Comparing the pre-settlement risk implications of alternative clearing by yxx13897



                                                                                        Comparing the
                                                                                        pre-settlement risk
                                                                                        implications of
                                                                                        alternative clearing
                                                       John Jackson
             Systemic Risk Reduction Division, Financial
                             Stability, Bank of England

                                                      Mark Manning
             Systemic Risk Reduction Division, Financial
                             Stability, Bank of England1

                                                                                        In recent years, there has been a marked expansion in the
                                                                                        range of products cleared through central counterparty
                                                                                        clearing houses, accompanied by a trend towards consolida-
                                                                                        tion in the clearing infrastructure. The financial stability
                                                                                        implications of these developments are of considerable poli-
                                                                                        cy interest. In this paper, we use a simulation approach to
                                                                                        analyze, in a systematic way, the potential pre-settlement
                                                                                        cost and risk implications of these developments. Our results
                                                                                        point towards substantial risk-reduction benefits from multi-
                                                                                        lateral clearing arrangements, arising from multilateral net-
                                                                                        ting and mutualization. The paper also examines individual
                                                                                        incentives to join multilateral clearing arrangements. We sug-
                                                                                        gest that arrangements with restricted direct participation
                                                                                        and tiered membership may be a natural response to the
                                                                                        uneven distribution of total pre-settlement costs when agents
                                                                                        are of heterogeneous credit quality and it is costly to individ-
                                                                                        ually tailor margins.

1   The views in this paper are those of the authors and do not necessarily reflect       Saporta, Alan Sheppard, Matthew Willison, an anonymous referee, seminar partici-
    those of the Bank of England. Helpful comments and advice were received from a        pants at the Bank of England, and conference participants at the ECB/Federal       113
    number of parties during the preparation of this work. In particular, the authors     Reserve Bank of Chicago conference on ‘Issues related to central counterparty
    are very grateful to Grigoria Christodoulou, Rory Cunningham, Johan Devriese,         clearing.’ This work also builds on a methodology established in earlier work on
    Jennie France, Charles Kahn, Steve Millard, Jim Moser, Pat Parkinson, Victoria        market structure undertaken jointly with Jing Yang.
      Comparing the pre-settlement risk implications of alternative clearing

      This paper analyses the risk implications of different                                   pre-settlement costs and risks under alternative bilateral
      arrangements for clearing financial market trades involving                              and multilateral clearing arrangements. Simulation facili-
      securities and derivatives2. In recent years there have been                             tates the examination of a richer array of scenarios than
      two distinct trends in the clearing arena. Firstly, there has                            would be possible with a purely analytical approach.
      been a marked expansion in the range of products cleared                                 Importantly, this approach yields some quantitative compar-
      through central counterparty clearing houses (CCPs). For                                 isons and allows us to both introduce several sources of ex-
      example, since 1999 the London Clearing House (LCH) has                                  post heterogeneity and examine some complex interactions,
      introduced CCP services for swaps, repos, and, most recent-                              such as that between ex-post heterogeneity in trading posi-
      ly, securities traded on the London Stock Exchange.                                      tions and the concentration of replacement cost losses. We
      Secondly, there has been a trend towards consolidation in                                restrict attention to two metrics for pre-settlement risk, the
      the clearing infrastructure, notably the London Clearing                                 magnitude of replacement cost losses and the distribution of
      House and Clearnet merging in 2003, and the Chicago                                      such losses. To capture the relevant factor in the decisions of
      Mercantile Exchange (CME) Clearing House taking over the                                 risk-neutral agents, we also compare total pre-settlement
      clearing of trades for the Chicago Board of Trade (CBOT) in                              costs borne by agents, which include both replacement cost
      the same year. These developments are of considerable pol-                               losses and the opportunity cost of posting margin/collateral3.
      icy interest. For instance, there is a live and active debate
      underway in both policy and financial market circles regard-                             Replacement cost risk arises during the period between
      ing the potential risk-reduction benefits of centralized clear-                          trade and settlement and reflects the cost to a trader of
      ing arrangements for OTC derivative products [(BIS) (1998,                               replacing a trade on which a counterparty has defaulted.
      2007), Geithner (2004), Counterparty Risk Management                                     Consider a bilateral trade between agents i and j: should the
      Policy Group II (2005)], and in particular, whether CCP clear-                           former default prior to settlement, the latter does not incur
      ing for a wider range of products is feasible, or desirable.                             a loss on the principal, because the asset has not yet been
                                                                                               delivered and no money has changed hands; but, should the
      There is a sizable literature describing the key features of                             market price of the asset have moved adversely since the
      alternative clearing arrangements, their historical evolution,                           deal was struck (or since the trade was last marked-to-mar-
      and their current roles [Moser (1998), Hills et al. (1999),                              ket and variation margin collected), agent j may face a loss
      Kroszner (1999), and Ripatti (2004)]. These papers also                                  from replacing the trade.
      identify the risks that can arise in clearing arrangements,
      and describe the infrastructural innovations that have                                   Agents can mitigate replacement cost risk by collecting mar-
      emerged to deal with them. BIS (2004), in the context of                                 gin from their trading counterparties during the pre-settle-
      CCPs, also gives a comprehensive overview of risks and risk-                             ment period; hence a trader (or CCP) will only incur a
      management issues. However, to our knowledge, there is no                                replacement cost loss if there is a coincidence of events: an
      established analytical framework for evaluating, quantita-                               adverse change in the underlying contract price in excess of
      tively, the relative cost and risk implications of a range of                            the per-unit value of margin collected from a counterparty,
      clearing methods, covering different constellations of prod-                             combined with a default by that counterparty. However, the
      ucts, trader profiles, and market structures. This paper seeks                           requirement to post collateral may impose a significant cost
      to provide such a framework.                                                             on agents, which in our analysis is quantified and compared
                                                                                               across arrangements. Moser (1998) identifies three distinct
      The approach we take here is to construct an analytical                                  clearing and settlement arrangements for futures markets:
      framework for the simulation and quantification of agents’                               clearing by direct settlement (bilateral clearing), clearing

