Can banks default overnight? Modeling endogenous contagion on O/N interbank market
Paweł Smaga, Mateusz Wiliński, Piotr Ochnicki, Piotr Arendarski, Tomasz Gubiec
aa r X i v : . [ q -f i n . E C ] M a r Can banks default overnight? Modeling endogenous contagion on O / N interbankmarket
Paweł Smaga c,d , Mateusz Wili´nski a , Piotr Ochnicki a , Piotr Arendarski b , Tomasz Gubiec a a Faculty of Physics, University of Warsaw b The Poznan University of Economics and Business c Warsaw School of Economics d National Bank of Poland
Abstract
We propose a new model of the liquidity driven banking system focusing on overnight interbank loans. This significantbranch of the interbank market is commonly neglected in the banking system modeling and systemic risk analysis.We construct a model where banks are allowed to use both the interbank and the securities markets to manage theirliquidity demand and supply as driven by prudential requirements in a volatile environment. The network of interbankloans is dynamic and simulated every day. We show how only the intrasystem cash fluctuations, without any externalshocks, may lead to systemic defaults, what may be a symptom of the self-organized criticality of the system. We alsoanalyze the impact of di ff erent prudential regulations and market conditions on the interbank market resilience. Weconfirm that central bank’s asset purchase programs, limiting the declines in government bond prices, can successfullystabilize bank’s liquidity demand. The model can be used to analyze the interbank market impact of macroprudentialtools. Keywords: contagion, interbank market, network analysis, systemic risk, quantitative easing, macroprudential policy
Acknowledgements
Support of Fundation For Polish Science (28 / UD / SKILLS / Preprint submitted to Elsevier March 17, 2016 . Introduction
The interbank market activity in many countries has been severely impaired during the recent global financialcrisis. The events of 2007 were the hard way to find out how a single shock can lead to disastrous e ff ects on the wholeinternational financial system. The network of complicated relations and dependencies between financial institutionsacross the globe was the main reason for which a single crash spread through the world like a disease [44]. From thismoment on, the term contagion [78] became an important topic in financial stability research.The central term in mentioned area of research is systemic risk . In economy and finance, risk is often describedin terms of volatility and uncertainty. A more precise description and at the same time a good measure of risk, wouldbe to say that it is a probability of an event multiplied by its negative consequences. What this approach lacks arethe dependencies and correlations between events. Thus, systemic risk is not about a single, unrelated crashes, it isabout connected series of negative events. In more descriptive way, it is about financial domino e ff ect or an avalancheof failures, where even smaller but correlated events, may lead to system breakdown. Study of systemic risk aims atdescribing the odds of the whole system collapse, instead of concentrating only on individual institutions risks. A veryelegant description of the systemic risk concept can be found in Haldane et al. [42]. One of the crucial elements inthe rise of so called cascades of failures are connections between di ff erent elements of the system. These connectionsmay transmit negative e ff ects from one institution to another causing a great damage to the whole economy. In orderto approach this problem, we need to precisely define the links. Having that, we will be able to use the networkformalism, a common tool used by researchers in many areas [26] including finance and economy . This popularityis partly because of clear analogies between financial systems and other systems where this approach turned out to bevery succesful [60].Allen and Gale [7] where the first to show that contagion risk prevails in incomplete bank network structures wheresmall shocks lead to large e ff ects through contagion mechanism. Freixas et al. [29] further show that interbank marketused for liquidity management purposes endogenously leads to a coordination failure which exposes the system tocontagion in case of a single too-interconnected-to-fail bank default. Therefore, the loosened market discipline on theinterbank market requires the central bank to act as a crisis manager. This notion is further strengthened by Montagnaand Lux [63], who show that there are non-linearities in the way bank-specific shocks are propagated and structure See [19] and [76] for an overview of the systemic risk concept. In 2013, Nature Physics published a special issue, which main subject was ’Complex Networks in Finance’.http: // / nphys / journal / v9 / n3 / index.html
2f the various layers of interbank relations matters for contagion assessment. Such studies show that the networkstructure determines the stability of the interbank market (for a contrasting view see Birch and Aste [14], who arguethat the network structure has less importance).The inherent instability of the network structure is exemplified by a robust-yet-fragile character of financial net-works [33]. The network structures are resistant to shocks in general or to peripheral nodes, yet vulnerable to conta-gion from failure of nodes with concentrated exposures [3, 22, 53]. This is confirmed by other studies [16, 71, 30, 18]which find that majority of real interbank networks have strong tiered and core-periphery structures, meaning thatthey have low density and the exposures distribution is concentrated in a small number of nodes that lay in the core.Therefore, tiered networks may be inherently less stable [74].Most of interbank network analyses are country studies based on static interbank network structures, while as-suming idiosyncratic or common shocks (e.g. [75, 31, 81, 16, 80, 56, 21, 73, 58, 61, 28]). They are surveyed byUpper [79], who concludes that the common finding is that contagion in core-periphery structured networks can beconsidered as a low probability, but high impact event. The drawback of those studies is that they are based on apoint-in-time structure of the interbank network and due to its constant evolution the resulting contagion risk shouldbe assessed with caution. Moreover, the studies analyzed by Upper usually include contagion e ff ects only in oneparticular segment of the interbank market (the lending market), excluding other layers of interconnectedness (e.g.cross-holding of securities). However, di ff erent studies include randomly generated distribution of possible networksand provide more robust results [40]. Taking into account banks’ behavioral reactions motivated by liquidity man-agement strategies leads to liquidity contagion (e.g. [49, 2, 15]) which cannot be neglected. We contribute to thisdebate by simulating a dynamic market structure with liquidity being one of the main drivers of banks’ behavior inour model.The main idea behind the network analysis is that the properties and behavior of a node have to take into accountthe behavior of nodes directly or indirectly linked to it [23]. In most cases of systemic risk research, nodes in theanalysed network are simply financial institutions. In this particular paper we focus on the interbank system, thusanalysed network will consider only banks. Moreover, we want to concentrate on the transactions with short-termmaturities, mainly overnight loans. This type of loans is a substantial part of the whole interbank activity, and theirmain purpose is to manage liquidity. In