Stock Market Network Indicators

The codes in the 'StockMarkNetIndicators' repository can be used to filter cross-correlation matrices of stocks in a financial market to construct network of stocks based on Minimum Spanning Tree (MST) and a chosen threshold. Thereafter, the filtered network in the form of edge list or file can be characterized by computing several network measures including edge-based curvature measures.

Code Details:

The following script can be used to filter the cross-correlation matrices and generate edge files and node files of the filtered networks:

• mst_wt.py : Python script to generate a weighted or unweighted filtered minimum spanning tree + thresholded network from the weighted network of cross-correlation values.

The following scripts can be used to compute the different network measures for the filtered networks:

• comm_eff.py : Python script to calculate the communcation efficiency of the network

• FormanUndirected.cpp : C++ code to calculate the Forman-Ricci curvature of edges in the network

• graph_measures.py : Python script to calculate the following measures on the network, namely, Number of edges, Average degree, Average Weighted Degree, Edge Density, Average Clustering coefficient

• MengerHaantjesUndirected.py : Python script to compute Menger-curvature and Haantjes-curvature for all the edges in an unweighted network

• network_entropy.py : Python script to calculate network entropy using degree and remaining degree distribution

• OR-Undir.py : Python script to compute the Ollivier-Ricci curvature of edges in the network

• Folder 'louvain-generic' within folder 'CODE' contains the code to compute the Louvain modularity of the network; this is a copy of the open source code made available by the original authors of the method

  To run:
  (1) ./louvain-generic/convert -i "insert edge file" -o ./temp/$folder/graph.bin -w ./temp/$folder/graph.weights
  (2) ./louvain-generic/louvain ./temp/$folder/graph.bin -w ./temp/$folder/graph.weights >& ./temp/$folder/graph.tree

The following MATLAB 2020a program can be used to compute different traditional market indicators:

• analysis_matlab.m : Matlab code to generate index log-returns, mean market correlation, GARCH volatility, minimum risk Markowitz portfolio. The moving epochs and the price time series are the input parameters to code.

Data description:

• The data was collected from the public domain of Yahoo finance database for two stock markets in two different countries, namely, USA S&P-500 index for 194 stocks and Japanese Nikkei-225 index for 165 stocks spanning a 32-year period from 2 January 1985 (02-01-1985) to 30 December 2016 (30-12-2016).

• Archived folders 'USA22d22s' and 'JPN22d22s' contain cross-correlation matrices computed using non-overlapping time windows with epoch of 22 days while folders 'USA22d5s' and 'JPN22d5s' contain cross-correlation matrices computed using overlapping time windows with epoch of 22 days and overlap of 5 days. These cross-correlation matrices were used in the construction of the networks. The above-mentioned archived folder can be downloaded from :
  (1) Folder 'USA22d22s' - https://www.imsc.res.in/~asamal/data/StockMarkIndicators/USA22d22s.tar.gz
  (2) Folder 'USA22d5s' - https://www.imsc.res.in/~asamal/data/StockMarkIndicators/USA22d5s.tar.gz
  (3) Folder 'JPN22d22s' - https://www.imsc.res.in/~asamal/data/StockMarkIndicators/JPN22d22s.tar.gz
  (4) Folder 'JPN22d5s' - https://www.imsc.res.in/~asamal/data/StockMarkIndicators/JPN22d5s.tar.gz

• The cross-correlation matrices contained in different files in the above-mentioned archived folders are in the form:
  "stock1 stock2 Correlation Distance", where distance is computed as Distance=sqrt(2*(1-c)) with c as correlation.

• The files USA22d5s.xlsx, USA22d22s.xlsx, JPN22d5s.xlsx and JPN22d22s.xlsx contain dictionaries relating cross-correlation matrices in the folders 'USA22d5s', 'USA22d22s', 'JPN22d5s' and 'JPN22d22s', respectively, and the start date / end date of different cross-correlation matrices.

These codes were written while carrying out research reported in the following manuscripts:

[1] A. Samal, H.K. Pharasi, S. J. Ramaia, H. Kannan, E. Saucan, J. Jost & A. Chakraborti, Network geometry and market instability, R. Soc. Open Sci. 8: 201734 (2021). https://doi.org/10.1098/rsos.201734
[2] S. Venkatesan, R.P. Vivek-Ananth, R.P. Sreejith, P. Mangalapandi, A.A. Hassanali & A. Samal, Network approach towards understanding the crazing in glassy amorphous polymers, Journal of Statistical Mechanics: Theory and Experiment 043305 (2018). https://doi.org/10.1088/1742-5468/aab688
[3] A. Samal, R.P. Sreejith, J. Gu, S. Liu, E. Saucan & J. Jost, Comparative analysis of two discretizations of Ricci curvature for complex networks, Scientific Reports 8: 8650 (2018). https://doi.org/10.1038/s41598-018-27001-3
[4] R.P. Sreejith, K. Mohanraj, J. Jost, E. Saucan & A. Samal, Forman curvature for complex networks, Journal of Statistical Mechanics: Theory and Experiment 063206 (2016). https://doi.org/10.1088/1742-5468/2016/06/063206

Please cite the above manuscripts if you use the codes in this repository for your work.