      2 BIS (2003) defines ‘clearance’ as the ‘process of calculating the mutual obligations   3 This paper does not discuss the implications of different clearing arrangements
114     of market participants, usually on a net basis, for the exchange of securities and       for ‘single point of failure’ operational risks or moral hazard issues often raised in
        money.’ It is recognized that the term is sometimes also used with reference to the      the context of consolidation of infrastructure. We leave analysis of these risks for
        process of transferring securities on settlement date, but our focus here is on          future research.
        arrangements for the management of risks arising during the pre-settlement peri-
Comparing the pre-settlement risk implications of alternative clearing

through ‘rings’ (multilateral clearing, without novation to a                            In his historical overview, Kroszner (1999) remarks that
CCP), and complete clearing (CCP clearing). These alterna-                               “credit risk [in ringing arrangements] continued to vary with
tive arrangements form the basis for our comparative exer-                               the individual counterparties or members of the trading
cise in this paper. Although one can trace a natural evolution                           rings.” In short, members’ contracts were not perfect substi-
from direct settlement, through ringing, to complete clear-                              tutes for one another. A ‘complete clearing’ arrangement
ing, the emergence of new products and other financial inno-                             thus ultimately emerged, taking ringing a step further by
vations means that multiple clearing arrangements can, and                               introducing novation of all trades to a central counterparty;
do, coexist. In this regard, the model as presented is most                              the CCP interposes itself as the legal counterparty to both
consistent with clearing of vanilla OTC swap products, or                                the buy and sell-side of a trade. In the absence of counter-
futures contracts that are marked-to-market on a daily                                   party default, the CCP has a balanced book and does not,
basis4; these asset classes could feasibly be traded through                             therefore, face any market risk. By providing centralized risk
any one of these arrangements.                                                           management and facilitating anonymous trades, CCP clear-
                                                                                         ing is particularly beneficial in the case of exchange-traded
In the first of these, clearing by direct settlement, trading                            assets, particularly those with long settlement periods, such
agents calculate and perform on their original bilateral obli-                           as derivatives6.
gations. We, therefore, use the terminology ‘bilateral clear-
ing’ to describe this class of arrangement. This has histori-                            The starting point for our comparative simulation analysis is
cally been the most common clearing arrangement, and,                                    a matrix of normally distributed bilateral net trading expo-
though largely superseded by CCP clearing for exchange-                                  sures between agents, initially in a single asset. In this sense,
traded products in recent years, it remains the most com-                                our approach has much in common with simulation-based
mon arrangement for off-exchange and OTC trading, partic-                                analyses of trading systems or inter-bank loan markets
ularly in less standardized products. Margin will generally be                           [Elsinger et al. (2006), Wells (2004), Devriese and Mitchell
posted on the basis of the bilateral net position. The second                            (2005)]. The asset price distribution is assumed known and
approach, clearing through rings, is the next step in the his-                           agents’ ex-ante default probabilities are observed (we
torical evolution of clearing arrangements. Ringing is a vehi-                           assume costlessly) by bilateral counterparties. In order to
cle for achieving multilateral netting of exposures, but with-                           isolate the key factors affecting replacement cost risk in
out novation to a common central counterparty. Rather, the                               these arrangements, we build up from the case in which
original bilateral exposures are extinguished and multilater-                            homogeneous agents trade a single generic asset, to cases
al net exposures reallocated, according to some algorithm,                               with homogeneous agents trading two assets, and finally to
among members of the ring. In a traditional ringing arrange-                             heterogeneous agents trading a single asset.
ment, described in detail in Moser (1998), members of the
ring agree to offset trades within the group, thereby treating                           The analytical framework
each others’ contracts as perfect substitutes. Importantly                               In our comparative simulation analysis, we examine the
then, a ringing arrangement reduces collateral costs and                                 properties of the alternative clearing arrangements intro-
optimizes the liquidity cost of effecting settlement, but                                duced above: bilateral clearing, multilateral clearing via ring-
agents retain some counterparty credit exposure to one                                   ing, single-product CCP clearing, and ultimately, multi-prod-
another. There are, to our knowledge, no formal ringing                                  uct CCP clearing. This section introduces the modeling set-
arrangements in operation at present, although services for                              up to be applied in the simulation exercise.
multilateral contract terminations can achieve something

