Chapter 82 The Use of Simulations as an Analytical Tool for Payment Systems

Martin Diehl¹

Deutsche Bundesbank, Germany

ABSTRACT

Simulations are among the analytical tools in payment systems analysis. They can be used to overcome epistemological weaknesses of models and calibrations, and they are virtual experiments that do not affect the real performance of payment systems.

1. BASIC FEATURES OF PAYMENT SYSTEMS

The economics of payment systems requires a sound knowledge and understanding of institu­tional features. Payment economics mainly deals with features that were formerly subsumed under the term “transaction costs.” Without transaction costs such as costs for searching, transferring, monitoring, bookkeeping, etc., neither the ex­istence of money nor that of payment systems

DOI: 10.4018/978-1-4666-6268-1.ch082

would be explainable. Therefore, economics of payment systems deals by definition with devia­tions from a pure economic theory in the sense of an Arrow-Debreu-World. In addition, knowledge of institutional features of payments system is at the very heart of it. Therefore, we will first have a look at the prominent features of payment systems in our times.

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1.1. Settlement Procedure

The settlement procedure is the core of a pay­ment system. It defines how the incoming pay­ment orders are settled. The possible choices can be ranged on a continuum from delayed net settlement to gross settlement. Gross settlement means that the settlement of incoming orders is done individually, one by one. Net settlement, however, implies the netting of at least two (at least partially) offsetting orders. In an extreme version, all payment orders for a day are collected and cleared altogether, and the net demands are settled at the end of a day. Net settlement requires less liquidity since usually many offsetting pay­ments occur. It incurs, however, higher risks, since the whole bilateral credits could be at stake in case of a failure before settlement. Therefore, net settlement requires complex risk management schemes. On the other end of the continuum is a pure Real Time Gross Settlement (RTGS), which can be understood as settling all payment orders immediately after submission and with ultimate finality. This reduces the risk of settlement fail­ures significantly, requires, however, a lot more liquidity, particularly when offsetting payments are unevenly distributed over the day.

RTGS has become the dominating settlement procedure in Large Value Payment Systems (LVPS) where the settlement risk is more prominent due to the higher value and urgency of the payments. In 1985 only three central bank operated RTGS systems, ten years later already sixteen, mainly industrialized countries, used RTGS, by the end of 2006 the number had risen to 93 (CPSS, 2005; Bech, et al., 2008) and in 2008 the World Bank counted 112 RTGS-systems out of 142 payment systems (Allsopp, et al., 2008). Retail Payment Systems (RPS), however, still settle mainly with net settlement procedures.

Between the two pure procedures, many hybrid versions are conceivable and some of them are realized: e.g.

1.2. Governance

The higher the risks the more prominent is the role of central banks in payment systems. Central Banks are able to provide the ultimate settlement asset (central bank money) which in normal times does not bear a significant credit risk. Therefore, most LVPS and also some RPS settle in central bank money. Moreover, central banks have a decisive role in most LVPS, be it as operator, owner or overseer. This is warranted since the provision of the ultimate settlement asset creates a link for central banks between its role in payment systems and its functions in monetary policy and financial stability.

Some payment systems are settled in com­mercial bank money and are operated and owned by private institutions. They are, however, also subject of payment system oversight.

1.3. Systemic Interdependencies

LVPS are important financial infrastructures, and most other financial infrastructures rely on them. Foreign exchange settlement systems, security settlement systems, central counterparties and settlement banks, retail payment systems and sometimes other large value payment systems depend on LVPS. Frequently, LVPS also rely on other financial market infrastructures, such as security settlement systems that may play an important role in collateral management for liquidity provision.

1.4. Liquidity Provision

The operator of payment systems especially of LVPS faces several options about the intraday credit and liquidity: Whether or not they shall provide intraday credit, unlimited or with a lending cap, fee-based, or free of charge, whether or not they shall require collateral, partially or totally, and which set of eligible collateral they shall define in terms of currency, quality, and liquidity.

1.5. Detailed Transaction Rules

Every operator of a LVPS defines the criteria for accessibility and may agree on certain special settlement procedures for linked infrastructures (ancillary systems), such as parallel processing or liquidity reservation.

In addition to the settlement procedure and liquidity provision, a payment system operator may choose other parameters which may influence the timing of payments and order submission by the participants, such as transaction fees, throughput rules, grouping of accounts, liquidity pooling, and technical requirements.

1.6. Outside Regulations

Banking supervision and liquidity rules do affect the participants and their payment behavior.

