The summer was a busy time for research on financial networks, ranging from interlinkages between economies via interbank money markets to financial infrastructures. One sentence summaries of eight papers are below.  Let me know if you have a relevant paper or work that I can add to the list.

“Analysing Interconnectivity among Economies”

Alfred Wong and Tom Fong study how interconnected relationships between economies can be disentangled into simple and quantifiable bilateral interdependence linkages, using 11 Asia-Pacific economies as an example.  Hong Kong Monetary Authority Working Papers No. 1003. (download)

“Systemic risk, financial contagion and financial fragility”

Serafín Martínez-Jaramillo, Omar Pérez Péreza, Fernando Avila Embriza and Fabrizio López Gallo Deya model systemic risk with two main components: a random shock that weakens one or more financial institutions and a transmission mechanism which transmits and possibly exacerbates such negative effects to the rest of the banking network. Journal of Economic Dynamics and Control (in press, link to sciencedirect)

“Systemic risk in a network model of interbank markets with central bank activity”

Co-Pierre Georg and Jenny Poschmann investigate which influence central bank activity has on interbank markets. Jena Economic Research Papers No. 2010-033. (download)

“Peer monitoring or contagion? Interbank market exposure and bank risk”

F.R. Liedorp, L. Medema, M. Koetter, R.H. Koning, and I. van Lelyveld test if interconnectedness in the interbank market is a channel through which banks affect each others riskiness. The evidence is based on quarterly bilateral exposures of all banks active in the Dutch interbank market between 1998 and 2008.  DNB working paper No. 248. (download).

“The sterling unsecured loan market during 2006-08: insights from network theory”

Anne Wetherilt, Peter Zimmerman and Kimmo Soramäki analyze empirically the unsecured overnight money market in the United Kingdom as a network of relationships and examine how the structure has changed over the recent period of crisis. Bank of England Working Paper No 398. (download)

“What do network theory and endogenous risk theory have to say about the effects of central counterparties on systemic stability?”

Jean-Pierre Zigrand’s paper considers what network theory can say about the effects of CCPs on systemic stability and how do different CCP structures (e.g. one vs multiple CCPs) alter systemic risk. Banque de France Financial Stability Review No 14. (download)

“Liquidity costs and tiering in large-value payment systems”

Mark Adams, Marco Galbiati and Simone Giansante develop and simulates a model of the emergence of networks in an interbank RTGS payment system. Bank of England Working Paper No. 399. (download)

“Liquidity-saving mechanisms and bank behaviour”

Marco Galbiati and Kimmo Soramäki develop a simple agent based model and investigate the effect of liquidity-saving mechanisms (LSMs) in interbank payment systems.  The paper is published as Bank of England Working Paper No 400. (download)

A new paper by Farooq Akram and Casper Christophersen entitled “Interbank overnight interest rates – gains from systemic importance” analyses the Norvegian overnight interbank interest rates paid by banks. They find that during the Financial crisis, the interest rates were substantially below indicative quotes of interest rates provided by major banks. The interest rate variation is explained by the relative size and connectedness of the banks, implying favorable terms for banks of systemic importance.

Moreover, interest rates are found to depend not only on overall liquidity in the interbank market, but possibly on its distribution among banks as well, suggesting exploitation of market power by banks with surplus liquidity. They also find evidence of stronger effects on interest rates of systemic importance, credit ratings and liquidity demand and supply since the start of the current financial crisis.

An open-source implementation of the algorithm for uncovering the interbank loans was developed as part of this project. The algorithm is available as part of the Financial Network Analyzer.

The European Central Bank published on 1 June a special feature entitled “Financial Networks and Financial Stability” in its Financial Stability Review.

The recent global financial crisis has illustrated the role of financial linkages as a channel for the propagation of shocks. It also brought to the fore the concept that institutions may be “too interconnected to fail”, in addition to the traditional concept of being “too big to fail”. [full article]

The article provides an overview on literature on financial network analysis and discusses what network theory can bring to the understanding of the concept of “too interconnected to fail”. The article was prepared by me and Silvia Gabrieli.

Cross-Border Financial Surveillance: A Network Perspective (IMF Working Paper 105 , April 2010 ) by Marco Espinosa-Vega and Juan Sole simulates different credit and funding shocks to the banking systems of a number of countries. Using cross-country bilateral exposures data from BIS they illustrate the contagion algorithms presented in the paper.