4 Our approach to modeling the margining process (especially when we consider              counterparty credit exposure, the system searches for offsetting positions among
  multi-product clearing), cannot, for example, deal with collateralization of cumula-     all those submitted.                                                                  115
  tive value in option products.                                                         6 Derivatives prime brokerage does something similar for OTC trades. Here, the
5 For example, triReduce, a swap termination service provided by TriOptima                 derivatives prime broker interposes itself in a trade between a buy-side client and
  (, runs regular multilateral termination cycles in vanilla OTC         an executing broker.
  swap products. Subject to a set of user-defined constraints, including limits on
      Comparing the pre-settlement risk implications of alternative clearing

      The system                                                                                 by the bilateral matrix in (1) are extinguished and replaced by
      We model a system of n risk-neutral agents trading a single                                a vector of net settlement exposures between the CCP and
      generic asset k with one another7. The bilateral exposures gen-                            each trader. The CCP’s positions with each trader are given by
      erated in this system, denoted by the superscript, b, can be                               (2) above, where Vic,k > 0 denotes that agent i has a long posi-
      described in an n x n matrix,               Vb,k.   Our starting point is a sys-           tion with the CCP. Replacement cost losses will only arise to
      tem of n homogeneous agents, in which each agent trades                                    the extent that a counterparty default coincides with an
      with every other agent, and each bilateral trade is drawn from                             adverse price movement in excess of the per-unit margin col-
      the same distribution. These assumptions are relaxed later.                                lected from that counterparty; therefore to quantify replace-
      Vijb,k represents the bilateral net position8, which may be inter-                         ment costs we need to model price changes, margin policy,
      preted as the net number of outstanding contracts, between                                 and counterparty default.
      agent i and agent j awaiting settlement, where Vijb,k > 0
      denotes that agent i has a long position with agent j. As these                            Price changes
      are net bilateral positions, this matrix is exactly negatively                             We capture the change in the price of asset k, Δpk, by once
      symmetric about the diagonal. This is illustrated in (1):                                  again drawing from a normal distribution: this time with
                                                                                                 mean 0 and standard deviation σΔpk. The potential for
                 0           Vb,k . . . Vb,k                                                     replacement cost losses thus arises if and only if the draw
                               12            1n
                                                                                                 from this distribution exceeds the per-unit level of margin
      Vb,k =   Vb,k            0           Vb,k     , where Vij   b,k   = -Vji   b,k   (1)       posted, mik, and both the position held in the asset and the
                21                          2n
                                                                                                 sign of the price change are the same (i.e., in the bilateral