1.7. Economic Rationale for Participants

The participants use payment systems to settle transactions in order to fulfill their customer orders and their own trades on money markets, security exchanges, foreign currency exchanges and the like. Given the existence of the underlying order or trade, they face a two-fold decision: Firstly, about the payment system to use and, secondly, when to submit the payment order. The increas­ing compatibility and interoperability between payment systems may widen the relevance for the first choice (Manning, et al., 2009). In general, this choice should be based on cost and risk consider­ations. For the second choice, the participants will face a trade-off between liquidity costs, credit risk costs (unless the central bank provides intraday credit) and delay costs. In contrast, the impact of operational costs seems to be rather small. Some participants use an automated routing device to help them follow some sophisticated internal liquidity and risk considerations.

1.8. Business and Financial Environment

The environment of a payment system can make a large difference. The size and structure of the banking system, the features of financial markets (other payment systems, and post-trade infrastruc­ture), the solvency of the respective institutions and the overall role(s) of the central bank may have an impact.

1.9. Technology

Payment systems require a substantial amount of technology, mostly communication and account­ing technologies (FFIEC, 2010). At the heart of the system is a messaging and routing platform providing the communication infrastructure for the participants. The incoming messages have to be validated and transformed into orders account­able. That is done via clearing and settlement. Clearing establishes the final order to be settled. Settlement means, that the orders are credited or debited to the accounts of the parties of the trans­actions. Reliability and accuracy of the clearing and settlement system is of utmost importance to the integrity of the payment system. However, the rise in transaction volumes and values as well as the rising demand for user related services (e.g., communication and interaction modules) require an ongoing push for more elaborated and sophis­ticated systems including more powerful servers and faster communication channels.

All of these features make a difference to the performance of payment systems. They have-as far as possible-to be taken into account when analysing payment systems for functional development or oversight purpose. In addition, the world of payment system is permanently changing (Kahn & Roberds, 2009). It reacts to technological developments (e.g. rising capacity of computational power), to market developments, be they of competitive or cooperative nature, and to regulation policies.

2. EPISTEMOLOGICAL ASSESSMENT OF SIMULATIONS AS ANALYTICAL TOOL

This section compares simulations, theoretical models, real experiments, and calibrations as possible analytical tools from an epistemologi­cal point of view. Given the features of payment systems, we will see why simulations rank very prominently among the analytical tools to study payment systems and which drawbacks they have.

Before starting the epistemological assess­ment, we need first a stylised description of what is done during simulations of payment systems³.

In general, theoretical models and real experi­ments are superior analytical tools. Theory predicts an outcome and the analyst may prove that the theory cannot be rejected with the given data by experiments. This scientific approach has hitherto not rendered sufficient success in payment system analysis. To start with, real experiments are not really feasible in real payment systems, since they form the backbone of the financial system that is of systemic importance. Also, theoretical models of payment systems, although they have become quite sophisticated, are usually not able (yet) to cover all the relevant features. There are two rea­sons for this. The weaker one is the complexity of the processes before, during, and after a pay­ment settlement. There is an outstanding plurality of features of payment systems. In addition, the transactions in payment systems do reflect the maj ority of transactions in an economy. In modern economies, barter trade is almost negligible and cash transactions are declining in importance⁴. Therefore, a sound model replicating the outcome of a payment system must be able to mimic al­most all motivations and rationales of almost all agents in an economy. Moreover, microeconomic and macroeconomic policy issues intertwine in payment economics (Kahn & Roberds, 2009). Other reasons, which have hampered the theo­retical modeling of payment systems, are their macro-features. Payment systems are subject to increasing returns to scale and strong network externalities. Moreover, they produce significant (positive and negative) externalities for the effi­ciency and stability of the system. Taken together, analytical models of payment systems must deal with non-linearities, an ongoing concentration process, hampered competition, and a high degree of public intervention.

One can neglect that and take a given sequence of submitted payments as given in order to analyse just the technical outcome of different processing rules. However, by doing so we are subject to the second reason for the inability of existing models to precisely predict the outcome of a LVPS, which is the sequential nature of real time payment order processing. Every payment order, which is settled, changes the liquidity level of the respective participants. It may trigger another payment from the receiver of the first payment and may hamper subsequent payments of the sender, because her available liquidity is reduced. Depending on the settlement procedure (e.g. queuing rules) and the available liquidity, the process of settling of in­coming payment orders may change after a single payment order was settled or queued or rejected.

