Discussion of the Papers:“Sharing the Risk of Settlement Failure” by Fujiki, et al.; “Risks in Interlinked
Settlement Systems: How to Measure the Impact of Settlement Delay in Italian
RTGS System” by Impenna and Masi; and “Systemic Risk, Interbank Relationsand Liquidity Provision by the Central Bank” by Freixas, et al.

William C. Hunter*
Federal Reserve Bank of Chicago

The papers presented in this session address interesting and important questions
regarding the design and operation of payments systems and each makes a contribution to the literature. In my discussion, I will first comment on the two theorypapers and then turn to the empirical paper dealing with the costs of settlement
delay.
Let me start with the elegant and technically demanding paper by Fujiki,Green, and Yamazaki. First, let me say that this paper is very promising and will
be important in setting a new standard in the modeling of payments systems risk
and related issues. Informal discussions of the costs of settlement failure often
focus on the indirect effects on parties who are not direct participants in a transaction. For example, the “cascades of defaults” story has the failure of bank A
to make its payments to B adversely affect a bank C that has no direct dealings
with bank A, as long as C has transactions with B. So a question arises whether it
would be better to simply have all transactions bilateral, with no involvement of
third (fourth, fifth, etc.) parties.
I interpret the Fujiki, et. al. paper as seeking to justify involvement of parties
in the settlement system who have no direct relation to the transacting parties.
The rationale for such involvement is that these “extraneous” parties can share therisk of payments failure (with appropriate compensation paid to take on thisinsurance role), resulting in a Pareto-improved outcome.
The key feature of the model in the paper involves the specification of preferences of the agents. As structured, the specification implies that in the absence ofrisk agent 4 would not trade with agents 1, 2, or 3. The reason is that agent 4
places low value on agent 3’s endowment and agent 3 places low value on agent
4’s endowment. In contrast, agents 1, 2, and 3, place high value on the endowment of each other and hence are willing to trade with each other. So, in the case
*I am indebted to David Marshall and James Moser for helpful discussions of the papers
presented in this session. Errors of interpretation are my own. The views expressed are my own andnot necessarily those of the Federal Reserve Bank of Chicago or the Federal Reserve System.

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William C. Hunterof certainty, agent 4 is somewhat a fifth wheel. The authors introduce the possibility of payments failure into the model by having the transfer from agent 2 toagent 3 fail with positive probability. In this case, agent 3 would like to receive aninsurance payment from agent 4 conditional on the failure of the agent 2 to agent
3 transfer. To get this “insurance policy,” agent 3 must make an unconditionaltransfer to agent 4 (the “insurance premium”). The paper rigorously proves thatthe equilibrium where this holds is Pareto optimal.
The questions I have regarding this major result of the paper revolve aroundthe interpretation the authors give to agent 4. They interpret agent 4 as a government or central bank or something like a government guarantee (like the guaranteed finality in FEDWIRE, for example). While this is a plausible interpretation,
it does raise the question of how dependent the insurance result is on the particular preference specifications assumed for the agents in the model. As the model isspecified, agent 4 has his own preferences and endowment. However, one would
think that a true central bank or system guarantor would have preferences which
are a function (directly or indirectly) of all agent payments (that is, the payments
among agents 1, 2, and 3). In the banking interpretation of the model, the reason
is that bank failure is presumed to have systemic or system-wide consequencesthat the central bank does not like. So, an obvious question is how would thingschange if bank failure or agent payment transfer failure is directly affected byagent 4’s (the central bank’s) utility? A related question relates to the reasonableness of interpreting agent 4 as a “clearing house coalition” that stands ready toprovide liquidity in the event of a payment failure by one of its members. The
appendix to the paper suggests that this is reasonable. I am not totally convincedof this. In particular, a model based on a clearing house coalition would be more
symmetric than the set-up in this paper. Each agent would have a positive probability of direct transfer failure, but would stand ready to provide funds in theevent that a transfer fails to which it is not a direct party. I think that this “clearinghouse coalition” could be modeled using a strategy analogous to this paper, andwould provide a theoretical rationale for the development of private clearing
arrangements with risk sharing. These arrangements are quite common and wereeven more common in the era prior to Federal Reserve guarantees. It should bequite easy to show that where all agents’ utility involve all others’ consumption
and where all agents are risk averse, their willingness to share in the risk offailure (losses) will be proportional to their individual degrees of risk aversion
and not necessarily the volume of transactions. Another question I have involves
the role of moral hazard in the model presented in the paper. Specifically, it wouldappear that moral hazard considerations would come into play since the role ofagent 4 is to guarantee the system.
The paper by Freixas, et al. attempts to model the incentives of clearinghouseparticipants to default in a game-theoretic context. In the model, each bank receives deposits, which can be prematurely liquidated (at a gross return belowunity) or can be held to maturity (which pays a gross return exceeding unity). In
addition, agents can forego the banking sector and “store” their wealth, for a grossDiscussion of the papers

