Экономические науки / 3

Экономические науки / 3.Финансовые отношения

Ph.D. Olena Primierova

National University of Kyiv-Mohyla academy, Ukraine

Financial contagion in banking sector

Financial contagion or any other reason of instability in the financial network may hit the system of financial institutions in any given period. Financial networks are more or less being naturally formed in order to reduce the risk of one-two banks’ problems to cause the fall of the entire system (Jackson and Wolinsky, 1996). Despite all the advantages that those kinds of networks bring, they definitely cannot be called entirely natural and “market-driven”. From time to time there are certain agents, most often governmental organizations and structures, that interfere in order influence on the game of the market (Babus, 2006). The specific kind of influence that I want to talk in this paper is the one, when governmental, or so-called “regulatory” agents interfere in the market with the specific task to save certain institutions from going bankrupt, and as a consequence, being liquidated. There is a growing point of view stating that regulatory forces should not directly loan insolvent institutions (Schwartz, 1995), and the role of the regulatory agents should be limited to a certain operations on the open market (Goodfriend and King, 1988).

However, for the purpose of this paper, we will not be discussing the necessity of bailing our certain institutions in order to save the entire system. In this paper we assume that the practice of acting as a Loaner of Last Resort is a necessity for the system, and government should act like it did in previous critical situations (Dowd, 1999). Failures of the markets are often avoided by the massive bailouts the largest financial institutions, which are characterized to be “Too Big To Fail” (Elliot, Golub and Jackson, 2014). These kinds of institutions are recognized as most interrelated, interconnected and important for the system. The failure of this kind of institution will inevitably (according to the belief of regulatory bodies) cause the fall of the entire financial network. It is crucial to mention, that “Too Big To Fail” (TBTF) are not simply financial institutions that are the biggest by size (assets, locations, employees etc.). According to the TBTF policy, biggest banks are the ones that are most interconnected and which occupy most important place in the networks (Freixas, Parigi and Rochet, 2000).

In this paper we are trying to research a question of TBTF policy from a slightly different prospective. The main purpose of the proposed model is to answer the question will the TBTF policy be different for the systems where there are multiple large banks. In other words, it is interesting to look at the network, where there are 2 or more similarly large and interconnected financial institutions. Will this fact change the application of the TBTF policy? Is it necessary to bailout all of these “largest” banks, or it will be sufficient to save only one of them in order to ensure the integrity of the system.

For the purpose of making the model adequate and possible to operate, many of the aspects of the “real world” have been simplified. First of all, unlike in many other models from majority of the authors our model has only 2 periods, which are t=0 and t=1. In the period t=0 the depositors go to the bank at their respective location and deposit the certain amount of money in the bank. Customers deposit their funds under condition of receiving an investment return with the rate R (1<R). All the customers obtain their deposits with the investment gross return at t=1. In this model there is no additional ‘middle’ period between depositing and withdrawing the goods (money), because prematurely liquidated deposits are not relevant for the purpose of illustrating the situation of TBTF occurrence in this model in particular. In any other model the additional period may be necessary in order to illustrate the influence of premature withdrawal on the liquidity of banks in the system, but not in our model.

As a consequence, in this model every consumer will receive the whole investment return, under the condition that the bank at the location where he decides to withdraw the money, has not been liquidated due to the contagion, liquidity shortage or any other extraordinary conditions. For the sake of convenience, in our model each bank at the period t=0 receives the equal amount of deposits. More than that each deposit holds the same amount of money (cash). Every bank holds the amount of good equal to 1.

Overall there are N banks in the system, which means that the overall number of goods (deposits) in the system is z=N*1. Number of banks equals to the number of locations -‐ one bank in one location. There is no cost for moving goods (money) between the banks, neither there is a limit of what amount of its deposits bank can transfer to another institution, as a consequence there are no limitations of how ^{many depositors from one location
can consumer at another location
at t=1. Let d}ij be the fraction of depositors that are travelling from the bank i to the bank j to ^{withdraw at time t=1, where (0< d}ij ^<1).^{In addition let T be
the overall number of} deposits that are being withdrawn (or attempted to be withdrawn) at the bank N at time t=1.