                                                                                                 clearing case, Vi,jb,kΔpk > |Vi,jb,k|mik. We impose the condition
                             Vn2 . . .      0
                                                                                                 that agents can never profit from a counterparty default.
                                                                                                 Therefore, any profit or excess margin remaining after the
      In our simulation exercise, we populate this matrix by drawing                             defaulted position has been closed out is returned to the
      from a normal distribution with mean 0 and standard devia-                                 defaulting agent10.
      tion   σkV.   To model the multilateral ringing case, we first calcu-
      late each agent’s net exposure to all other members of the                                 Margin policy
      ring. Multilateral positions are denoted by the superscript, r, in                         Trading agents (and CCPs) typically seek margin from their
      the ring case, and c in the CCP case. Agent i’s multilateral net                           counterparties (or, in the case of CCPs, their members) to mit-
      positions, Vir,k, Vic,k, are simply the sum of its bilateral posi-                         igate replacement cost risk during the pre-settlement period.
      tions with each agent, j: Vir,k = Vic,k = Σj=1¬nVijb,k (2).                                We assume in our simulation exercise that margin is set
                                                                                                 according to an optimization approach, and apply a variant of
      We model the multilateral netting that takes place in a ring-                              the model developed in Baer et al. (2004). In the bilateral
      ing arrangement by application of a simple netting algorithm,                              case, the optimization approach assumes that the two parties
      which extinguishes the original bilateral trades and then,                                 to a transaction set margin levels so as to jointly minimize
      based on the agents’ net positions, generates a new bilateral                              total expected pre-settlement costs. In the CCP case, under
      matrix with the smallest possible number of new trades . In                                the assumption that the CCP is owned by its participants,
      the case of CCP clearing, all bilateral obligations between                                margin will be set so as to minimize the joint expected pre-
      traders are novated to the CCP. Hence, positions represented                               settlement costs of all participants11. For each agent, i, there

      7 In thinking about the application of this approach and the interpretation of the         9 It can be shown that the maximum number of new bilateral positions generated by
        results, it is convenient to assume that the agents are large, professional financial       this algorithm is n-1. In practice, any one of a number of algorithms could be
        firms. And to generalize the results, one might interpret each generic asset as a           applied here, applying a variety of constraints.
        set of homogeneous or highly correlated assets.                                          10 We understand this to be accepted practice, at least for CCPs. Consider, for exam-
116   8 We assume that agents would have legally robust (i.e., enforceable) bilateral net-          ple, the case of Drexel Burnham Lambert Ltd (DBL), who defaulted on margin calls
        ting agreements in place. For example, in the context of OTC derivatives, the               from the London Clearing House in February 1990. Settlement of DBL’s positions
        International Swaps and Derivatives Association (ISDA) Master Agreement is typi-            left a net surplus of approximately U.S.$18 million which was repaid to DBL’s
        cally employed to establish the terms of the trade, including provisions for close-         administrator. See London Clearing House (2002) for further details.
        out netting in case of default.                                                          11 Under a demutualized ownership structure, it is conceivable that (continued)
Comparing the pre-settlement risk implications of alternative clearing

are two distinct components to expected pre-settlement cost,                            that the losses are shared in proportion to the size of each
E[TCi]: the (opportunity) cost of posting collateral and the                            agent’s positions with the CCP, which becomes important
expected replacement cost loss, E[Ri], should the counterpar-                           when we compare the concentration of losses across differ-
ty to the trade default. In our analysis, we abstract from bar-                         ent clearing arrangements. Alternative loss-sharing rules
gaining problems, appealing to competitive market condi-                                could of course be considered.
tions that drive the market to an efficient solution.
                                                                                        In the bilateral and ringing cases, residual losses, once the
Counterparty default                                                                    defaulting party’s margin has been exhausted, are borne
In the application by Baer et al. (2004), default occurs                                entirely by the bilateral counterparty, the original counter-
endogenously, with agents choosing to strategically default                             party in the bilateral case, and the new ring counterparty
on positions that have moved sufficiently far out of the                                (once positions have been multilaterally offset and reallocat-
money. By contrast, we assume that agent i defaults exoge-                              ed) in the multilateral ringing case. A further necessary
nously, with ex-ante probability δi, where δi is observed by                            assumption in the bilateral and ringing cases is that a trader
both parties. The exogenous default vector, D, is generated on                          can always recover, in full, any margin posted with a default-
the basis of δi; that is, default shocks arise ex-post in accor-                        ing counterparty.
dance with ex-ante probabilities.
                                                                                        Metrics for comparison
Di = 1 with prob δi; 0 with prob (1– δi) (3)                                            In this section, we introduce the relevant metrics for compar-
                                                                                        ing cost and risk outcomes under the three alternative clear-
While there is some variation in CCPs’ post-default proce-                              ing arrangements considered, which are the magnitude of
dures, replacement cost risk exposures are typically managed                            replacement cost losses, the concentration of replacement
through the collection of both margin and default fund con-                             cost losses, and the total pre-settlement costs borne by
tributions. In the event of default, initial recourse is typically                      agents, which comprises the sum of the opportunity cost of
to the margin posted by the defaulting party, then to the                               posting collateral and the replacement cost loss. Given our
default fund contribution of the defaulting party, and finally                          assumption that ex-ante default probabilities are realized,
to default fund contributions of survivors. Should these                                and that we make repeated draws from the distribution of
resources be insufficient to cover replacement cost losses, a                           price changes and trading positions, these metrics can be
CCP would typically first draw upon its own capital and then                            interpreted as expected replacement cost losses and pre-set-
seek additional contributions from surviving participants12.                            tlement costs.
Margin posted by survivors cannot be drawn upon to cover
replacement cost losses faced by a CCP. As our metric for                               The magnitude of replacement cost losses
replacement cost risk is expected losses borne by surviving                             Under all clearing scenarios the metric of interest is replace-
participants, we are able to simplify matters in our analysis:                          ment cost losses borne by surviving members. In the case of
we make no distinction between collateral contributed by sur-                           bilateral clearing, the mean ex-post replacement cost loss
vivors ex-ante (as default fund contributions) and any addi-                            faced by agent i, Rib,k, is calculated by summing across coun-
tional contributions made ex-post. Therefore, once the mar-                             terparties the products of the mark-to-market losses on open
gin posted by defaulting agents has been exhausted, all resid-                          positions (allowing for the margin held against default), and
ual losses are shared among survivors and classified as                                 the default realizations of those counterparties. The mini-
replacement cost losses. Hence, we assume that there is no                              mum replacement cost loss is zero, given the rule that any
possibility of a default by a CCP. For simplicity, we assume                            profit made on closing out positions is returned to the