Since simulations make use of the sequential nature of payment systems, they can produce re­sults reliably. Simulations are virtual experiments. Just as real experiments, they make use of the full set of institutional features and of every single payment instruction of a payment system to be analysed. No information from the micro level is lost by abstracting from any individual case. In addition, the outcome of simulations of payment systems is as multifaceted as the real system.

Another approach for analysing data would be calibrations. Calibrations, however, do require tested behavioural assumptions, structural regu­larities, etc., to formulate at least a simple model. Hitherto, payment economists have rather begun to formulate some stylised facts rather than tested hypotheses. In addition, the plurality of busi­ness cases for transactions requires a plurality of hypotheses. In addition, calibrations of payment systems may at the current state of the art largely lack a micro foundation.

As a consequence, payment systems have emerged as a suitable subject for simulations. Simulation leads to a “what ι !"-analysis that forms a basis for scenarios. They do have weaknesses, however. The most important one is that the par­ticipants in a payment system are assumed not to react. The economic agents are taken to react mechanically rather than rationally. This feature is one of the problems articulated in the Lucas critique (Lucas, 1975). Simulations take the se­quence of payment submissions as given and alter one or more of the institutional features or take out voluntarily some payment instructions with­out changing the other submitted payments. That will lead to a “what if” analysis, e.g. a simulation will show the outcome of a day’s payments for the case that one participant has stopped submit­ting payments at noon. Everything besides the “technical intervention” of a participant failing to submit payments after noon will be calculated mechanically. No behavioural adjustments are taken into account and no consequences will be taken into account. Thus the “what if” analysis of a simulations intervenes and by the same time assumes that all (other) participants behave as if the intervention has not taken place.

This epistemological weakness weighs stron­ger with increasing intensity and widening scope of the intervention and with increasing time-span of simulated processes. In reality, a change of a basic feature of the payment system or a signifi­cant change of payment behaviour of a participant will trigger behavioural consequences very soon. Therefore, the results of a simulation are more re­alistic the less severe the assumed intervention and the shorter the time-span of simulated settlement.

Other measures to mitigate the epistemologi­cal weakness of simulations would include the robust design of simulations, the combination of simulations with other descriptive tools and agent based modeling. Robust design of simulations is a basic request for each analyst. Robustness can be enhanced by performing multiple simulations with similar but changing scenarios whereby the interventions should reflect a broad range of realistic changes as well as different time-spans and levels of intensity of intervention.

In current simulation approaches many analysts combine simulations with the use of descrip­tive analysis such as payment flow distribution (Northcott, 2002), network analysis (Lubloy, 2006; Wetherilt, et al., 2009; Schmitz & Puhr, 2007; Boss, et al., 2008), and participants’ pay­ment pattern analysis. If during the course of a simulation the resulting payment flows, structural coefficients, and payment patterns happened to change significantly, the outcome would have to be subject to further scrutiny. The result may seem inevitable from the individual point of view and can be taken as a possible outcome. The result may also seem to be beyond realistic expectation and would-by best judging from the experience of payment patterns-not occur in reality. In that case, the simulation needs to be improved by additionally assuming behavioural changes of one or the other participant. It requires “agent based modeling.”

Agent based modeling and simulation⁵ mean, basically, deviating from the assumption of ho­mogenous participants ignorant of the specific features of a payment system. It includes hetero­geneous agents, strategic rules and sometimes, adaptive learning⁶. Whereas simulations, as an analytical tool, can overcome the problems of cap­turing the real complexity in theoretical models, they do abstract from behavioural reaction func­tion of economic agents. On the other extreme are game-theoretic techniques. They derive a new equilibrium, if any, by abstracting from the real institutional complexity and tracking the moves given an explicit behavioural function. Somewhere in between these two tools are agent-based models. In fact, agent based modeling is intensively used in the design of decision support systems⁷.

When using agent based modeling the analysts stay close to the complexity of the real systems (many banks, many links, and many features ofthe system) and assume that the agents (e.g. banks) react according to pre-defined rules (Arciero, et al., 2010a). Ideally, these pre-defined rules do reflect the known stylised facts of payment patterns, etc. They can differ from one agent to another and, thereby, create heterogeneous agents. The rules can comprise some sort of adaptive learning (and maybe also forgetting) and, thereby, create system dynamics.