In our system there are 10 institutions (N=10), which implies that z=10. There are 2 banks that are much better interconnected with other banks in the system than the rest ones. System that contains one or multiple banks that may be considered TBTFs, by definition can be called incomplete network. By contrast, complete networks have their goods (deposits) evenly distributed across other members of the network, which means that in complete network each bank holds deposits in the amount of T = Z/N. For the purpose of our research question, as was mentioned above the system has 2 main big institutions that have more interbank relations that other 8. These 2 main banks are somehow mini centers for each of other 4 banks. In addition bigger banks are not connected between each other, as they are independent centers that are TBTF. 8 smaller banks have half of its depositors travel to the other small bank and half of depositors travel to a “center” bank.

^Banks^N9 ^and^N10 ^are^{center banks;
each one is the mini-center for 4 other banks.}Each of these 4 banks moves half of its deposits to central bank, and half to the next small bank if chain, so that 8 small banks deposit half of its goods clockwise in each ^{other. Finally, center banks N}9 ^{and N}10 ^{are
distributing its deposits among respective}4 banks ‐ 0.25z into each.

^d12 ^{= d}23 ^{= d}34 ^{= d}45 ^{= d}56 ^{= d}67 ^{= d}78 ^{= d}81 ⁼^0.5z^{(small bank to small bank
clockwise)}

^d19 ^{= d}29 ^{= d}79 ^{= d}89 ⁼^0.5z^{(4 small
banks to local center N}9⁾

^{d3.10 = d4.10 = d5.10 =
d6.10 =}^0.5z^{(4 small
banks to local center N}10)

^d91 ^{= d}92 ^{= d}97 ^{= d}98 ⁼^0.25z^{(center bank N}9 ^{into 4 smaller banks)}

^{d10.3 = d10.4
= d10.5 = d10.6 =}^0.5z^{(center bank N10
into 4 smaller banks})

Deposits at each bank at the time t=1:

^T9 ^{= T}10 ^{= 4*0.5z = 2z}^{(Banks N}9 ^{and N}10 ^{are holding)}

^T9 ^{= T}10 ^{= T}9 ^{= T}10 ^{= T}9 ^{= T}10 ^{= T}9 ^{= T}10 ^{= 0.5z + 0.25z = 0.75z}^{(Banks N}1 ^–
N8 ^areholding)

To sum up, there are 2 banks that are noticeably more interconnected and integrated into the system than other banks. In addition local centered banks hold more than twice of what smaller banks are holding.

The main research proposition: In the system where there are multiple TBTF banks, in the situation when all the banks in the system are experiencing liquidity shortage, it is necessary to bailout all of the big, more interconnected‐centered banks in order to save the overall system from contagion. Saving only one of the centers and liquidating others will not stop the contagion and system will go bankrupt. In the system when centered banks are interchanging deposits between each other, bailout of all the centered banks is necessary condition to save the system from financial contagion and liquidation.

References:

1. Jackson, M.O., & A. Wolinsky, 1996, A strategic model of social and economic networks, Journal of Economic Theory Vol. 71, pp. 44-74.

2. Babus, A., 2006, The Formation Of Financial Networks, Erasmus University Rotterdam, Working Paper, pp. 1-29.

3. Schwartz, A. 1995, “Systematic risk and the Macroeconomy” in G. Kaufman, ed., Banking, Financial Markets, and Systematic Risk, Vol. 7, Research in Financial Services, Private and Public Policy. Greenwich, Connecticut, Jai Press, pp. 19-30.

4. Goodfriend M., & King R.G., 1988, Financial Deregulation, Monetary Policy, and Central Banking, Federal Reserve Bank of Richmond's Economic Review, 1988 Vol. 74, No. 3.

5. Dowd K., 1999, Too Big To Fail? Long- -Term Capital Management and the Federal Reserve, CATO Institute Briefing Papers, No. 52, pp. 1—12.

6. Elliott, Matthew, Benjamin Golub, and Matthew O. Jackson. 2014. "Financial Networks and Contagion." American Economic Review, 104(10): 3115-53.

7. Freixas, X., Bruno M. P., and Rochet J.‐C. 2000, “Systemic risk, interbank relations, and liquidity provision by the central bank.” Journal of Money, Credit and Banking, 32, 611–63.