Network Analysis

By Titus Chirchir and Dhanoosha Penmetsa

The algorithms presented in this project were initially intended for analysing contagion effect within a financial system. The following is the procedure for the construction of a network:

1. Initialize a matrix representing the interbank relationships: To be able to propagate contagion through the system, we would need to know whether bank A is exposed to bank B and so forth. The matrix creation utilizes an Erdos Renyi probability-type graph whereby the exposure between two banks is dependent on a given probability, p. The higher the probability, the more likely that the banks are coupled.

2. Construct a system of N banks: A bank is represented by a balance sheet containing

   • Assets
     • External Assets
     • Interbank Loans (Lending)
   • Liabilities
     • Customer Deposits
     • Interbank Loans (Borrowing)
   • Capital (Equity / Royalties/ Accumulated profit and Loss)

   Each bank's balance sheet has to conform with the accounting identity of Assets = Liabilities + Capital. This means that overall, the entire network should satisfy this identy as well i.e. Total Assets = Total Liabilities + Total Capital. The total assets of the network is seleted by the user. The user can also select the proportion capital/asset ratio (Gamma) and ratio of interbank lending to external assets (Theta).

3. Trigger a Shock: After the network has been initialized with banking institutions, each with a specified balance sheet defining its capitalization and exposure to other banks in the network, we then trigger a credit event. This event takes the form of a wipe-out of one of the banks' external assets. We then track the reverberation of the credit event throughout the system. A bank is deemed to have defaulted when the shock it feels is of a greater magnitude than its capital. i.e.

   • if shock > capital, bank defaults
   • In terms of the impact of the shock on the bank's stakeholders, capital will be eaten away first, followed by a default on interbank loans (up to the residual shock from capital cushion) and finally a failure to reimburse customer deposits (up to the residual shock from interbank loans).
   • if the shock is not absorbed fully by the banks's capital, the shock is transmitted equally to the lending banks and the process begins again.
   • the reverberation ends when it has been fully absorbed by the system or all the linked institutions have defaulted.

4. Report the results: We use R to generate graphs simulating the transmission of the shock in the system. In addition, we plot graphs to analyse the impact of toggling the inputs of the system such as interbank assets to asset ratio, capital to asset ratio, gamma, Number of Banks, N and Interconnectivity (Erdos Renyi Probability), p.

Example: Shock Reverberation in a 5-Bank Network (p=50%, gamma=5%, theta=20%)