most countries they represent about 30% of all interbank loans volume,making them an important and not negligible part of the market. Furthermore, in countries like Russia, Poland,Czech Republic or Belarus, overnight loans dominate entirely, having more than 90% share in the interbank market.3herefore, we believe that analysing the impact of overnight loans on market stability, is an important part of systemicrisk research, maybe the most important for some parts of the world. As a result, in our model links between banksdescribe overnight loans. The main obstacle in majority of networks analysis studies is lack of data on bilateralinterbank exposures either from financial reporting or payment system flows. This data is confidential and usuallyunavailable even for supervisory authorities and central banks. As a solution to these problems, many researchers usevarious methods, in order to estimate the structure of connections between banks [55, 41, 64].Network approach has been intensively used to analyze the interbank market contagion. This market can onthe one hand act as a shock absorber, bank liquidity management mechanism and induce market discipline throughincentivizing monitoring (e.g. [72]). But on the other hand, interbank market may serve as a transmission channel forcontagion e ff ect [68, 6]. There are two crucial propagation mechanisms in the interbank market. The most obviousone is simply through insolvency of debtors, who are unable to pay o ff their liabilities. In this case, negative e ff ectsspread along the edges of our network. This transmission channel is direct. In contrast, the trust e ff ect causes afinancial crisis to propagates indirectly. In response to other institutions financial problems, a bank may decide tolimit its participation in the interbank market. Such behavior leads to an overall reduction in bank funding supplyon the interbank market or selectively only towards banks perceived as unhealthy [9, 49, 20, 8, 32]. As shown byGai and Kapadia [34], this propagation mechanism may cause severe cascade e ff ects. However, interbank is not theonly source of failure propagation. Crisis may also spread due to common external assets held by di ff erent banks.If a failing bank decides to sale its assets in order to maintain liquidity, he may cause a significant loss in value of aparticular asset or even a whole class of assets, making him also su ff er a loss. If other banks, with a similar portfolioof external assets, are on the verge of solvency, it may trigger a series of defaults across the system [5, 36]. The modelpresented in the paper accounts for all of the above mechanisms of contagion.The approach to modelling economical phenomena, shown in this work, is a part of an increasingly popularconcept of agent based modelling in finance and economy [35]. Complexity theory, agent based models and networkscience are the elements that may give rise to a new quality in modern economy and finance [27, 12], and they are alljointly used in our research. The structure of our model, which will be described in further sections, is in some aspectssimilar to model B proposed in paper by Iori et al. [48]. Instead of analysing single shocks, we try to find a relationbetween the size of banks cash fluctuations and the stability of the market. In such a case, collapse will be a resultof the internal system dynamics. We make several assumptions regarding the response of a bank to these fluctuationsgiven the need to fulfill the simplified prudential requirements. We also need to remember that those random changes4n bank’s balance sheet may be both positive and negative. Finally, even though banks react in a rational way fromtheir individual perspective, the decisions they make often have a negative impact on the system as a whole. Theirstrategy may even assume other banks failure as long as it keeps them solvent [70].First step of the model simulation is to build a network of bilateral interbank exposures, according to the supplyand demand on the interbank system. Since it is very unlikely to get a perfect matching across all the banks that needmoney and those who want to lend money, banks need to reach to the securities market next. At every step, banksneed to check the status of their debt and the regulatory requirements that they need to fulfill. The central questionsof our paper is to what extent does the interbank market stabilize the system, what is its impact on propagation ofdefaults and how the regulations a ff ect both stability and contagion process.The contributions of the paper are threefold. First, unlike most previous models which tested system’s reactionto an external shock, in our dynamic model crashes of the entire banking system may occur as a result of an internalfeature of the system (cash fluctuations). Secondly, our interbank network structure is dynamic and while otherstudies mainly analyze static network structures (see [79] for a survey), the network structure in our model is uniquei.e. simulated every day on the basis of interbank transactions from the previous day. From this perspective, our workis a part of large branch of science which is dedicated to systems described with evolving networks [82] (or even morepopular lately, temporal networks [45]). Thirdly, we take into account three types of interconnectedness channels atthe same time together with an array of capital and liquidity requirements. We show to what extent do prudential ratiosdampen or magnify contagion on the interbank market. We also confirm that central bank’s asset purchase programs,limiting the declines in government bond prices, may successfully stabilize bank liquidity demand.In our study, we used data from Polish interbank market. To the best of our knowledge, there are scarcely anystudies of the interbank contagion in Poland, all of which find a limited contagion risk. Hałaj [39], studying dominoe ff ects, suggests that it results only from the failure of some of the largest interbank players and the second rounde ff ects of the initial default are negligible. The Polish central bank (NBP) study also confirms a low probability of adomino e ff ect [65]. Gr ˛at-Osi´nska and Pawliszyn [38], using BoF-PSS2 Payment System Simulator, come to a similarconclusion that banks hold excess liquidity for the settlement of intraday payments, while the queue management andcentral bank’s intraday credit in the payments systems contribute to low liquidity contagion potential [66].Our study has several practical applications. It may be successfully applied to a stress testing framework to gaugethe probability and impact of shocks and the resulting network resilience. The model may also be used to test theinterbank impact of macroprudential requirements and their calibration before they are implemented. Moreover, if5xtended, the model might prove helpful in assessing the systemic importance of particular nodes to identify thesuper-spreaders, which is of great relevance to both central bank liquidity management for monetary policy purposes,as well as to detection of too-interconnected-to-fail institutions [54]. It would be particularly fruitful to combine thismodel with models of long-term maturity loans, which would give us a more comprehensive picture of the interbankmarket.The article is structured as follows. First, we describe the stylized facts about the interbank market in Poland anddata used in the model. Model assumptions and its construction are presented in the subsequent section. After that wediscuss the results. In the last part we present policy implications of our research and conclusions.