As an example, Beyeler et al. (2006) used a rule for the decision whether to pay or delay given a level of liquidity and showed the reaction of the system on changing liquidity levels. These consid­erations were extended in Galbiati and Soramaki (2008) by deriving the liquidity levels endog­enously via a game-theoretic approach. Banks choose their level of liquidity in many succeeding rounds and trade-off liquidity costs against cost of delay. Their ex-post costs are determined by their liquidity-level and the liquidity provided by others. In succeeding rounds, banks react on this outcome and adjust their initial level of liquidity until equilibrium is reached. A recent approach by Arciero et al. (2010b), made use of an explicit model of money market behaviour, calibrated it with real data, and simulated by taking into ac­count some strategic behaviour of multiple agents.

An important methodological question is the use of real versus artificial data in simulations. Clearly, real data are real, not just realistic, and they are therefore superior. However, real data are of a sensitive nature and cannot be subject to public discussions. This forms a considerable hurdle for scientific exchange about simulations even across the insiders of a single LVPS. The use of artificial data does not touch any privacy issues. The data should, however, be created as realistic as possible making use of advanced descrip­tions of payment patterns. When artificial data are simulated according to some counterfactual assumptions, they become even more artificial. A case for using artificial data is to compare the real outcome with a hypothesis about patterns or structural features, e.g. Denbee et al. (2010) use random walk distribution of given payments to determine the degree of free riding on liquidity. Most simulations use real data since they are per­formed by central bankers having access to at least a single data set of a LVPS. Examples for the use of artificial data can be found in McAndrews and Wasilyew (1995) and Schulz (2010). Somewhere in between is a study using real data but artificially merging participants to increase step by step the degree of tiering in the system (Lasaosa & Tudela, 2008). Clearly, a rising degree of artificiality is intended and warranted since the study provided a picture of potential risks and efficiency gains by a changing tiering-structure.

3. SIMULATIONS FOR THE FUNCTIONAL DEVELOPMENT OF PAYMENT SYSTEMS

From the very start of complex systems, simula­tions had to be used for the functional development. Whoever wanted to build or improve a system as complex as a payment system had to rely on a number of simulation-runs to test the functional­ity, stability, and efficiency. Therefore, it is safe to say simulations were initially created and used for the sake of the functional development. This holds for the ongoing technical refinements and new releases, which needed to be checked in a simulation before being used in real production. This holds also for one-off events such as the introduction of the Euro. Preceding the introduc­tion of the Euro was a simulation of the newly established TARGET-system over several months in order to be on the safe side when the new cur­rency was launched in January 1999 (Hartmann, 1998). Another one-off event was the preparation for the year 2000. In an international large-scale one-off simulation nearly 500 internationally operating credit institutions from 20 countries, using 34 systems worldwide participated in the simulation. The so-called “Global Year 2000 test” was indeed a major simulation with multiple play­ers participating (Hartmann, 1999).

The majority of these simulations for functional development are not published. They are part of the private research memory of system owners and were not designed for public debate. Published studies with respect to the functional develop­ment of payment systems cover usually topics of broad interest to more than one payment system, and usually more than one topic. Nevertheless, the following discussion is divided according the most important topics:

1. Introduction of RTGS-systems

2. Bottleneck solutions and analysis of liquidity requirements

3. Liquidity saving mechanisms/hybrid design of RTGS-systems

4. Interdependencies with other systems

5. Capacity analysis and structure of participants

6. Simulation of Retail Payment Systems

3.1. Introduction of RTGS-Systems

During the 1980s, a trend started to introduce RTGS-systems at least for LVPS. The major driver was the intended reduction of credit risk (Manning, 2009). A study by Humphrey (1986) can be called path breaking, although its detailed validity for other payment systems was limited. The study depicted a significant degree of systemic spillover in the US CHIPS system, which was at that time a Deferred Net Settlement System (DNS). Humphrey removed one participant and recalculated all remaining net settlement obliga­tions. Some banks failed, because they were left with insufficient liquidity to fund the increase in net settlement obligations. Now the settlement was repeated and the net settlement obligations recalculated with the remaining banks. Humphrey observed quite sizable systemic effects. Out of a total of 134 banks some 50 banks failed within six iterations.

As the debate went on the results were further qualified, and more and more payment systems were designed as RTGS-systems. Using artificial data McAndrews and Wasilyew (1995) concluded that the risk of contagious default increased with the value of payments settled and the number of banks participating. A high degree of concentra­tion means a higher propensity for contagion. Real data of the Italian LVPS were used to show that roughly four percent of failures are large enough to trigger systemic problems (Angelini, et al., 1996). Similarly, for the Finnish Interbank Payment System little risk of contagion was found for two major reasons: Firstly, the counterparty exposures did not exceed ten percent of the bank’s own funds, and secondly, there existed hardly any long interbank chains (Kuussaari, 1996). Likewise were the results for the Danish Interbank Netting System (Bech, et al., 2002) and for the Canadian Automated Clearing Settlement System (North- cott, 2002). Both studies conclude also relatively low systemic risks. These two studies are not fully comparable to other related studies. Firstly, both simulated payment systems covered only small value payments, and, secondly, the banks in the Danish Interbank Netting System benefitted in the observed period from an extremely abundant liquidity position. In a further ramification, Bech and Soramaki (2005) took the network effects into account. They qualified the results according the structural features of the given payment system using the centrality of a participant with respect to the solvency of the counterparts.

