SIMULATING PAYMENT SYSTEMS BY AGENT BASED MODELING

A promising way to introduce endogeneity in pay­ment system analysis and at the same time to re­produce the complexity that microfounded models are not able to tackle is by employing Agent Based Models (ABM).

Although the ABM literature dealing with the payment systems is still scarce, the few con­tributions produced so far show that there are several fields where ABM may prove to be able to be a useful simulation tool for payment system analysis, which allows for an endogenous liquidity management⁸.

First, ABM may be used in payment system analysis to deepen the understanding of the fund­ing strategies in an RTGS system as well as well as to evaluate the system’s efficiency: Galbiati and Soramaki (2011) analyse the trade off that treasurers face whenever the alternation of in- and outflows makes their cash balances insufficient to settle immediately the due amounts⁹.

The simulations rely on a cost function, which provides the overall cost borne by the bank for each level of externally borrowed liquidity. It is assumed that the participant can opt only once a day for external liquidity, namely at the beginning of the day, so that before the onset of the settlement process, it has to decide how much funds it wants to raise. The overall bank’s cost is, therefore, given by the penalties for delays as well as by the cost of raising external liquidity at the beginning of the day. Rather than taking each day as a separate experience, a repeated game is introduced in which the daily initial level of liquidity chosen by each bank depends on its expectations of the others market participants’ choice (fictitious play).

The authors find out that for intermediate levels of unit delay costs, the aggregate external liquid­ity level in equilibrium is lower than the optimal one. The inefficiency of the system results from its comparison with a social optimal equilibrium, where agents minimise the total social costs of all market participants instead of their own one. An inefficient level of liquidity absorption seems to be caused by relative low delay cost per each unit of liquidity in comparison to the cost of external liquidity, which fosters free-riding and determines a suboptimal funding of external liquidity.

For those critical levels of unit delay costs the authors investigate whether in a smaller and sim­pler network, greater efficiency can be expected. A proportional increase of system’s size (total value of payments) and complexity (number of participants) determines an efficiency reduction: it is speculated that since the internal liquidity sources are more variable and therefore, less reliable, agents recur to higher levels of external liquidity per payment. A decrease in the number of participants, while keeping the system’s size constant, would increase the efficiency even more, since the liquidity provision would benefit from ‘liquidity pooling’ effects.

Secondly, ABM can be employed to draw les­sons to shape the design of Large Value Payment System. ABM can, in fact, facilitate the evaluation of the either new policies’ or functioning rules’ effects that directly involve or have impacts on the participants’ endogenous funding decisions, since it allows to assess their impact on the functioning of the system and on the participant’s behaviour. The policy maker can therefore test second round effects, which might arise from market partici­pants’ behaviours interaction and which otherwise might be difficult to gauge in advance.

The ABM usage for such purpose is exploited by Markose et al. (2011), who uses an Agent Based Model to evaluate the introduction of a policy rule that allows banks to borrow uncollat­eralized funds, against the payment of interests, from the Central Bank at any time during the day. Since this work investigates the impact in terms of liquidity circulation of different policy rules, the paper can be collocated in the stream of the “policy oriented” contributions.

Two alternative frameworks are simulated: in the first group of simulations, falling into the so-called “opening liquidity” framework, banks can withdraw collateralised liquidity from the Central Bank only at the beginning of the day; in the second group, “the just-in-time liquidity” set up, banks can borrow uncollateralized funds at any time during the day according to their needs, against the payment of interests.

Comparing the two frameworks for the same amount of external liquidity, the “opening liquid­ity” system appears more liquidity efficient than the “just-in-time liquidity” one, since the cumu­lated percentage of settled payments’ value for each given time during the day is higher when liquidity is borrowed intraday according to the banks’ needs¹⁰. This result might be addressed to the fact that in the second framework, banks bor­row more money than effectively needed, since the incoming payments are not netted (see Figure 1).

Furthermore, within each of the two frame­works (“opening liquidity” and “just-in-time liquidity”), the performance of the system is tested for two queue processing rules: a FIFO approach (first in first out) minimising the value of delayed payments and a size priority criterion (first the smallest) minimising their volume. Gridlock ef­fects are proven to be more likely to occur in the second case.

A third rational for Agent Based Modelling in payment systems lies in the field financial stabil­ity assessment.

Figure 1. Trade off between liquidity posted and time weighted delays (2011 Bank of England)

Large value payment systems-which link together intermediaries, infrastructures, and post-trading platforms-represent one of the most critical market infrastructure since possible delays or settlement failures from one or more partici­pants can have a snowball effect due to the strict interdependencies within its participants.

As mentioned in the previous paragraph, a large body of literature using simulation has emerged to assess the resiliency of the system in case of shocks that affect the available liquidity of pay­ment system participants.