2. Stylized facts about the interbank market in Poland and data used
We study the Polish unsecured segment of the interbank market that includes transactions between banks used forliquidity management purposes. According to the National Bank of Poland data [67] the unsecured segment dominatedin Poland in 2013 (almost 60% of the total volume of interbank transactions), while it played a marginal role in theeuro area, dominated by repos (60%). Polish banking sector has a structural liquidity surplus and the counterpartyexposure limits between banks on interbank market are set relatively low to limit credit risk. The interbank marketis stable and O / N constituted almost all (93%) unsecured transactions in 2013 (both in terms of volume and value)with very few transactions for longer periods. In the euro area the term structure of interbank transactions is morebalanced. An average daily turnover of unsecured O / N transactions in Poland equaled 4.36 bilion PLN in 2013, halfcompared to pre-crisis period.There is a clearly visible core-periphery structure of the Polish interbank network – almost half of the unsecuredinterbank market turnover (both the demand and the supply sides) is concentrated in 5 banks (75% of O / N), accordingto KNF data [50]. These banks have structural liquidity surpluses and determine the liquidity of the whole market.For payment settlement purposes banks can also use the secured overnight credit (standing facility) from the centralbank or lombard credit, yet their use is negligible. The obligatory reserve ratio is 3.5% and banks hold marginal excessreserves at the NBP.There are also three features of the banking system in Poland relevant to the perspective of our model approach.First, the Polish banking sector has a large home bias. According to the ESRB [25], at end-2013, holdings of sovereign Polish Financial Supervision Authority / holding of domestic + euro area sovereign debt) stood at 98% in Poland. Second, equity in the Polishbanking system is of very high quality i.e. it consists almost entirely of fully loss-absorbing Tier 1 capital. Accordingtho KNF data [51], Tier 1 capital constituted 90.2% of the total equity in the banking sector at the end of 2013.Third, there is a significant maturity mismatch in the Polish banking sector for short-term maturities. Liabilities withmaturity of up to 1 year constituted 73.5% of the total liabilities, while on the asset side this share equaled only 29%[51]. Therefore, liquidity risk is an important determinant of banking system stability in Poland.As a sample set in the simulation we use end-2013 data collected for 31 largest banks in Poland from theirrespective annual reports on a standalone basis. In our sample we have included only the banks fulfilling the followingtwo conditions. First, the bank had to participate in the Elixir system (interbank payments clearing system in Poland).At the end of 2013 there were 46 banks active in Elixir. Second, the bank had to provide complete financial reportingdata in its annual reports. We exclude the central bank (NBP) and the State Development Bank of Poland. The finallist of banks used in the model simulation is included in appendix 1. Our sample, thus, covers 79.8% of banking sectorassets in Poland as of end-2013 (including assets of commercial banks, cooperative banks and branches of foreigncredit institutions). This is a relatively high share, given that the interbank transactions in Poland are performed mainlywithin the pool of commercial banks and branches of foreign credit institutions, while numerous small cooperativebanks usually use their associated banks for liquidity purposes and do not engage in interbank transactions directly.All regulatory ratios are calculated using the same end-2013 data.
3. The model (assumptions and construction)
In the previous section we briefly presented characteristics of the Polish interbank market. As already mentioned,in contrast to most European countries, unsecured O / N loans dominate the interbank market in Poland. For thatreason, a majority of models present in the literature tested on di ff erent market structures cannot be directly appliedto the Polish market. In fact, the network of loan connections on the Polish interbank market di ff ers every single day,while most of hitherto models analyzed the dynamics of a static loan network only. This explains why creating a newliquidity-driven interbank market model was necessary.In this section we introduce a new model of an interbank system dominated by transactions with short maturities.Our aim is to model the condition and behavior of each bank on a daily basis. Since our model focuses on the shortterm, we analyze banks’ reactions to changes in their liquidity demand and supply, shaped by internal as well as7xternal factors. Our approach is founded on a stylized bank balance sheet-based model with a simplified structureand is similar to those presented by e.g. [52, 57, 62, 77, 14, 43, 4]. In addition, it also develops the initial work onnetwork modeling performed by Gai and Kapadia [33] and May and Arinaminpathy [59]. We construct a bankingsystem network from heterogeneous banks, all of which have a di ff erent size and balance sheet structure, based on thedata extracted from their financial reports.Our model has several assumptions: • the entire market of interbank transactions consists only of unsecured O / N loans (in other words, we excludeinterbank transactions with longer maturities and secured interbank transactions) • banks’ behavior is motivated by the need to fulfill the liquidity demand and maintain the regulatory ratios • O / N loans are granted each day and repaid the following day • banks’ securities portfolios consist only of liquid Polish government bonds available for sale and valued usingmark-to-market accounting • after a bank defaults, its counterparty banks immediately experience losses on their interbank loans equal to theamount of the exposure (we assume the Recovery Rate is zero and Loss Given Default equals 100%) • any losses incurred by the bank are directly reducing its equity • troubled banks cannot raise additional capital overnight or be bailed out (no state aid provision by public au-thorities and no recourse to the Lender of Last Resort from the central bank is possible) • we focus on short-term reactions of banks, changes in business models are not considered • we analyze the impact only on the balance sheet items and exclude any income statement adjustments • counterparty (interbank exposures) and market risks (bond prices) are not being hedged • we analyze the dynamics within a closed system – only the banks from Poland participate in the domesticinterbank marketOur stylized bank balance sheet structure includes several items. They are used as variables representing the stateof each bank every day. We assume that assets may be described by the following four variables: • Loans - total amount of loans to the nonfinancial and public sector at their book value8
Cash - cash and balances with the central bank • Securities - consisting only of liquid government bond portfolio of a single bond type; current price of a singlebond is described by the variable p , so the mark-to-market value of securities is equal to p times Securities • Interbank Assets - total amount of all interbank O / N loans grantedLiabilities of the bank may be described by only two variables, namely: • Deposits - total amount of deposits from the nonfinancial and public sector at their book value as well as anybank bonds issued that can be redeemed at notice by the bank before their maturity without loss of value • Interbank Liabilities - total amount of all interbank O / N loans receivedTotal Assets is a sum of
Loans , Cash , Securities times p , and Interbank Assets , while Total Liabilities is a sum of
Deposits and
Interbank Liabilities . Equity of the bank is defined as the di ff erence between Total Assets and TotalLiabilities. Loans to the nonfinancial and public sector remain constant.