In a similar vein Assessing the Systemic Implications of Financial Linkages (Chapter II in IMF’s Global Financial Stability Report, April 2009) by Jorge Chan-Lau, Marco A. Espinosa-Vega, Kay Giesecke, and Juan Sole discusses four complementary approaches to assess direct and indirect financial sector systemic linkages:

• network approach which relies primarily on institutional data to contagion triggered by financial distress
• co-risk model which assesses common risk factors
• distress dependence matrix which is based on market data, but instead of looking at bilateral relationships as above, uses a composite time-varying multivariate distribution that captures linear (correlation) and nonlinear interdependence
• default intensity model which measures the probability of failures of a large fraction of financial institutions due to both direct and indirect systemic linkages

Network Analysis: Contagion Path Triggered by U.K. Failure in the model (Jorge Chan-Lau, Espinosa-Vega, Giesecke, and Solé, 2010)

Contagion in Financial Networks (Bank of England Working Paper No. 383, March 2010) by Prasanna Gai and Sujit Kapadia develops an analytical model of contagion in financial networks. The paper explores how the probability and potential impact of contagion is influenced by aggregate and idiosyncratic shocks, changes in network structure, and asset market liquidity. The paper is forthcoming in Proceedings of the Royal Society A.

Optimal Fragile Financial Networks (forthcoming) by Fabio Castiglionesi and NoemNavarro studies the endogenous formation of a financial network under a model where banks establish connection to co-insure their liquidity needs. The paper rationalizes the evidence of sparse network structures observed in the topology of interbank networks.

The year 2009 is now gone and its time to look back at the research on financial networks and related topics from that year. Here are some that I found. Please help me add to the list.

Liasons Dangereuses: Incresing connectivity, risk sharing and systemic risk (by Stefano Battiston, Domenico Delli Gatti, Mauro Gallegati, Bruce C. Greenwald and Joseph E. Stiglitz). [link]

Rethinking the Financial Network (A speech by Andrew Haldane t the Financial Student Association, Amsterdam April 2009). [link]

On the Informational Properties of Trading Networks (by Lada Adamic, Celso Brunetti, Jeffrey H. Harris, and Andrei A. Kirilenko). [link]

The Financial Crisis and the Systemic Failure of Academic Economics (by David Colander, Hans Föllmer, Armin Haas, Michael D. Goldberg, Katarina Juselius, Alan Kirman, Thomas Lux, and Birgitte Sloth). Univ. of Copenhagen Dept. of Economics Discussion Paper No. 09-03. [link]

Identifying Community Structures from Network Data via Maximum Likelihood Methods (by Jernej Copi, Matthew O. Jackson, and Alan Kirman), The B.E. Journal of Theoretical Economics: Vol. 9 : Iss. 1 (Contributions), Article 30. [link]

Pedro Romero has three papers on banking networks: “The Evolution of Economic Networks” [link], “Banking Crises and Institutional Arrangements”. [link], and “Bank Runs, Banking Contracts, and Social Networks” [link]

A Comparison of the Director Networks of the Main Listed Companies in France, Germany, Italy, the United Kingdom, and the United States (by Paolo Santella, Carlo Drago, Andrea Polo, and Enrico Gagliardi). [link]

Structure and Stability in Payment Networks – A Panel Data Analysis of ARTIS Simulations (by Stefan Schmitz and Claus Puhr). [link]

Visualizing Stock-Mutual Fund Relationships through Social Network Analysis (by Rafael Solis), Global Journal of Finance and Banking Issues Vol. 3. No. 3. 2009. [link]

The sterling unsecured loan market during 2006-2008: insights from network topology (Anne Wetherilt, Peter Zimmerman and Kimmo Soramaki); in Leinonen (ed) Simulation analyses and stress testing of payment networks, Bank of Finland Scientific monographs E:42. [link]

MITACS is organizing a Workshop on Financial Networks and Risk Assessment, taking place in Toronto from May 19 to May 21, 2010. The workshop is part of the MITACS International Focus Period on Advances in Network Analysis and its Applications and will be attended by 30-50 specialists in the field (from academia and business) as well as students. The 3 day event will consist of plenary talks, tutorials and contributed talks.

There is a new interesting paper "On the Informational Properties of Trading Networks" by Adamic, Brunetti Harris and Kirilenko using transaction level data for all regular transactions in September 2008 E-mini S&P 500 futures contracts.

They construct networks from executed trades and then look at the structure of these networks and relate them to returns, volatility, volume, and duration. Interestingly they find that assortativity, low clustering coefficient and connectedness are positively related to returns and volume and negatively related to duration and volatility. In contrast, topologies with centralization and assortativity close to zero, high transitivity and high connectedness are associated with average returns and volatility, and positively related to volume and duration.

European Central Bank (ECB) organized a workshop with the above title last Monday, 5th of October. It was the first event of this scale gathering researchers applying network theory and network analysis on banking, financial stability and systemic risk topics. The introductory remarks to the workshop were given by Gertrude Tumpel-Gugerell, Member of the ECB’s Executive Board.