  alternative preferences would be reflected in the CCP’s objective function. For       12 In some cases, CCP participants are obliged to make additional contributions in
  instance, Koeppl and Monnet (2005) consider the extent to which margin levels            such an event; in other cases, there is no such explicit provision.               117
  influence the scale of trading activity, and how this might influence a CCP’s risk-
  management approach.
      Comparing the pre-settlement risk implications of alternative clearing

      defaulting agent. Therefore, for agent i:                                                    TCb,k = cΣj=1¬nΣi=1¬n |Vijb,k|mib,k + Rb,k (5)

      Rib,k = Σj=1¬nDj max[0, Vijb,kΔpk – |Vijb,k|mjk)] (4)                                        Again, total costs for the ringing and CCP cases are calculat-
                                                                                                   ed in an analogous fashion.
      Extension to the multi-asset case is straightforward, with the
      max. expression in (4) simply becoming max[0, Vijb,kΔpk –                                    The risk implications of alternative clearing
      |Vijb,k|mjk) + (Vijb,lΔpl – |Vijb,l|mjl)]. And, to obtain replacement                        arrangements: comparative simulations
      cost losses for the system as a whole, Rb,k, we sum across                                   Taking the set-up described above, this section uses simula-
      agents. Calculation of agent i’s replacement cost loss in the                                tion analysis to investigate the cost and risk implications of
      multilateral ringing and CCP clearing cases is analogous13.                                  the alternative clearing arrangements considered. For each
                                                                                                   of the simulations carried out in this section, we evaluate
      The concentration of replacement cost losses                                                 2,500 trading position matrices, drawing from a normal dis-
      The degree of concentration of replacement cost losses                                       tribution of positions in each asset, k, with N(0, σTk) = N(0,
      across agents may have implications for social welfare. While                                √20). We also generate 2,500 different scenarios for price
      we do not explicitly model spillover effects, it is likely that, for                         changes in asset k, drawing from a price-change distribution
      a given level of replacement cost loss, knock-on default or liq-                             with N(0, σΔpk) = N(0, √2), and 2,500 default realizations for
      uidity strains arising outside of the model will be increasing in                            each agent, applying default vector, D. We assume that the
      the extent to which this loss falls disproportionately on a sin-                             latter is based on ex-ante default probability, δi = 1%. Margin
      gle counterparty. We measure concentration of losses by cal-                                 coverage is based upon this default probability, the price dis-
      culating the ratio of the maximum replacement cost loss                                      tribution, an assumed collateral cost of 15 basis points, and a
      incurred by a single agent, i, over total replacement cost loss                              recovery rate, r, of zero14. We pair the price and default sce-
      incurred by all agents. We calculate this measure in all sce-                                narios and apply each of the 2,500 pairs to every distinct
      narios where losses occur, and take the mean. In the bilateral                               trading position matrix; therefore, a total of 6.25 million dis-
      and ringing cases we use observed replacement cost losses to                                 tinct position, price, and default scenarios are evaluated. It is
      calculate concentration. In the CCP case, on the other hand,                                 necessary to undertake a large number of simulations if accu-
      agents’ relative multilateral net positions can be used to cal-                              rate results are to be obtained, given that the price-change
      culate concentration, as this is the basis on which losses are                               and default scenarios chosen make significant default events
      assumed to be shared.                                                                        rare occurrences.