Cash and
Securities serve as liquidity bu ff er.Although the fundamental aim of banks’ activity is to make profit, this activity is limited by the need to fulfillnumerous prudential regulations. In our model we assume several simplified prudential regulatory constraints onbanking activity that banks try to maintain at all time. These ratios act, therefore, as drivers of banks’ behavior andtheir responses to changes in their liquidity demand . As our model focuses solely on the short term, we assumethat two prudential ratios are crucial: Reserve Requirement and Liquidity Ratio. These ratios can be expressed in themodel in terms of the variables defined.Reserve requirement is a monetary policy tool. It is an obligatory level of banks reserves set aside for liquidityreasons. It is dependent on the reserve rate set by the NBP (3.5% as of end-2013). It is calculated on the basis ofnonfinancial deposits (500k EUR is subtracted from the required reserve level), excluding interbank deposits. Wemodel it as follows: Reserve Requirement = CashDeposits (1)Liquidity Ratio represents bank’s ability to service its short term obligations. It is also based on Basel III LiquidityCoverage Ratio (LCR). LCR is defined as high quality liquid assets devided by total net cash outflows over the next We go further than Aldasoro et al. [4] where bank’s optimization decisions are subject only to two standard regulatory requirements: liquidityand capital adequacy ratios
90 calendar days. In our model we assume that the Liquidity Ratio is defined as:Liquidity Ratio = ( Cash + p · Securities ) Deposits (2)Although only a fraction of deposits in the denominator may be regarded as short-term liabilities, we can multiplyboth sides of the equation by this fraction without a loss of generality. As a result, the regulatory limit is lower as it ismultiplied by the share of short-term deposits in total deposits (which is lower than 100%).When those two crucial regulatory requirements are fulfilled, bank considers three other ratios. The first one isthe Leverage Ratio representing the overall level of bank’s risk exposure. It has to be equal to or greater than 3%according to Basel standards. Another one is the Capital Adequacy Ratio which represents bank’s resilience andoverall soundness. It is modeled on the basis of Basel methodology of risk-weighted assets (RWA) and has to equalat least 8%. RWA includes bank’s exposure to credit risk, which is the most important element of RWA for Polishbanks . We account for market and operational risk by setting slightly higher risk weights. Risk weights for cash andother assets (i.e. government bonds) equal 0%. The third ratio considered is the large exposure limit representing partof bank’s credit risk management requirements. It is based on Article 111 of Directive 2006 / / EC and limits bank’soverall exposure to interbank market. These ratios are estimated in our model as follows:Leverage Ratio = EquityTotal Assets (3)Capital Adequacy Ratio = EquityRWA where
RWA = · Loans + · Interbank Assets (4)Large Exposure Limit = Interbank AssetsEquity ≤
25% (5)The definitions of all five regulatory ratios outlined above are naturally a simplification of the real regulatory require-ments and the exact values of those ratios in our model should not be directly compared with regulatory limits. Sincewe do not have access to granular bank financial reporting data used for supervisory purposes, we had to rely onbanks’ annual reports, which rarely used exact definitions of particular balance sheet items. To mitigate this problemwe calculate values of four regulatory ratios (Reserve Requirement, Liquidity Ratio, CAR, Leverage Ratio) basedon empirical data for end-2013 and assume that these values are actually the regulatory requirement i.e. during thesimulation each bank is trying to maintain the ratios higher or equal to their initial value. This is analogical to theassumption in the DebtRank method [13, 10]. For the large exposure limit we are using the actual regulatory require-ment of 25% of equity. Of course, contrary to the four other ratios, the bank is trying to maintain its Large Exposurevalue below this threshold. It constituted 87.3% of the total bank capital requirement at the end of 2013, according to KNF data [51]
10s mentioned before, we assume that our interbank system model is driven by the fluctuations in the environmentwhich a ff ect banks’ balance sheets. Some loans are not repaid, assets are changing their values, customers’ banktransfers are changing the level of cash and deposits. Moreover, we cannot neglect banks commercial activity, forexample on FX swaps market. All of these factors would have to be taken into account in our model. At the same timewe want to keep our model as simple as possible. Without a doubt, all of the defined variables describing the balancesheet of a single bank should fluctuate daily. As a compromise between simplicity of the model and its accuracy,we assume that the impact of the above-mentioned factors is approximated by Cash fluctuation only. Moreover,fluctuation of
Cash level of each bank should somehow depend on its size. As a result, we assume that every day, forthe period of one day,
Cash level of each bank di ff ers by(initial Cash) · σ · N (0 , , (6)where N(0,1) is a random number drawn from the normal distribution. Such a change in Cash level can be bothpositive and negative. Let us emphasize that on average such an assumption does not change the total amount of cashavailable in the whole banking system. Parameter sigma measures the amplitude of fluctuation a ff ecting the bankingsystem. For σ = Cash level, and the higher σ the higher the Cash fluctuations and the moreunpredictable and dangerous the environment of the banking system becomes (exemplifying a bank run, for instance).It may be regarded as an analogue of a physical quantity – the temperature of the banking system.So far we defined the variables describing the state of the system and external factors influencing them. However,the most important part of our model are the system’s dynamics, determined by banks’ activity. Since we focus ona daily time scale, we only consider actions that a real bank would be able to take within one day, which include:selling / buying of securities, interbank lending / borrowing and – following the DebtRank model – repurchase of bondsissued, as included in the Deposits . This way we exclude external financial support to the bank, or changes in retailloans and deposit policies. Such actions are usually taken by the management of the bank and require some adjustmenttime to be reflected in balance sheet items, which does not happen on a daily basis. This limits the applicability ofour model to approximately 60 working days. A detailed description of the actions that can be taken by banks in ourmodel is provided below. • Interbank lending: decreases the amount of