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return of unity. Some of the depositors need liquid assets early (the “early diers,”in the language of the paper). The remaining depositors (“late diers”) move to a
new location where they present a check on their original deposits to the bank intheir new location. The new bank gives the late dier funds in exchange for thecheck, and then presents the check to the original bank. Now, the original bankcould have prematurely liquidated its entire holdings, in which case this check isworthless. If every bank did this, we would be in the “gridlock equilibrium”
described in the paper. This would be gridlock, because no payments would bemade. In contrast, the original bank could have prematurely liquidated nothing, inwhich case our “late dier” could write a check for his entire deposits, and thischeck would be honored in full. If every bank did this, we would be in the“credit-line equilibrium” described in the paper. There is a continuum of possible
equilibria between these two poles.
The paper provides a welfare ranking of the various equilibriums. The creditline equilibrium dominates autarky (in which agents forego the banking system
and use only storage), which in turn dominates the gridlock equilibrium. Unfortunately, the credit line equilibrium is unstable. That is, it is subject to coordination
failure. Therefore, the policy question is how to set up a bank transfer mechanismthat minimizes the danger of gridlock? Unfortunately, I think the paper says too
little about how to implement the credit line equilibrium. While there is somecomment on the role of real time gross settlement systems and deposit insurance,
it seems to me that the paper is somewhat incomplete along this dimension.
It should be noted that the paper focuses on the problem of “strategic default”:
The gridlock equilibrium in the paper arises because banks choose not to honor
checks drawn on their accounts. I am not sure that this type of strategic default isreally what we are afraid of as central bankers. I would think that in a dynamic
version of the game described in the paper, reputation effects (or simple legal
punishments for default) would extinguish the “gridlock.” Rather, the problem
central bankers fear most is that resulting from an exogenous payment system
failure which reduces the volume of credit transactions (with the accompanying
welfare losses). I believe that a version of this model could be constructed thatformally addresses this issue.
The second part of the paper is a multi-bank extension of an earlier
Freixas/Parigi paper recently published in the Journal of Financial Intermediation.
In this part, there is an exogenous bank-specific shock that can induce bankfailure. The bank’s depositors have information that their bank will fail, but thisinformation is private. So, they have an incentive to write checks against theirfailed bank. This possibility induces all banks to not honor all checks, resulting ingridlock. That is, the credit-line equilibrium cannot be implemented. As is obvious, if the shock realization is publicly observable ex post, the central bank canimplement the credit line equilibrium by guaranteeing overdrafts to solvent
institutions (“collateralized overdrafts”).
A key feature of this second part (and of the earlier paper) is that inefficiencies arise if bad banks are not closed early. In other words, we want to liquidate

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William C. Hunterbanks that cannot honor checks before the checks are actually written. To do so inthis model, we need the depositors (who know whether their bank is good or bad)to run all bad banks rather than writing checks on them as the checks would allow
one bank’s failure to spread to other banks. Is this realistic? In a world withdeposit insurance, depositors, no matter how knowledgeable, can not be counted
on to discipline bad banks by running. It is up to the deposit insurer to do so. Thus,
this part of the paper is more relevant to bank closure policy. It is not clear what
this part of the paper contributes to payments system design, per se.
The final paper I want to discuss (by Impenna and Masi) examines risks ininterlinked settlement systems. The paper attempts to measure the maximum costthat a disruption of the Italian payments would have, taking into consideration thefact that two linked settlement systems exist: the large-value payments system
BIREL, which is a real-time gross settlement system, and the securities settlement
system, SSS, which involves net settlement. The paper does not describe in detailthe exact nature of the linkages. This inhibits the reader’s ability to carefully
judge the severity of the potential problems which could arise out of the interrelationships. For example, the claim that settlement delays in the netting system(SSS) could result in a settlement delay in the RTGS system, potentially mitigating the supposed advantages of RTGS, are difficult to verify.
The paper constructs a stylized model of the “maximum cost of settlement
delay” due to a delay in the SSS link. The paper simply takes the average daily
net outflows of the cash leg of SSS, and multiplies that by an estimate of theprobability of delay. This, in a sense, gives the “expected shortfall” due to a delay,
under the assumption that the amount of the shortfall is uncorrelated with thelikelihood of a delay in payments. However, it is not clear that this is a “maximum cost.” It looks more to be an “average cost,” under this independence assumption.
The key equation in the paper defines the so-called probability of settlement
delay. The underpinnings of this equation are not well spelled-out in the paper.
This probability is increasing in the variability of daily cash outflows of SSS.
Also, this probability is decreasing in the turnover ratio. So, less reserves imply ahigher probability of delay. The model also has the probability of delay increasingin the quantity, nf/NDB, the ratio of the number of daily settlement failures to thenumber of negative daily balances in the whole system. This is very opaque. Whymodel the probability of settlement delay as in equation (3) of the paper? Whychoose the functional form given in equation (3), where the elasticities of theprobability of delay with respect to CV and nf/NBD are unity and the elasticity ofthis probability with respect to V is minus one? How do we know that p in equation (3) is actually a true probability measure (i.e., between zero and one)? It isvery important that one gets these elasticities right, since the key result of thepaper is that the probability is relatively small in the case of the Italian payments
system. The quantitative estimates of this probability (given in Table 3) will
obviously be affected by the elasticity assumptions embedded in equation (3) ofthe paper.

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The contribution of this paper lies in its attempt to quantify the costs of settlement failure, using actual daily data. However, I am not totally convinced thatthe framework chosen by the authors is the most robust one for estimating thiscost. At best, the model seems to give an estimate of the “average cost of an
average delay.” However, the concern of regulators is not with “average costs,”
but with “tail events”; that is, low probability events that trigger a breakdown in
the payments system, with potential large-scale real economic effects. In otherwords, our concern is with the maximum cost that can occur (with some small,but non-zero, probability) over some reasonable time period. The reason we areconcerned with tail events is our belief that the cost of systemic events is not
linear in the magnitude of the event. Rather, we have an (unmodelled) belief thatthe social cost of systemic crises is convex in the size of the crisis. So, learning
about the probability of small problems does not tell us much about the true social
cost of systemic failure. Perhaps the authors will focus their attention on this issue
in their future research.
In closing, I want to note that each of these papers offers unique insights into
payments systems operations and risks. I encourage the authors to continue theirimportant work and the readers of this volume to study these papers carefully.