      Total costs                                                                                  Single-asset clearing with homogeneous agents
      Recall that, throughout our analysis, we assume that agents                                  We begin with the case in which a single asset is traded bilat-
      are risk-neutral and therefore care only about expected                                      erally by a group of n homogeneous agents, and cleared
      costs. From an agent’s perspective, total pre-settlement                                     either bilaterally or multilaterally via a ringing arrangement
      costs, TCi, are simply given by the sum of collateral costs and                              or a CCP. This set-up allows us to isolate the effect a shift
      replacement cost losses. At the level of the system, we add                                  from bilateral to multilateral netting will have on expected
      all agents’ collateral costs and all replacement cost losses                                 replacement cost losses and total expected pre-settlement
      arising in the system. In the bilateral case, total costs borne                              costs. Our first key result is that multilateral netting, via
      are as given in (5):                                                                         either novation or direct offset of positions, will reduce the

      13 In the ringing case, the relevant positions are those in the new bilateral matrix           volatility of price changes to determine the relative importance of collateral hold-
         generated from agents’ multilateral net positions. Under CCP clearing, the calcula-         ing costs and replacement costs. Our parameters imply that agents will require
         tion is based on the multilateral net position vector.                                      margin up to an 85% coverage level when default probability is 1%. This is signifi-
      14 Our parameters for the standard deviation of positions and price changes are                cantly lower than the 99% coverage that would typically be regarded as a mini-
118      essentially arbitrary. However, their precise values have little effect on our results.     mum requirement for CCPs. However it may be more accurate in a bilateral set-
         Default probability is chosen to capture the fact that defaults are rare events,            ting, to the extent that agents are willing to take some unsecured exposure to
         without making default events so rare as to require an inefficiently high number of         high-quality counterparties. The important consideration in this analysis is to use
         simulations to obtain accurate results. Collateral cost is assumed to reflect the dif-      the same coverage level across all clearing scenarios.
         ference between secured and unsecured borrowing rates. This interacts with the
Comparing the pre-settlement risk implications of alternative clearing

level of outstanding trading exposures in the market, and                                         price change in asset k is independent of the clearing
hence will also reduce replacement cost losses and total                                          arrangement, as is margin per-unit when agents are homo-
expected pre-settlement costs.                                                                    geneous.

Proposition 1 – The reduction in replacement cost losses                                          The analytical result in Proposition 1 is borne out by our sim-
associated with a shift from bilateral to multilateral clearing                                   ulation exercise for the single-asset/homogeneous agent
will reflect a netting ratio applied to absolute trading expo-                                    case (applying the parameter values introduced above). The
sures under each arrangement. With trading positions drawn                                        results, calculated for a complete bilateral trading matrix, are
from a symmetric distribution, the netting ratio will be                                          shown in Figure 1. We also confirm that total cost differentials
increasing in the number of each agent’s trading counterpar-                                      are dependent solely on the netting ratio. The outcome for
ties, but at a decreasing rate.                                                                   concentration of losses is particularly interesting, and reveals
                                                                                                  the crucial difference between the two multilateral clearing
Proof – With trading positions in a single asset drawn from a                                     arrangements. This leads us to Corollary 1:
normal distribution, and each agent trading with every other
member of the system, the netting ratio can be expressed for-                                     Corollary 1 – While the magnitude of replacement cost losses
mally as in (6), below. This expression shows that the netting                                    will be equivalent under ringing and CCP clearing, losses will
ratio is equal to the square-root of the number of trading                                        typically be more concentrated when multilateral netting has
counterparties with whom each agent transacts.                                                    been achieved via ringing. This corollary reflects the fact that
                                                                                                  agents’ multilateral net positions are reallocated among the
NR = [Σi=1¬nΣj=1¬n|Vij        ÷ [Σi=1¬n|Vic,k|] = [Σi=1¬nΣj=1¬n|Vijb,k|] ÷
                           b,k|]                                                                  members of the ring according to an algorithm which ensures
[Σi=1¬n|Σj=1¬nVij b,k|] = [n(n-1) √(2/π)σ k] ÷ [n √(n-1) √(2/π)σ k] =                             the fewest new bilateral positions. Hence, in the new bilateral
                                          V                         V
√(n-1) (6), where: Vijb,k ~ N[0, (σVk)2] ⇒ E(|Vijb,k|) = √(2/π)σVk                                matrix, traders will typically have exposures to just a small
                                                                                                  subset of counterparties. In the event of a default, losses will
It can readily be shown that the first and second derivatives                                     be borne only by those counterparties with a direct exposure
of (6) with respect to n are positive and negative, respective-                                   to the defaulting agent. In the CCP case, by contrast, losses
ly. Replacement cost losses under bilateral and multilateral                                      are shared across all members, in proportion to the size of
clearing will be dependent only on the netting ratio applied to                                   their exposures to the CCP, rather than their exposures to the
absolute trading exposures. This reflects the fact that the unit                                  defaulting trader. The differences in the concentration ratios