Cash and increases the
Interbank Assets . By lending on the in-terbank market, the bank makes profit (although our model does not explicitly account for that profit) so weassume that it prefers to lend the amount of money exceeding the amount of
Cash needed to fulfill the regulatory11ank Action ReserveRatio LiquidityRatio LeverageRatio CapitalAdequacy Ratio LargeExposure LimitGrant interbank loan ⇓ ⇓ ⇓ ⇑ Receive interbank loan ⇑ ⇑ ⇓ ⇓ ⇑ ⇓ ⇓ ⇑ Table 1: Bank actions and their impact. requirements, rather than to put its excess aside. From the regulatory point of view interbank lending: decreasesLiquidity Ratio, decreases CAR, but increases Large Exposure ratio. • Interbank borrowing: increases the amount of
Cash and increases
Interbank Liabilities . As a result both TotalAssets and Total Liabilities increase. It is the cheapest and the fastest way to satisfy
Cash demand needed tofulfill regulatory requirements (Reserve Requirement and Liquidity Ratio). Impact on the regulatory ratios:increases Liquidity Ratio and decreases Leverage Ratio. • Buying of securities: decreases the amount of
Cash and increases
Securities . The bank profits from holdingsecurities so we assume that it prefers to buy
Securities instead of just holding excess of
Cash that cannot belent on the interbank market and exceeds the amount needed to fulfill the regulatory requirements. • Selling of securities: increases the amount of
Cash and decreases
Securities . If a bank does not have enough
Cash to fulfill the Reserve Requirement, it can sell its
Securities , if it has any. In this way the bank does notchange any other regulatory ratios except the Reserve ratio. • Repurchase of bonds issued: decreases the amount of
Cash and decreases
Deposits . This operation is the onlyway a bank may improve its leverage ratio in the short term. It will only be taken in case of a too low leverageratio and only until this requirement is fulfilled.The impact of each of the actions outlined above on particular regulatory ratios is summarized in Table 1. Thearrows indicate improvement / worsening of the ratio, while 0 signifies no impact.Let us now analyze the net impact of all five actions considered and the need to fulfill the defined regulatory12atios, on the variables describing banks’ balance sheets. For the purposes of this analysis we assume that there areno transactional costs related to trading securities. The most important observation is that in such conditions theseactions cannot a ff ect banks’ Equity. Equity will decrease only if a bank experiences losses on defaulted interbankloans or is hit by a negative daily random Cash fluctuation. Within a single day a bank cannot increase its equity inany way, but it can only manage its liquidity and adjust the amount of
Cash and
Securities . In such case we cannotapply the standard condition of banks default being Equity lower than or equal to zero. Hence, in our model thedefault condition had to be defined in a di ff erent way which will be described further in the text. In order to preciselydefine the possible interactions and dynamics of the model we need to specify the simulation scenario of a single dayin a sequential manner.1. Repayment of O / N loans.
At the beginning of the day all banks are repaying their yesterday’s interbankliabilities. After this action it is possible that bank’s
Cash level is negative. However, we assume that at thisstage such situation is possible as it may use the intraday overdraft facility o ff ered by the central bank free ofcharge (we do not include the impact of collateralization of the intraday overdraft). As an exception, this stepis not included in the very first day of the simulation.2. Cash fluctuations.
Bank transfers executed by the customers and banks’ trading activity result in changes inbanks’ Cash level, as described and justified previously.3.
Check of leverage level and possibly repurchase of bonds issued.
If the current state of a bank satisfiesboth Reserve Requirement and Liquidity Ratio, we are dealing with
Cash surplus. In such a case, and onlyin such a case, the bank will use this surplus to redeem the bonds issued, provided the leverage ratio exceedsthe regulatory requirement as well. By repurchasing the bonds issued, the bank lowers its Total Liabilites andTotal Assets, and thus, the leverage ratio. However, the bank is limited by the requirement to satisfy ReserveRequirement and Liquidity Ratio.4.
Specifying the demand for Cash.
Before any interbank loan is executed we need to specify the cash supplyand demand for all banks. As mentioned, if a bank satisfies both Reserve Requirement and Liquidity Ratio, weare dealing with
Cash surplus. In such a case the bank is able to allocate the remaining excess of cash (X) onthe interbank market. We decided to include another way of financial contagion which we called the trust e ff ect .It is well-known that during a crisis the banks do not fully trust each other and are not willing to grant loansin the same amount as before. To model this phenomenon we assume that if any of the banks in the systemdefaulted the trust between the banks is reduced. In such a case, instead of the whole surplus Cash (X) the13anks are willing to lend only 20% of it (X / Cash supply of a bank is limited to a value which ensures Reserve Requirement, Liquidity Ratio,CAR and Large exposure limit are satisfied.If the current state of a bank does not satisfy Reserve Requirement or Liquidity Ratio we are dealing with a
Cash deficit. In such a case the bank disregards other regulatory requirements and seeks to borrow the amountneeded to meet the shortfall to fulfill these two ratios.5.
Interbank loans market.
Once we divided banks into groups of potential creditors (with Cash surplus) anddebtors (with
Cash deficit) we need to specify the loans’ amounts. If the total Cash supply is not equal to thetotal
Cash demand, the total amount of interbank loans granted is limited to the inferior of the two. In thefirst model we assume that loans are distributed perfectly evenly i.e. every creditor lends to every debtor. Theamount is proportional both to the creditor’s supply and the debtor’s demand. This may be regarded as the firststep of proportional fitting used by Battiston et al.[11].6.
Specifying the demand for Securities.