I provided an introduction to network theory and financial network analysis entitled “Is network theory the best hope for regulating systemic risk?” in which I developed topics of an earlier post with the same title: How to measure the systemic importance of a bank, can regulators promote safer financial topologies and is it possible to devise early-warning indicators from real-time transaction data?

Sheri Markose presented a working paper “Too interconnected to fail” where she, Simone Giansante and colleagues do stress tests on US the Credit default swaps (CDS) market. The paper uses a multi-agent simulator developed for this purpose. A demo version of the simulator is available on the above link as well.

Olli Castren (ECB) presented some novel work with Ilja Kavonius (ECB) modeling contagion across sectors of the economy using contingent claims analysis and flow of funds data. The paper “Balance sheet contagion and the transmission of risk in the euro area financial system” was recently published in the ECB Financial Stability Review. The presentation is also available.

NEW: These and other papers and presentations of the workshop are summarized in the ECB publication “Recent advances in modelling systemic risk using network analysis” (7 January 2010). See also the press release.

The Receipt Reactive Gross Settlement (RRGS) method was proposed by Jamie McAndrews in Johnson-McAndrews and Soramaki (2004) as a new, incentive compatible liquidity saving mechanism. The basic idea of RRGS is that banks are sure to use only incoming funds to settle their less urgent payments. Each bank has the incentive to submit payments to the RRGS queue as costly liquidity is consumed only when the bank receives funds from other banks.

This simulator allows simulations of one version of RRGS with historical payment data. It is easy to use and efficient, being able to simulate a day with half a million payments in less than 60 seconds. The fast speed of the simulations and quick set-up allows one to test many alternative scenarios easily.

Read the rest of the entry for instructions on downloading and using this application. You are welcome to get in touch with me for any questions.

Input files

Payment data file

The data must have the following fields in the following order: id, date, time, value, sender, receiver, priority. NOTE: payments must be ordered ascending by date and time. The file can contain multiple days of data. If the time field is shorter than the expected format, a leading zero is added to the beginning (e.g. to fix a time string 55959 to 055959 – one second to 6am). The priority must be 1 (high) or 2 (low). The field and decimal separators used in the file are defined in Input parameters.

Funds data file

The data must have the following fields in the following order: date, bank, balance. The ‘bank’ field must match the ’sender’ and ‘receiver’ fields in the payment data. It must be ordered by date. A balance is used for subsequent days until a new balance is defined in the file. The field and decimal separators used in the file are defined in Input parameters.

Input parameters

• ‘Payments file’: Select the file with the payment data
• ‘Funds file’: Select the file with the opening balances for each day.
• ‘Overdrafts file’: Select the file with overdraft limits per bank for each day. A value of e.g. 100 means that the balance of the bank can go up to -100.
• ‘Date format’: date format in both Payment data and Funds data files, see possible formats.
• ‘Time format’: time format used in ‘Payment data file’, see possible formats.
• ‘Opening time’: Opening time of the system. The simulator will throw an error in case payments before opening time are encountered. Format as given by ‘Time format’.
• ‘Closing time’: Closing time of the system. The simulator will throw an error in case payments after closing time are encountered. Format as given by ‘Time format’.
• ‘Do queue optimization’: Optimizes the RTGS queue (if ‘Settlement method’ = RTGS) and RRGS queue (if ‘Settlement method’ = RRGS).
• ‘Allow negative balance’: Allows balance in RTGS or RRGS to become negative.
• ‘Settlement method’: RTGS or RRGS, see above.
• ‘Splitting method’: ‘Threshold’ refers to value above which payments are split into equal sizes each under the given threshold value. ‘Liquidity’ method will split the original payment into two: one worth the available liquidity by the bank, and one worth the rest of the value. In both methods payments are split only if liquidity for settling them in whole is not available. In ‘liquidity’ method the liquidity available must also be above the minimum value given as a parameter.
• ‘Field separator’: field separator used in Payments and Rates files, usually ‘;’ or ‘,’
• ‘Decimal separator’: decimal separator used in Payments and Rates files, usually ‘,’ or ‘.’
• ‘Load parameters’ and ‘Save parameters’: loads/saves parameters onscreen from/to a file

Operation

1) Settlement by RTGS

In RTGS settlement a payment is settled immediately if there are sufficient funds. In case there are not sufficient funds to cover the payment, the payment is queued – and released immediately as sufficient funds become available from incoming payments. The RTGS balance is reduced by outgoing payments, and increased by incoming payments.

2) Settlement by RRGS

In RRGS payments marked with priority 1 are settled immediately, irrespective of available liquidity. Payments marked with priority 2 are settled by RRGS against the balance in RRGS. The RRGS balance is reduced by outgoing priority 2 payments, and increased by incoming priority 1 and priority 2 payments.

