Networks in Finance

The goal of this course work is that you prepare a Report where you analyse some papers describing real-world application of Networks in Finance. For preparing your report you must consider first a general introduction based on the Review papers provided. Such general introduction must describe the state-of-the-art of the use of networks in finance and in particular the importance of network analysis for the study of systemic risk and contagion in financial networks.

Then, you must select ONE of the Working papers to carry out your analysis. This analysis should contain the following:

1) A description of the research carried out in the paper, highlighting the methods used and the main results obtained;

2) A critical analysis of the results, not only on those obtained in the paper but also those that can be used taking into account your current knowledge of network theory for the better analysis of the problem stated in the paper;

3) Create two networks G1 and G2 having 500 nodes each and the same density that the network analysed in the Working paper that you have selected. Use an Erdos-Rényi mechanism for G1 and a Barabási-Albert for G2;

4) Using extensive simulation analysis, compare the output of the epidemic spreading on these two networks using the SIR model. You can change systematically the values of the birth rate and recovery rate of the epidemic. You must report the time at which the peak of the epidemic is reached for each of the systems and compare them;

5) You must calculate the degree distributions of the two networks, average Watts- Strogatz clustering coefficient, average path length and extract useful information about the importance of these parameters for the dynamics of the epidemic spreading on the two networks;

6) Consider the influence of the initiator of the epidemic by changing the node that start the infection, using a low degree node and a high degree one. Use centrality measures to account for the centrality of these nodes and investigate its influence on the epidemic propagation of the networks;

7) Compare all the results with what is reported in the Working paper you selected and extract useful conclusions.

For all the calculations you can use codes previously developed for network analysis, such as those provided in the Appendix based on Matlab.

How to write your Report

Write a report containing:

1) Introduction
2) Methods
3) Results
4) Discussion
5) Conclusions
6) References
7) Appendices

- Think like if you were writing a scientific paper.

- Describe in the Methods in a clear and direct language all the terms you are using and use their mathematical expressions were needed.

- State clearly what are the results you have obtained for each of the points to be considered. Use plots, graphics, tables, etc. to condensate your results.

- Discuss your results by using as much graphics and tables as needed, but do not exceed their number making boring the reading of this section. Remember you can place secondary information into Appendices.

- Make clear conclusions in one or two paragraphs. Conclusions are not a list of the topics that you have considered in your Report but what you have learned from the analysis of this network, which would be interesting for the reader.

- Refer to all the literature that you have used, including webpages. The references must be properly cited in the text, e.g., using numbers. The list of references must include the authors, title of the paper, journal, volume, year and pages.

- Include any program or code used into the Appendices as well as any secondary information, Tables or figures. If the code is taken from a given site please refers to it in the references. Otherwise make clear you have created this code.

About the programs to be used

There are many codes available for manipulating and making calculations of parameters on the web. For Matlab users the following is a non-exhaustive list of sites where you can find a few of them:
a. http://strategic.mit.edu/downloads.php?page=matlab_networks
b. http://igraph.sourceforge.net/
c. http://www.levmuchnik.net/Content/Networks/ComplexNetworksPackage.html
d. http://strategic.mit.edu/downloads.php?page=matlab_networks
e. http://www.mathstat.strath.ac.uk/outreach/contest/toolbox.html
f. http://www.mathworks.com/matlabcentral/fileexchange/4266-grtheory-graph-theory- toolbox

In particular you can download the codes "erdrey.m" and "pref.m" (e) to generate random networks with Poisson and power-law degree distributions.

For doing the calculations of epidemic spreading you can use the program "Program_7_7.m" which I have properly modified for doing the calculations of the SIR model with Erdos-Rényi and a Barabási-Albert network.

Any available code can be used to calculate the centrality measures that you have selected for your work.

Attachment:- Program.rar