Since the interbank lending may not satisfy the demand for
Cash onthe market in full or not allocate the cash supply available, we take into account an alternative way of gainingand allocating
Cash , namely we allow the banks to buy or sell
Securities . Such an operation involves a riskof loss, therefore, the interbank market is the preferred way of acquiring and allocating
Cash on the daily timescale. Analogically to the previously-analyzed interbank loans market, we specify banks’ supply and demandfor
Securities . If after the interbank market transactions the current state of a bank still does not satisfy ReserveRequirement or Liquidity Ratio, it needs to sell
Securities in the amount necessary to cover the
Cash deficit. Onthe other hand, if a bank is dealing with a
Cash surplus even after allocating the excess on the interbank market,it uses the rest of it to buy
Securities .7.
Securities market.
The securities market di ff ers from the interbank market significantly. It is not a closedmarket and banks are not its only participants. For the purpose of the model we assume that other participants’supply and demand are constant, which means that only supply and demand of the banks’ may influence theprice of Securities . We calculate the excess demand (ED = total demand - total supply) and following [17]assume that the price of the securities changes according to the following formula: d pp = η · ED (7)14here parameter η is called the market depth and p is the price of security. As we may easily notice, if η = Securities and
Cash . It may be interpreted as an intervention of the Central Bankwhich decides to buy or sell
Securities at a specific price. In the real market η >
0. We assume η = − whichmeans that if banks decide to sell 10% of all their Securities, their price will decrease by 3%. This assumptionmay be slightly too lenient to be realistic. It should, however, be enough to show the impact of this phenomenon.8. Update of the state.
Although banks operate in such a way to fulfill all the regulatory requirements, we assumethat the only default condition is
Cash < ff er losses, which worsens their financial standing by reducing their equity. The secondchannel we analyze is the asset price contagion [15] (indirect interconnectedness) through government bonds. Afalling bank, after su ff ering a drop in equity is forced to sell its securities (government bonds) in significant amountsin order to maintain regulatory ratios. This in turn results in an immediate and significant decrease in their value. Ine ff ect, the bank not only does not recover the full value of the bonds held, but also a ff ects the market price of the bond(fire sale e ff ect). As a result, this decreases the value of securities held by other banks thus aggravating their condition.Lastly, we also consider a reduction of availability of interbank credit due to a loss of confidence.
4. Results
The dynamics of the model proposed in this paper are driven by cash fluctuations. These random changes ofbanks’ assets are fundamental to the whole concept, determine banks’ reactions and the stability of the system. Theamplitude of these fluctuations is controlled by a single parameter σ , strongly a ff ecting the results of a single simu-lation. The most interesting outcome of the simulation is the fraction of defaulted banks at the end of the assumedsimulation period (the number of defaulted banks divided by the total number of banks in the simulation). Becauseour assumptions are valid only at the time scale of days, we assume that 3 months (60 working days) is the maximumperiod of applicability of the model. Hence, the average number of defaulted banks at the end of 60 days period as15 function of parameter σ seems to be the most reliable default metric. Further in this section we focus on the plotspresenting this metric in di ff erent model versions.A computer simulation of the banking system gives us a unique opportunity to analyze its behavior in conditionssimilar to the real world. We may easily exclude the selected features of the system, and thus assess their influenceon the system. From this perspective, the most basic model we can think of is a case without the securities and theinterbank market. In this scenario the banks cannot react in any way, so their default is just a matter of strong enoughfluctuations. Since the bank goes bankrupt when its Cash falls below zero, the probability of default in each step issimply the probability of a negative fluctuation exceeding bank’s initial cash. The distribution of the changes describedis Gaussian with standard deviation equal to the initial cash multiplied by the parameter σ . Therefore, the probabilityof default is every day equal to Φ (cid:16) − σ (cid:17) , where Φ ( . ) is the Gaussian cumulative distribution function. Furthermore, theprobability of bankruptcy during the time period T =
60 days equals: p T ( σ ) = − Φ T ( − /σ ) . (8)This leads to a formula for the expected fraction of banks which went bankrupt, as a function of σ : h f def( σ ) i = − Φ T ( − /σ ) , (9)where h . i is the ensemble average of the process. This result is presented in the Fig. 1 with a dashed line. We analyzedthe result for σ from 0 to 8. Even for relatively small values of sigma, below unity, almost all banks in the systemdefaulted. As expected, without the interbank market and any possibility to liquidate the assets, even a relatively smallfluctuation may result in a default. In this version of the model the banks are fully independent, but despite that thewhole system collapses very quickly.The obvious next step is to allow the banks to sell their securities and analyze the di ff erence compared to theprevious case. For simplicity reasons we assume that the securities market is perfect i.e. selling or buying any amountof securities does not a ff ect their price. In our model such situation is equivalent to η = σ is givenby: h f def( σ ) i = N N X i = − Φ T − + Securities i / InitialCash i σ !! , (10)16here N is a number of banks in the system. This dependance is presented in the Fig. 1 with a solid line. When 〈 fr ac ti on s o f d e f a u lt s 〉 σ - amplitude of Cash fluctuationsno interbank, η =0interbank, η =0no interbank, η >0interbank, η >0no interbank, no securities market Figure 1: Average fraction of defaults as a function of σ for various versions of the model with two regulatory ratios (Reserve Requirement andLiquidity Ratio): solid black line - η =
0, without the interbank, black squares - η =
0, with the interbank, black circles - η = − , without theinterbank, black traingles - η = − , with the interbank, dashed black line - without the securities market, without the interbank. selling of securities is allowed, the behavior of the system is considerably di ff erent compared to the previous case.A significant fraction of defaults is observed only for σ > σ ≈
8) only about 80%of the banks defaulted. Even such a simple example shows that purchase of government bonds in quantities largeenough to stabilize their prices ( quantitative easing ) may significantly decrease the number of defaulted banks duringthe crisis or even prevent the defaults. In this model banks are still independent, so let us now focus on the model withinteractions leading to inter-dependencies.The most natural way of interaction between the banks is via the interbank loans market. Let us consider theprevious version of the model with perfect securities market ( η = σ , obtained by averaging over 100 realizations, is presented in Fig. 1 with black squares. The result fullyconfirms the expectations presented in the literature (e.g. [1, 24, 37]), when compared to the version without the17nterbank market. First of all, with the interbank market the number of defaults became noticable for σ > .