 Benchmark: CCP                                                                                    Number of traders                            5            10           20

 Position matrices evaluated: 2,500
 Default scenarios: 2,500                                                                          Expected replacement cost loss
 Default probability: 1%                                                                           Bilateral                                    2.0          3.0          4.4
 Cost of collateral: 15 basis points                                                               Multilateral ring                            1.0          1.0          1.0
 Margin coverage: 85%                                                                              Total expected pre-settlement cost
 σΔpk = √2; σTk = √20                                                                              Bilateral                                    2.0          3.0          4.4
                                                                                                   Multilateral ring                            1.0          1.0          1.0
                                                                                                   Concentration (% of total losses)
                                                                                                   Bilateral                                    74           45           25
                                                                                                   Multilateral ring                            88           87           89
                                                                                                   CCP                                          39           24           14

 Figure 1 – Ratio of replacement cost losses, total pre-settlement costs, and concentration under alternative clearing arrangements (with differing numbers of traders)

            Comparing the pre-settlement risk implications of alternative clearing

            between the ringing and CCP cases will be increasing in n. In      The analysis in this subsection is based initially on the case in
            practice, even for exchange-traded assets, a complete bilat-       which margin is calculated on an asset-by-asset basis under all
            eral trading matrix would not be observed. Corollary 2 gener-      arrangements. We then go on to consider the case of portfo-
            alizes the result in Proposition 1 accordingly.                    lio-based margining (i.e., the practice of granting margin off-
                                                                               sets to reflect the diversification in a trader’s asset portfolio.
            Corollary 2 – Where the trading position matrix is not com-
            plete, the netting ratio equals the square root of the weight-     Asset-by-asset margining – equal price-change
            ed-average number of counterparties with whom each agent           variances and equal position variances
            transacts. By way of illustration, consider a case with n=10, in   In the context of CCP consolidation, the implications of mar-
            which 50% of agents are ‘complete agents,’ who have trading        gin pooling are summarized in Proposition 2, below.
            exposures with all other agents, while the remaining 50% of
            agents only have trading exposures with these complete             Proposition 2 – When margin is set on an asset-by-asset
            agents. The relevant netting ratio in this case will thus be √7,   basis, and both asset prices and trading positions are imper-
            rather than √9 in the complete matrix case. Hence, the ratio       fectly correlated, expected replacement cost losses will be
            of replacement cost losses (total expected pre-settlement          lower when all assets are cleared through a single CCP than
            costs), will be 2.65, rather than the 3.0 reported in Figure 1.    when they are each cleared through separate CCPs.
            More generally, for a given number of traders, the ratio of
            risks and costs between the bilateral and multilateral             Proof – Proposition 2 may be expressed as a comparison of
            arrangements will decline as the matrix becomes less com-          expected replacement cost losses when clearing two assets
            plete.                                                             through either a single or two CCPs. Under the assumption
                                                                               that margin is calculated on an asset-by-asset basis, the total
            Multi-asset clearing with homogeneous agents                       value of margin posted by agent i is the same in the two
            Introducing a second asset, we are able to analyze the effect      cases: |Vic,k| mk + |Vic,l| ml. Importantly, however, clearing
            of portfolio diversification and margin pooling. By margin         through a single CCP allows margin posted by agent i to be
            pooling, we refer to the fact that, even though a bilateral        pooled across assets and applied to meet replacement cost
            counterparty or a multi-product CCP may calculate an               losses in either. Equally, trading positions are pooled when
            agent’s margin obligations on an asset-by-asset (or position-      assets are cleared through a single CCP, and although, in set-
            by-position) basis, the margin is pooled once collected.           ting margin levels, the CCP ignores any portfolio effects, the
            Should that agent then default, any margin in the pool may         expected replacement cost loss associated with agent i’s
            be drawn upon to meet replacement cost losses arising on           position will take into account the true covariance of both
            that agent’s positions. With imperfectly correlated price          asset price changes and trading positions. Hence, it must be
            changes, a replacement cost loss arising on one asset may          true that: E[|Vic,kΔpk| + |Vic,lΔpl|] ≥ E[|Vic,kΔpk + Vic,lΔpl|]. This
            then be mitigated by drawing upon residual margin posted in        expression will only hold with equality if both trading posi-
            respect of the other. This allows us, in particular, to offer      tions and price changes in the two assets are perfectly corre-
            some initial insight into the risk implications of consolidation   lated (either both positively or both negatively correlated).
            of product-specific CCPs. When each asset is cleared through       For imperfectly correlated assets and/or trading positions,
            a separate, product-specific, CCP, only the effects analyzed       expected replacement cost losses will be lower when assets
            above will be observed. However, when an agent’s positions in      are cleared through a single CCP. It follows, therefore, that
            both assets are cleared together through a multi-product           the ratio of replacement cost losses between the single-prod-
            CCP, then margin-pooling effects can be important .                uct and multi-product CCP-clearing cases will depend on the

