Hierarchies in Communities of Borsa Istanbul Stock Exchange

Abstract

Nowadays, increase of the analyzing stock markets as complex systems lead graph theory to play key role. For instance detecting graph communities is an important task in the analysis of stocks, and minimum spanning trees let us to get important information for the topology of the market. In this paper, we introduce a method to build a connected graph representation of Borsa Istanbul based on the spectrum. We, then, detect graph communities and internal hierarchies by using the minimum spanning trees. The results suggest that the approach is demonstrably eective for Borsa Istanbul sessionally data returns.

Fractional Interaction of Financial Agents in a Stock Market Network

“…Such subgraphs are called as Minimum Spanning Tree (MST) and involve the junction vertices which are dominant in the flow of information and comes up with subdominant ultra-metric structure [40,41]. In the case of financial agents are the vertices of the network, MST gives the hierarchical structure of the financial network [42][43][44]. A planar graph is a simple graph that can be embedded on the plane, which is none of the graph edges intersect.…”

“…Hence, even though XU100 has 100 operating companies, we only consider 93 of them which have the equal time length. Trading hours for the stocks are held by two sessions on business days with mid-day break, and one session in some official holidays [44,48]. The tickers of the companies operating in XU100 and that are considered in this study is given in Table 1.…”

“…The tickers of the companies operating in XU100 and that are considered in this study is given in Table 1. The more details on the data can be found in [44]. The data we use is available with sessional closure price, therefore we calculate sessional closure price logarithmic return as…”

“…Pearson correlation coefficient varies between -1 and 1. ρ i j = 1 indicates that the stocks i and j are completely correlated whilst ρ i j indicates that the stocks i and j are completely uncorrelated [42]. Hence, it is also possible to introduce a new distance d Corr := 2(1 − ρ i j )/2 as in [13,44]. We can conclude that if d Corr (i, j) = 0, then the stocks i and j are completely correlated, and if d Corr (i, j) = 1, then the stocks i and j are completely uncorrelated.…”

Hierarchies in communities of UK stock market from the perspective of Brexit

“…The first stage of our approach is to identify vertex clusters on the network. Various studies have shown that clusters are stronger in financial threshold networks [1,6,12,35]. The presented novel threshold method works with very low computational complexity depending on the spectrum of the network's Laplacian matrix.…”