5, whichmeans that the system can survive without any defaults even for relatively large fluctuations. Moreover, for σ < . σ > . η =
0. Suchassumption does not, however, describe the real banking system without central bank’s intervention. The next questionwe pondered over was the influence of a positive η . Since we do not have the data about transactions on Polishgovernment bonds market, we were unable to estimate the price impact function in this case and the market depth. Welimited our analysis to the qualitative study of the impact of an infinitesimally small η = − . Both versions with andwithout the interbank market were analyzed with positive η . The results obtained are shown in Fig. 1 with trianglesand circles respectively. With a positive η a single bank with a Cash deficit selling securities may – via fire sales –decrease the value of the bonds held by other banks and hence a ff ect their financial standing. The securities market inthis form may be viewed as a second channel of contagion in our model. As we may see in Fig. 1 in both cases higher η increased the fraction of defaulted banks. The influence of the interbank market is qualitatively similar to the caseof η = σ it stabilizes the system and reduces the number of defaults, while for larger σ it amplifiesthe contagion. Yet, the stabilizing e ff ect of the interbank market is it this case much weaker and is suppressed alreadyfor σ ≈ .
5. The influence of η > trust e ff ect , as described in the previous section. The comparison of the fraction of defaultedbanks for various σ , with present interbank market and two cases of η equal to zero and greater than zero are shown inFig. 2. In both cases, η = η >
0, the influence of the trust e ff ect is not as significant as the alterations discussedpreviously. The defaults start approximately at the same point σ ≈ .
5. For smaller sigmas the trust e ff ect increasesthe fraction of defaults, but it decreases it for larger ones. This confirms the conjecture that a decrease in interbanktrust may propagate the crisis. However, this e ff ect is of little relevance in case of η >
0. In the case of η =
0, whichcan be viewed as an intervention of the central bank, the negative impact of the trust e ff ect is much more explicit. For18 〈 fr ac ti on s o f d e f a u lt s 〉 σ - amplitude of Cash fluctuationsno trust effect, η =0trust effect, η =0no trust effect, η >0trust effect, η >0 Figure 2: Impact of the trust e ff ect . Average fraction of defaults as a function of σ for various versions of the model with interbank market and tworegulatory ratios (Reserve Requirement and Liquidity Ratio): black squares - η =
0, without the trust e ff ect , white squares - η =
0, with the truste ff ect , black traingles - η = − , without the trust e ff ect , white traingles - η = − , with the trust e ff ect . large fluctuations the behavior described by the trust e ff ect is reasonable not only from the point of view of a singlebank but also from the point of view of the whole system, and it slightly reduces the fraction of defaulted banks. Andwhile this e ff ect significantly reduces the total volume of the interbank loans, it does not influence the fraction ofdefaults in a similar way.The final inquiry made by this analysis is the impact at the daily time scale of all the remaining regulatory require-ments. Besides Reserve Requirement and Liquidity Ratio already applied, we described Capital Adequacy Ratio,Leverage Ratio, and Large Exposures limit. The result of the simulation including all of them is presented in Fig. 3.There is almost no di ff erence compared to the previous version of the model with the trust e ff ect, the version closestto the real banking system both in case of η = η >
0. Upon closer inspection we are able to see two e ff ects,both of them increasing the number of deafults. First of them, present in the case of η =
0, increases the fractionof defaults for σ ∈ [1 . ,
3] and is caused by the Large Exposure Limit . Second e ff ect infinitesimally increases the We analyzed all combinations of the regulatory requirements (Capital Adequacy Ratio, Leverage Ratio, Large Exposure Limit) added to thestandard two (Reserve Requirement and Liquidity Ratio). In all cases with Large Exposure Limit the e ff ect was present. Without the LargeExposure Limit the results overlapped the result without additional requirements. 〈 fr ac ti on s o f d e f a u lt s 〉 σ - amplitude of Cash fluctuations η =0, Reserve, Liquidity η =0, all ratios η >0, Reserve, Liquidity η >0, all ratios Figure 3: Impact of the regulatory ratios. Average fraction of defaults as a function of σ for various versions of the model with interbank marketand ”the trust e ff ect”: white squares - two regulatory ratios: Reserve Requirement and Liquidity Ratio, η = black squares - all analyzedregulatory requirements (Reserve Requirement, Liquidity Ratio, Capital Adequacy Ratio, Leverage Ratio, Large Exposure Limit), η = whitetriangles - two regulatory ratios: Reserve Requirement and Liquidity Ratio, η = − , black triangles - all analyzed regulatory requirements(Reserve Requirement, Liquidity Ratio, Capital Adequacy Ratio, Leverage Ratio, Large Exposure Limit), η = − . fraction of defaults for large Cash fluctuations, σ >
3. The latter is caused by the Leverage Ratio Requirement . Wemay, therefore, conclude that currently used regulatory requirements have a very limited impact on the fraction ofdefaults for any σ and their influence is almost negligible.
