （Markose et al. 2012）， this paper develops a model for contagion analysis.

2 Mathematic principle of Financial Network： Gross matrix， netted matrix and Θ matrix

A network can be defined by a pair of sets （N， E）. N is the number of nodes and E is the total amount of edges.

We firstly build the gross financial flows matrix， the X matrix， using the bilateral financial obligation. Then we netted the gross matrix to obtain the net M matrix （ ） which delivers the net exposures of an agent to its counterparties. To see how the exposures from to cause losses to country ， we use the Θ matrix， which contains no negative values and gives the ratio of losses of country to its capital.

In the matrix X， the element xij represents the flow of gross financial obligation from i （the row entities） to j （the column entities）.

In matrix M， the symbolic element mij is given by （ xij-xji）， the netted payables of country i to country j.

To analyse the domino effect of failure of country i， we use a matrix Θ that only contains the positive numbers of matrix M， the negative ones are replaced by zeros.

When country j’s net exposures to country i relative to its initial capital Cj0 （at a certain time t） is greater than a threshold （a proportion of j’s capital）， j is going to fail.

3 Metrics defined in Contagion analysis

3.1 Default criteria

We first choose the trigger country and assume that this country loses its entire capital buffer. The infected country would fail when satisfying the following condition in （3）.

The threshold ρ signifies a proportion of capital.

More general situation can be given as following in （4）.

In this situation， country w survives the first q-1 rounds and failed at round q. Ds denotes the countries fail in round s and cause losses to country w through the financial obligations to country w.

3.2 Metrics for systemically important and risk-vulnerable financial entities

In Θ matrix， the sum of row i indicates the potential losses country i can cause to its counterparties and the severity of the losses is measured by the ratio of country j’s losses to its capital， which is denoted by （ xij-xji）/Cj0. Thus， could be used as a matric to determine systemic important entities.The sum of j column means vulnerability to risks from all its counterparties due to its exposures to other countries. Similarly， the severity of j’s losses is denoted by .

4 Conclusion

This model gives new metrics in financial contagion analysis. Given the increasing and continuing interconnectivity of world financial markets， further research should be done to develop new models which could detect systemic risk.

References

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Furfine， C.H. （2003）. Interbank exposures： Quantifying the risk of contagion. Journal of Money， Credit and Banking 35（1）： 111-128.

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Sheri Markose， Simone Giansante and Ali Rais Shaghaghi. ‘Too interconnected to fail’ financial network of US CDS market： Topological fragility and systemic risk. Journal of Economic Behavior Organization. 83 （2012） 627-646.

About the author：

Qi Zhang （1989-）， Postgraduate student in Finance of Hainan University.