In these stress testing exercises, payments executed from a bank hit by an either financial default or an operational outage, are simply dropped. To introduce a participant reaction, it is usually assumed that after a given time, the other banks become aware of the difficulties of the defaulted participant and stop sending payments: the incoming payments of the defaulted bank from any other market participant are therefore deleted as well. However, the residual liquidity flows, between banks that have not been affected by the outage, are kept unchanged.

This kind of stress testing is a sort static simulations of defaults and does not capture the impact of critical events like a bank’s default on the behaviour of other market participants. In this vein, it could be speculated that the effects captured by these simulation are biased, since they omit to consider “by side” effects of the event, incurring in the risk of overestimating the resiliency of the payment system under assessment.

Agent Based Modeling may be used to take into account that, in case a market participant defaults, the behaviour of the other banks could be affected since they do not receive incoming payments that in the actual world they would have received and that contributed to fund their outgoing payments. In the absence of such incoming payments, banks would have been likely to change their behavioural strategies, modeled in terms of cost functions and trade-offs between raising liquidity and delaying payments.

For example, Arciero et al. (2009) use an ABM to execute a simulation of a default, in a model that takes both the payment system and a stylised money market into account. They simulate a direct-debit based system with very few market players, in which each participant is endowed with daily initial cash and collateral balances. The model is calibrated with BI-REL’s data, the Italian gross settlement system in 2007: the five banks of the model are generated by collapsing a higher number of participants. The initial cash balances stem directly from the opening balances held at the RTGS system, while the opening col­lateral balances are estimated starting from the maximum collateral pledged at the central bank for intraday credit purposes. Payments between banks are generated for each participant through three random draws from a uniform distribution: the first determining whether a payment is executed or not, the second its exact quantity and the third one the receiver.

The behavioural rule of any agent requires him to compute the expected end-of-day balance at each tick of an internal clock of the model, i.e. the liquidity that the participant expects to hold at the closing of the trading day on the own cash account. It includes: 1) the initial liquidity level; 2) all the in- and outflows already settled; 3) all the pending in- and outgoing payments.

If the value of a due obligation is higher than the actual balances, so that it cannot be imme­diately settled, the agent can pledge collateral at the Central Bank to receive intraday credit as long as it has enough collateral. After hav­ing consumed its whole collateral endowment and provided that the outgoing payment value is higher than the current and expected end-of-day balances, the bank turns to the money market in order to raise the missing funds. The matching of opposite intents on the money market is only quantity-based: in case the expected liquidity of a randomly selected market participant is equal or higher than the requested deposit, the money market deal is executed; otherwise, the payment transaction is delayed and the deposit request is turned to a further randomly chosen bank. After a specific number of bounces, the payment is considered unsettled and is removed from the expected end-of-day balance. If the value of the due payment is higher than the current balances but lower than the expected end-of-day liquidity, the payment will be delayed and queued, waiting for new incoming funds to replenish the expected liquidity. The payment will be automatically re­submitted to settlement process in the following tick, when the current cash balance may have varied for effect of incoming payments: if liquid­ity is now available, the delayed payment will be automatically settled.

A default is introduced by simply letting a bank switch from this normal operational behav­iour to inactivity. At the beginning, other market participants are not aware of the event: they continue sending payments to the defaulted bank and including the future incoming payments from that bank in their liquidity expectations. After a certain amount of time, namely half an hour, the participants gain knowledge of the failure, stop sending payments to that participant and update their end-of-day balance eliminating the pend­ing payments from the defaulted agent. Since the end-of-day balance affects the behaviour of a participant towards any market participant, the default of a bank that causes a readjustment of the expected end-of-day balance has also effects on the behaviours towards the rest of the market.

The authors find out that immediately after the default the expected end-of-day balances of other market participants are inflated by the pending inflows, which are expected to come from the de­faulted bank. To face the own outgoing payments, after having used the whole endowment of collat­eral to get intraday credit from the Central Bank, money market activity is enhanced. Delays on the expected incoming payments from the defaulted bank start cumulating, up to the moment in which, through a random process, the other agents start becoming aware of the default. Pending inflows are switched to defaulted credits and eliminated from the expected end-of-day balances.

Interestingly in the simulations, an interven­tion from a lender of last resort is needed to help survived market participants to overcome the stress conditions and the losses, avoiding conse­quential defaults in a contagion whirl. A possible explanation for inability of the system to return automatically to an equilibrium without external interventions is that the number of agents in the simulated model is very restricted; since so that the relative importance of a single bank is on av­erage 20% of the whole payments, the failure of one of them would therefore imply the default of a relatively high percentage of payments, which would be hard to overcome by the remaining banks.

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