5. Conclusions and policy implications
The collapse of the interbank markets during the recent global financial crisis underlined the importance of theinterbank contagion due to network interconnectedness. We devised an interbank market model for an interbankmarket structure dominated by O / N transactions and tested it on a sample of Polish banking system data for end-2013.We demonstrated how does banks’ behavior, motivated by the need to fulfill the regulatory prudential requirements,determine the extent of contagion. We prove that internal model dynamics may lead to contagious default cascades.In the numerous versions of our model, we studied three possible channels of financial contagion (balance sheet The result confirmed in the same way as in the case of the first e ff ect. ff ect of the interbank market, although it seems to bethe weakest when all of the regulatory ratios considered need to be met by banks. This underlines the conclusion thatduring a systemic crisis less restrictive prudential requirements may reduce the default propensity on the interbankmarket by maintaining its e ff ective functioning. However, for significant fluctuations of cash, the interbank marketbegins to amplify instead of dampening the shocks, which also confirms the previous findings showing that the impactof the network connectivity on the banking system’s stability, depends on the magnitude of the shock (see [77] and[68]).Secondly, once the default cascade starts, the contagion spreads relatively quickly on the market, so interventionsof public authorities have to be prompt in order to be e ff ective. We also confirm the substitutive role of the interbankmarket and the government bond market as banks’ liquidity demand stabilizers. Moreover, we confirm that centralbank’s asset purchase programs, aimed at limiting the declines in government bond prices during the crisis, cansuccessfully stabilize banks’ liquidity demand and act as a crisis-management tool.Thirdly, in case of central bank’s asset purchase program, the need to fulfill the large exposure limit reducesthe volume of interbank transactions and slightly increases the number of defaults. It suggests that usage of such atool should be preceded by in-depth analyzes of applicable regulatory requirements. In conclusion, the supervisoryauthorities should be able to exercise discretion and flexibly adjust these requirements, as the crisis unfolds.We are fully aware of the limitations of our model, relating mainly to model assumptions, simplifications andassumed behavioral responses on the need to fulfill the regulatory ratios. Therefore, our model may surely be furtherenhanced in many di ff erent ways e.g. by introducing the central bank as an active interbank market player or morerealistic network of interbank loans connections. Moreover, it is possible to apply our model to data for di ff erentperiods and from other EU countries. Our model may also be directly applied to data of countries with similar maturitystructure of the interbank transactions e.g. the Czech Republic, Russia or Belarus, which would allow comparisonsof potential contagion in other banking systems, as well as over time. Similarily, it is possible to introduce additional(i.e. regulatory or idiosyncratic) factors determining banks liquidity demand.The results of our study contribute to the literature on the impact and e ff ectiveness of prudential requirements onthe interbank market, which is still scarce . Our short-term model underlines the importance of studying contagion See e.g. [46] or [69] for a comprehensive evaluation of the e ff ectiveness of macroprudential tools, yet not including their impact on the / N transactions dynamics could underestimate.
Appendix A. The algorithm
Below we describe the algorithm used in our simulation. In order to fully understand it, it is crucial for thereader to be aware of the exact structure of the objects used in the pseudo-code. These objects are defined as follows:Banks – elements of the interbank system, each characterized by the following attributes: Cash, Deposits, Equity,Loans, Securities, representing its assets and liabilities, and ReserveRatio, LeverageRatio, CapitalAdequacyRatio,LiquidityRatio, which represent the regulatory ratios imposed on each bank individually. interbank market. .Checking leverage ratio of every bank and repaying deposits if necessary.FOR EACH bank IN banks DO:IF( Equity / ( Loans + InterbankAssets + Securities) < LeverageRatio ):lackLR = Loans + InterbankAssets + Securities - Equity / LeverageRatiomaxLR = MAX((Securities - LiquidityRatio*Deposits )/(1 - LiquidityRatio),0)maxRR = MAX((Cash - ReserveRatio*Deposits)/(1 - ReserveRatio),0)Deposits = Deposits - MIN(lackLR,maxLR,maxRR)Cash = Cash - MIN(lackLR,maxLR,maxRR)4.Calculating demand for cash for each bank.FOR EACH bank IN banks DO:CashDemand = 0.0IF(Securities/ Deposits >= LiquidityRatio AND Cash >= ReserveRatio*Deposits):maxLR = MAX(Securities - LiquidityRatio*Deposits, 0)maxBE = MAX(0.25*Equity, 0)maxCAR = MAX(5.0*(Equity/CapitalAdequacyRatio - Loans), 0)CashDemand = -TrustRatio*(Cash - ReserveRatio*Deposits)IF(LiquidityRatioOn = TRUE):IF(CashDemand < -maxLR):CashDemand = -maxLRIF(BigExposureOn = TRUE):IF(CashDemand < -maxBE):CashDemand = -maxBEIF(CapitalAdequacyRatioOn = TRUE):IF(CashDemand < -maxCAR):CashDemand = -maxCARELSE:CashDemand = MAX(LiquidityRatio*Deposits - Securities,ReserveRatio*Deposits - Cash,0)5.Network of interbank loans is created according to banks’ demand and supply. ll of the loans are executed.Total = MIN(SUM(Supply), SUM(Demand))Sup = Supply/SUM(Supply)Dem = Demand/SUM(Demand)FOR i = 1 TO SIZE(Supply) DO:FOR j =1 TO SIZE(Demand) DO:Amount = Total*Sup*DemIF(Amount > 0):ADD Loan(Banks[i], Banks[j], Amount) TO LoansSupply[i] = Supply[i] + AmountDemand[j] = Demand[j] - Amount6.Calculating demand for securities for each bank.FOR EACH bank IN banks DO:ExpectedCash = ReserveRatio*DepositsSecuritiesDemand = MAX((Cash - ExpectedCash)/SecuritiesPrice,-Securities)7.Orders for securities are executed at a price calculated according to the demand size.TotalDemand = SUM([SecuritiesDemand FOR ALL banks])SecuritiesPrice = SecuritiesPrice*(1 + Eta*TotalDemand)FOR EACH bank IN banks DO:Securities = Securities + SecuritiesDemandCash = Cash - SecuritiesDemand*SecuritiesPriceSecuritiesDemand = 08.Every bank with cash < 0 defaults and cannot repay its loans nor participate in the system.9.Repeat from step 1. References [1] Acemoglu, D., Ozdaglar, A., Tahbaz-Salehi, A., February 2015. Systemic Risk and Stability in Financial Networks. American EconomicReview 105 (2), 564–608.[2] Aikman, D., Alessandri, P., Eklund, B., Gai, P., Kapadia, S., Martin, E., Mora, N., Sterne, G., Willison, M., 2011. Funding liquidity risk in aquantitative model of systemic stability. Central Banking, Analysis, and Economic Policies Book Series 15, 371–410.
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