Summing up, the studies point to the need to qualify the results according to the special situa­tion in each payment and banking system (Galos & Soramaki, 2005). However, the risk-reducing propensity of RTGS remained undisputed.

3.2. Bottleneck Solutions and Analysis of Liquidity Requirements

By the same token, an RTGS-system requires nec­essarily more liquidity than a pure net settlement system. Therefore, the trade-off between credit risk and liquidity costs as well as the trade-off between liquidity costs and delay costs (Arjani, 2007) became prominent topics in simulation studies. A basic idea was to find out a minimum level of liquidity (intraday liquidity) to settle the submitted payments in an RTGS-system. These studies (Leinonen & Soramaki, 2005; Hejmans, 2009; Petterson, 2005) helped to quantify the real liquidity needs of an RTGS-system above the Net- systems. The analysis about the impact of various liquidity levels on the system performance can be classified as studies for functional development as well as studies for oversight purposes.

As liquidity became a scarcer resource, analysts looked also into the possibility of banks allowing a larger degree of payment delays (meaning paying later than the set time, but still on the right day). The analysis of the trade-off between liquidity and delay costs suffers from the fact that delay costs are usually not observable by the system owner or overseer. However, as a simulation study was able to quantify the trade-off between liquidity levels and delay costs (Enge & 0verli, 2006) it provided at the same time estimates of delay costs.

This line of studies was also meant to take into consideration the behaviour of banks themselves. In an RTGS-system, banks rely heavily on incom­ing funds to finance their own submitted payments. If liquidity is costly, a bank may attempt to reserve liquidity, e.g. for the payments for which would cause higher delay costs. Thereby, banks would reduce the available level of liquidity in the system and may cause gridlock. In short, the simulations dealing with the trade-off between systemic risk and liquidity costs need to cover the payment pat­terns of banks (Afonso & Shin, 2008).

3.3. Liquidity Saving Mechanisms/ Hybrid Design of RTGS-Systems

Liquidity was seen as a public good by some au­thors (Denbee, et al., 2010). However, liquidity is no public good in the basic sense. It can only be used by the receiver of the payment. Surely, a high turnover ratio in a payment system leads to a higher liquidity efficiency. That means banks can send a multiple of their initial own liquidity as outgo­ing payments provided that offsetting incomings funds arrive. This is similar to a high velocity of money in the macro economy. Nevertheless, one would for the sake of a higher velocity of money not classify money as a public good.

The rising liquidity costs in RTGS and pos­sible repercussions on system risk seem to thwart the endeavours to reduce the settlement risk by introducing RTGS-systems. As a result of this insight, in part gained by simulation studies, the discussion about hybrid design of RTGS-systems set in.

Hybrid systems deviate in certain respect from pure RTGS. A very basic idea is to introduce multiple settlement streams operating on a single platform as in the Canadian LVTS and in TAR­GET (CPSS, 2005, p. 38). In that case, part of the liquidity is for a limited time-span reserved for a special purpose. The purpose is to avoid bottle­necks for systemic connections, e.g. large ancil­lary systems. In general, simple hybrid systems violate the First-In-First-Out (FIFO) rule of pure RTGS by other detailed queuing arrangements, e.g. simply bypassing the FIFO-rule, different levels of priority, or a reordering of payments (CPSS, 2005, p. 5).

The examples show that including hybrid ele­ments such as Liquidity Saving Mechanism (LSM) into RTGS does increase the rising complexity of algorithms in the system and does create an internal trade-off between liquidity and risk avoidance. First models with integrated LSM into RTGS focussing on CHAPS were provided by Jackson and McLaferty (2010).