3) Queue optimization

The queue optimization is run at the defined intervals. Any payments submitted at that time are settled before the optimization is run. An optimization is run before end of day procedures are begun. Queue optimization can be used to optimize either the RTGS queue, or the RRGS queue. Optimization is done according to algorithm in Bech and Soramaki (2001).

4) Splitting

When a payment is split the elements to be queued are put in the queue before the payment that can be processes is settled. This way a chain of events can cause the immediate settlement of the queued parts as well. For details of splitting, see Leinonen and Soramaki (2001).

5) End of day procedures

In end of day procedures all pending payments are settled not taking into account any constraints.

Output

-out.txt contains statistics on all individual payments

• [the same fields as in the input data]
• ’settlement_time’: time the payment was settled
• ‘delay’: (in seconds)
• ’senderbalance’: balance of sending bank after settlement of payment
• ‘receiverbalance’: balance of receiving bank after settlement of payment
• ‘bilateralbalance’: bilateral balance from sender’s perspective (positive if received more than sent)
• ’settlement_method’: method by which the payment was settled: rrgs (immediately by RRGS), rtgs (immediately by RTGS), rrgs_queue (released from RRGS queue), rtgs_queue (released from RTGS queue), rrgs_opt (released by optimization algorithm from RRGS queue), rtgs_opt (released by optimization algorithm from RTGS queue), rtgs_eod (settled by end of day procedures from RTGS queue), rrgs_eod (settled in end of day procedures from RRGS queue)

-stat.txt contains statistics on each bank

• ‘day’: date
• ‘id’: bank id
• ‘value_as_recipient’: value of payments in input data where the bank is a receiver
• ‘number_as_recipient’: number of payments in input data where the bank is a receiver
• ‘value_as_sender’: value of payments in input data where the bank is a sender
• ‘number_as_sender’: number of payments in input data where the bank is a sender
• ‘number_submitted’: number of payments submitted for settlement
• ‘value_settled’: value of payments settled during the operation hours
• ‘number_settled’: number of payments settled during the operation hours. Due to split payments may be higher than number_submitted.
• ‘value_settled_eod’: value of payments settled in end of day procedures
• ‘number_settled_eod’: value of payments settled in end of day procedures. Due to split payments may be higher than number_submitted.
• ‘opening_balance’: balance at the beginning of the day
• ‘overdraft’: overdraft limit for the bank
• ‘minbalance’: minimum balance during the day (also including end-of-day procedures)
• ‘maxbalance’: maximum balance during the day (also including end-of-day procedures)
• ‘avgbalance’: average balance during the day
• ‘eod_balance’: end of -day balance
• ‘minbilateral’: minimum bilateral balance against across all other banks
• ‘maxbilateral’: maximum bilateral balance against across all other banks
• ‘avgsubmissiontime_received’: average submission time of payments received (unweighted)
• ‘avgsubmissiontime_sent’: average submission time of payments sent (unweighted)
• ‘avgsettletime_received’: average settlement time of payments received (unweighted)
• ‘avgsettletime_sent’: average settlement time of payments sent (unweighted)
• ‘avgsubmissiontime_received_weighted’: average submission time of payments received (weighted by value)
• ‘avgsubmissiontime_sent_weighted’: average submission time of payments sent (weighted by value)
• ‘avgsettletime_received_weighted’: average settlement time of payments received (weighted by value)
• ‘avgsettletime_sent_weighted’: average settlement time of payments sent (weighted by value)
• ‘avgdelay’: average delay for a delaying payments, sum of delays divided by the number of all payments. In seconds.
• ‘avgdelayweighted’: value weighed delay for a delaying payments, in seconds
• ‘maxqueuesize’: maximum number of queued payments at any given time
• ‘maxqueuevalue’: maximum value of queued payments at any given time
• ‘number_queued’: number of payments queued
• ‘value_queued’: value of payments queued
• ‘number_split’: number of payments split
• ‘generated_payments’: number of payments generated by splitting

Download, installation and running

Simply copy and extract this file (rrgssimulator1.3) to a folder that you create. Double click run.bat to launch the application. The package contains example files payments.txt, overdrafts.txt and funds.txt files (in the /data folder) and a parameters.txt file that you can load into the application and test the example data (change the paths to the correct files in the /data folder before starting the simulation).

Credits & Usage

I would like to thank John Jackson, Joanne McLafferty and Edward Denbee and Balazs Godeny for their contributions to specifying and implementing this application.

You are free to use the program for any purpose. The .zip file contains the source code as well. Please make a reference to this blog entry in case you use the application for any research.

(updated 29 October 2010 with version 1.3 of the software and updates to documentation)