Complex Networks in Financial Markets

31.05.2017

In most natural and engineered systems, a set of entities interact with each other in complicated patterns that can involve multiple types of relationships, change in time and include multiple layers of connectivity. In order to gain understanding in such complex systems it is important to consider such features.

A network simply put, is a collection of points, called nodes, joined together in pairs by lines, called edges (Newman, 2010). There are three main levels of analysis (Battiston, 2010), the first is purely topological, where binary adjacency matrix describes only the existence or absence of edges, while the second level expands on the first by allowing edges to have weights and the third level assigns so called fitness to the nodes themselves.

Network theory has reformed the perception of complex systems across many domains. Many real world objects and interactions amongst them can be thought of as networks and doing so can lead to interesting and otherwise unobservable insights. This methodology also has the advantage of visualizing interrelationships directly over the graphic layout of the network.

Using network theory, we can observe how people, computers, proteins and other entities are connected among their kind. Famous examples include the findings about sexual partners (Liljeros, 2001), Internet and WWW (Faloutsos, 1999), (Albert, 1999), epidemic spreading (Pastor-Satorras, 2001), immunization strategies (Cohen, 2003), citation networks (Radicchi, 2008), structure of financial markets (Bonanno, 2003), structure of mobile communication network (Onnela, 2007) and many others. Network approach has been used to build a diversified portfolio that reduces investment risk (Pozzi, 2013), while analysis of abnormal motifs in complex trading networks can be used to detect possible price manipulation (Jiang, 2013), identified as significantly positive cumulative excess returns after buyer-initiated suspicious trades.

The advance in big data collection and processing allows a more wide-ranging research, enabling us to explore different and more complex network specifications. In financial markets, investors interact creating a complicated structure of relationships that can be represented by a complex system. This system has a bipartite nature – one set of nodes representing investors and the other representing exchange traded securities. Such heterogeneous system, where investors do not interact directly with each other, but rather purchase or sell securities, makes it very difficult to identify important links between investors. Using a large amount of investor level transaction data, we can infer multilayer networks across multiple securities and multiple timeframes and analyse the relation between the dynamics of those networks and market variables.

Usually two types of financial networks are considered – similarity based and direct interaction networks. In similarity based networks a link between two agents means that they share some feature: strategy, behaviour, portfolio composition, etc. and therefore, some criterion is required in order to establish whether the similarity between to agents is relevant enough. In direct interaction networks, a link between two nodes means the presence of an interaction between these two agents. In a bipartite network of investors and securities a direct interaction network can be drawn based on investor owned or traded securities, while a projection of this network into an investor trading network requires definition of a similarity measure that would be used to determine relevant links.

References

Albert, R. (1999). Internet: Diameter of the world-wide web. Nature, 130–131.

Battiston, S. (2010). The structure of financial networks.

Bonanno, G. (2003). Topology of correlation-based minimal spanning trees in real and. Physical Review E.

Cohen, R. (2003). Efficient immunization strategies for computer networks and populations. Physical review letters.

Faloutsos, M. (1999). On power-law relationships of the internet topology. ACM SIGCOMM computer communication review, vol. 29, 251–262.

Jiang, Z.-Q. (2013). Trading networks, abnormal motifs and stock manipulation. Quantitative Finance Letters.

Liljeros, F. (2001). The web of human sexual contacts. Nature, 907–908.

Newman, M. (2010). Networks: an introduction. Newman.

Onnela, J.-P. (2007). Structure and tie strengths in mobile communication networks. Proceedings of the National Academy os Sciences, (pp. 7332–7336).

Pastor-Satorras, R. (2001). Epidemic spreading in scale-free networks. Physical review letters.

Pozzi, F. (2013). Spread of risk across financial markets: better to invest in the peripheries. Scientific reports.

Radicchi, F. (2008). Universality of citation distributions: Toward an objective measure of scientific impact. Proceedings of the National Academy of Sciences, (pp. 17268–17272).

 

 

 

 

 

 

 

Kestutis Baltakys is based at Tampere University of Technology 2016-2019, and his research project is Complex Network Analysis in Stock Markets (WP2)