A widely debated question in simulation stud­ies was the specific variant of the queue-release algorithm for a hybrid system: Balance-reactive and receipt reactive. Balance-reactive algorithms release payments in reaction to a defined level of balance, whereas receipt-reactive algorithms react on a defined flow of incoming funds. In reality, only balance-reactive algorithms have been implemented. Nevertheless, a number of simulation studies focus on receipt-reactive sys­tems. They analyze in simulations whether the theoretical evidence of receipt reactive systems being superior to plain RTGS in terms of costs of liquidity and delay. Balance reactive systems are also perceived to dominate RTGS, however, only in situations without liquidity shocks. Simulations by Johnson et al. (2004) and by Ercevik and Jackson (2009) display the degree of liquidity savings and the trade-off between liquidity and delay costs in hybrid systems. While the former see a receipt- reactive mechanism as dominating a RTGS, the latter depict for CHAPS that the liquidity savings are unevenly distributed and depend critically on the liquidity efficiency in the system. Willison (2005) tries to model hybrid systems and calculated an overall optimistic outcome about the superior­ity of hybrid systems. This not-simulated result, however, seems to hinge critically on an assumed total transparency of payments to be submitted.

3.4. Interdependencies with Other Systems

The overwhelming majority of literature on simulations in settlement systems deals only with payments and do not cover other systems. Some simulation studies, however, took into account special interdependencies to other systems such as securities settlement systems. The simula­tion have and will be also applied in analyses of settlement systems (e.g. for securities). The basic judgments about simulations as an analytical tool do not differ in that case. Examples for using a simulation tool in securities or equities clearing and settlement systems analysis are given by Hellqvist and Koskinen (2005) and by Hellqvist and Snellmann (2007).

3.5. Capacity Analysis and Structure of Participants

There are a couple of other topics in payment system simulation studies. The study of Kabadjova (2010) deals with the overall capacity constraint of a payment system and the possible scope of LVPS thereby contributing to the assessment of a possible merging of LVPS and Mass payments.

Another issue of importance is the structure of participants. Depending not least on the overall monetary policy some countries display a certain degree of tiering. That means also a tiered struc­ture of participants in payment systems, direct and indirect participants. Lasaosa and Tudela (2008) simulated for CHAPS that a higher degree of tiering leads to liquidity savings and higher liquidity efficiency. The liquidity savings arise from liquidity pooling and to a lesser degree from internalization.

3.6. Simulation of Retail Payment Systems

RPS have also been subject to the above listed top­ics of simulation studies. In addition RPS differ in some respects to LVPS which has been a special focus of some studies. Firstly, RPS are subject to fiercer competition. Usually, there exist more than one RPS in a country and most of them are of proprietary nature (CPSS, 2011; CPSS, 2003). Therefore, the choice of a single RPS for various payments becomes an issue (Rigopoulos, et al., 2006). Secondly, the diversity of various RPS is much more pronounced than in LVPS. The clearing and settlement of retail payments has developed according the advances of payment instruments and their schemes. Separate clearing arrange­ments for cheques, credit transfers, direct debit, ATM transfers, and card payments may exist, and they differ in terms of the technology required (FFIEC, 2010). Therefore, capacity constraints and consolidation procedures for the various clearing arrangements have become an issue of interest.

4. SIMULATIONS OF RISKS IN PAYMENT SYSTEMS (SIMULATIONS FROM THE OVERSIGHT PERSPECTIVE)

In many cases, simulations for the functional development of payment systems cover risks and can also be used by overseers. Nevertheless, it is worth separating the simulations, which were performed mainly from an oversight perspective for the sake of clarity of the interesting topics and, more important, because the epistemological status of simulations from oversight perspective is somewhat different. Simulation studies from an oversight perspective usually answer a hypotheti­cal question. Of course, simulations for functional purpose are also of a virtual nature. However, as serious oversight-relevant problems occur, one might expect that participants would react more quickly. The basic assumption of a simple simula­tion-behavior will not change-is in oversight ques­tions more doubtful. Moreover, in simulations for functional development, analysts can use payment pattern studies or network features as additional aspects to double check the realistic setting of their scenario and thereby overcome somehow the problems of virtuality. However, simulations for oversight purpose cannot make use of that to the same extent, because severe incidents and cases of failures in payment and settlement systems are of a rare nature and rather short-lived. Incidents happening at participants are not often precisely known to system operators or overseers (Lubloy & Tanai, 2008). A serious economic modeling, however, would require a sizable number of simi­lar well-documented cases in order to estimate a reaction function of the system. Assessing risks requires two steps (Manning, et al., 2009): Firstly, estimating the probability that a given risk event occurs, and secondly, estimating a conditional loss distribution. In reality very few significant events in payment systems occur, meaning few sample points of the distribution function, which makes estimation questionable. The data constraints-due to limited occurrence of risk events-are a serious problem for quantification. Many conditional loss distributions can be approximated by a lognormal shape: A long tail with low probability for large impacts. Therefore, simulations play an even more important role in analysing oversight top­ics. However, they have to be treated with more caution than the functional oriented simulations.

There are four roots of settlement risk: credit risk, liquidity risk, operational risk, and business risk. The business risk means problems of the operator of the payment system, which hamper the proper functioning of the system. This risk would mean a dropout of the whole payment system. It is subject to Business Continuity Planning. That is, of course, beyond the realm of simulation studies. The other roots of settlement risks are all subject of related simulation studies for over­sight purposes in both manifestations: risks that have already matured and the risk of contagion. In addition, the impact of external changes like a shift in monetary policy implementation or a consolidation of participants or change in pay­ment patterns are subject of related simulations.

Studies simulating the aftermath of an opera­tional dysfunction at the level of a participant, an ancillary system, or the LVPS work with historical data. The studies vary on the number and size of affected participants, the timing of the assumed failure and its’ time-span. The aim is to find the degree of disturbances to the system in terms of liquidity and credit risks and in terms of contagion⁸. Since overseers are concerned with the ultimate risk, their most useful approach is to find the worst-case scenario as long as it is still reasonable given the counterfactual assumption of behavioural continuity. Studies cover a range of possible indicators to watch: share of unsettled transactions, queued transactions, delayed transac­tions (Lubloy & Tanai, 2008), loss functions after contagion (Boss, et al., 2008), and indicators for the liquidity drain and sink effect (Schmitz, et al., 2006).

The detailed results seem to differ related to the various systems simulated and the assumptions during simulation. Some studies (Bedford, et al., 2004; Schmitz, et al., 2006; Ledrut, 2007) covering CHAPS, the Dutch and the Austrian LVPS come to the conclusion that an operational shock to a single participant may not trigger systemic risks. Quite the opposite can be said about the results of similar simulations covering the Swiss system and the Hungarian system (Glaser & Haene, 2008; Lubloy & Tanai, 2008). Similar results were achieved in a simulation of the Norwegian payment system (Enge & 0verli, 2006). They did not explicitly perform a study of operational dys­functions but simply assumed shrinking levels of available liquidity and studied the outcome. They found considerable potential of the system and its participants to deal with significant outages and succeeding liquidity shocks for the Norwegian payment system⁹.

In general, the use of gridlock resolutions and bilateral limits for sending participants yield considerable impact in cases of operational fail­ure (Lubloy & Tanai, 2008; Mazars & Woelfel, 2005). Similarly, a simulation of the Japanese BOJ-NET Funds Transfer System demonstrated that Liquidity Saving Elements mitigated the contagion risks of liquidity shocks (Shirakawa, 2009). It is in this discussion about hybrid systems that simulations covered explicitly both functional development and oversight aspects. The trade­off between efficiency and risk was subject in a simulation of CHAPS. Lasaosa and Tudela (2008) found for CHAPS-which serves as the prominent highly tiered payment system-higher liquidity efficiency, but also higher concentration risks albeit somewhat lower credit risk in comparison to a not tiered system.

Simulations of risks in payment systems are not restricted to RTGS. An interesting topic is the possible reduction of the trade-off between risk and liquidity requirements in net settlement systems. There possible level of risks can be re­duced by securing the net settlements, e.g., through margining, central clearing, introducing a central counterparty, collateral, limits on exposures and rules for loss sharing. Galos and Soramaki (2005) show in a simulation that a secured net settlement system can by introducing loss sharing rules, limits to exposures and collateralization¹⁰ reduce the peak exposures in case of a failure by one half in comparison to an unsecured net settlement system.

To sum up, the various results point to the importance of the special national and systemic conditions, e.g. concentration ratio, the system specific algorithms, the liquidity available in the system, the existence of back-up procedures, and the like.

A beneficial side effect of simulation studies is used to find and prove the usefulness of indicators for the analysis of payment systems (Northcott, 2002; Lovin, 2010; Schmitz, et al., 2006), thus contributing to the understanding of descriptive statistics and the formulation of models.

For the future, it seems possible that a more pronounced split of simulations for functional development and those for oversight purposes or research may occur. The real systems are becom­ing more complex and realistic simulations may become more costly and complex, too. Assuming the related questions of functional development to become more detailed it seems plausible that simulations for functional development will be increasingly performed by the operators. The public discussion, however, may increasingly turn to oversight related questions.

5. EXAMPLES FOR SIMULATION TOOLS AND DIRECTIONS FOR FUTURE SIMULATIONS

The interested analyst is bound to the availability of appropriate data. Since these micro-data are of sensitive nature, analysis is mainly restricted to the operators and the oversight. On the side of the tools, a number of appropriate tools are avail­able. The pioneer of payment system simulators is the very widely used Bank of Finland Payment System Simulator (see: http://pss.bof.fi/Pages/ Defaulfaspx). The BOF-PSS is an easy to use tool capable of simulating a sizable number of possible payment systems and running on a PC. It provides for a number of options to mimic closely specific features of real payment and settlement systems. The tool is permanently improved and has an increasing range of output options for the use of complementary analytical tools (e.g., network analysis). The Bank of Finland is the only entity that can make adjustments and offers cooperation. The BOF-PSS is their contribution to the systemic analysis and are eager to serve a wide community of analysts using the BOF-PSS. A drawback of the BOF-PSS is its purely deterministic approach and difficulties to model strategic behaviour, e.g. for agent based modeling.

The Bank of England Interbank Payment and Settlement Simulator (Alentorne, et al., 2005) claims to have overcome these limitations. This simulator is, however, not publicly available and not used outside the B ank of England. It seems to be based on the Financial Network Analyser (FNA). The FNA (see: http://www.financialnetworkanaly- sis.com/) is a tool mainly developed by Kimmo Soramaki who came from the Finnish tradition of system analysis. It is an open-source project and used by a considerable number of researchers. The FNA is using methods developed in Social Network Analysis, Network Science and Agent based Modeling, but is also capable to perform a broad range of simulations of LVPS. It uses in its 2011 version a newly created simple user interface and covers a broad range of possible analytical tools. Another simulation tool, albeit somewhat sophisticated, is “Payment and Money Market Model” (P&3M). It was especially designed for Agent based simulations and developed by Pietro Terna (Terna & Bonafine, 2010). It is based on Swarm-Like Agent Protocol (SLAPP) in Python. Its main advantages are the flexible design to cover a large range of behavioral strategies and the openness of Python for future developments. The progress of the ongoing project is documented at http://web.econ.unito.it/terna.

What may be the directions for future simula­tion tools and simulations? I would like to mention three main trends:

1. We may see the design of standardized hypothetical scenarios for each LVPS with a regular check on certain variables; e.g.,

a. Identify critical participants,

b. Compute minimum liquidity level/ maximum liquidity required,

c. Search for bottlenecks.

2. Simulation approaches will increasingly be integrated with descriptive analysis and

a. Make use of tested behavioural assumptions,

b. Make use of stylised facts about the resulting network structure,

c. Derive plausible stochastic func­tions to substitute for deterministic simulations,

3. We may see a widely used integration of micro-founded agent based modeling into simulations.

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ENDNOTES

Dr Martin Diehl is payment system analyst at the Deutsche Bundesbank. This chapter represents his judgements and views and does not necessarily reflect the opinion of the Deutsche Bundesbank.

This list of features and concepts of payment systems is organized by their importance for the role of simulations as an analytical tool. A more detailed view on the complexity of payment systems and market infrastructures in general is provided by CPSS (2011) and Allsopp et al. (2008).

A basic description can be found in Leinonen and Soramaki (2003).

In addition, many cash transactions do also require preceding and succeeding non-cash transactions (e.g., if ATMs are used).

The literature often uses the term “agent based modeling,” although some approaches should from an epistemological point of view rather be called “agent based simulations.” The difference refers to the main analytical technique: Is it a solution of a model based on some calibrations or a simulation of

micro-data adjusted by some modeling as­sumptions to yield a counterfactual result. See the review article by Rocha (2006). Some examples are provided in Rigopoulos et al. (2006), who develop a multiagent based simulation for the behaviour towards

payment system selection.

After the publication of the independencies study of CPSS (CPSS, 2008), a number of simulations cared more about interdependen­cies (e.g. Lovin, 2010; Boss, et al., 2008).

Enge and 0verli (2006) also concluded from their results on the relation of liquidity and delay costs, thus proving the usefulness of simulations with real data to find estimators for hidden features of the real system.

¹⁰ The rules were designed to resemble EURO1.

This work was previously published in Simulation in Computational Finance and Economics, edited by Biliana Alexandrova- Kabadjova, Serafin Martinez-Jaramillo, Alma Lilia Garcia-Almanza, and Edward Tsang, pages 29-45, copyright 2013 by Business Science Reference (an imprint of IGI Global).