                                                                               15 We can assume that both assets will always be cleared together in the bilateral
120 – The              journal of financial transformation                        and multilateral ringing cases, so the cost and risk outcomes of these arrange-
                                                                                  ments relative to the multi-product CCP will be as before.
Comparing the pre-settlement risk implications of alternative clearing

degree of correlation in trading positions and asset prices. We                                (two CCPs) to those under multi-product CCP clearing, for
therefore turn, again, to simulation analysis in an attempt to                                 alternative combinations of price-change and position corre-
quantify this ratio for differing correlations between price                                   lations.
changes in two assets, k and l, ρΔp, and trading positions in
the two assets, ρV. Assuming Δpl and Δpind are independent                                     With ρΔp = 0, extreme price changes in both assets are unlike-
draws, Δpk may be calculated, as follows:                                                      ly, and hence multi-product CCP clearing generates signifi-
                                                                                               cant margin-pooling benefits16. As |ρΔp| ¬ 1, the likelihood that
Δpk    =   [σΔpk]÷[σΔpl]   ρΔpΔpl   +   Δpind     √(1 –   ρΔp2)      (7)                       extreme price moves will occur in both assets simultaneously
                                                                                               increases, and therefore the benefits of margin pooling are
Correlated trading positions are calculated in an analogous                                    determined increasingly by the degree of position correla-
fashion. It is clear that with ρΔp = 0, Δpk = Δpind, and Δpk and                               tion, and the interaction between price change and position
Δpl    are completely uncorrelated; while with ρΔp = 1,                            Δpk     =   correlations. If these correlations have the same sign, then
[(ρΔpk)÷(σΔpl)]Δpl and Δpk and Δpl are perfectly correlated. In                                margin-pooling benefits will be reduced; if they have different
our exercise, we start by assuming that the two asset prices                                   signs, then these benefits will be increased (hence the asym-
are equally volatile, each being drawn from a normal distri-                                   metric pattern evident in Figure 2). The extreme cases are
bution with N(0,      σΔpk)=    N(0,     σΔpl)    = N(0, √2); and that trading                 worthy of note. With ρΔp = ρV = 1, expected replacement cost
positions are also drawn from the same distribution: N(0, σVk)                                 losses are equivalent in the single and multi-product cases,
= N(0, σVl) = N(0, √20). The important message from this                                       whereas with ρΔp = -ρV = 1, replacement cost losses fall to zero
analysis is that the most significant margin-pooling benefits                                  in the multi-product case.
from CCP consolidation will occur when one of the following
holds: either the correlation between either price changes or                                  The impact of consolidation on total pre-settlement costs is
trading positions is low or the correlations between price                                     less significant than the impact on replacement costs
changes and trading positions take opposite signs. These                                       described above. As margin setting is carried out on an asset-
effects are illustrated in Figure 2, which plots the ratio of                                  by-asset basis, the opportunity cost of posting collateral is
replacement cost losses under single-product CCP clearing                                      equal in the two arrangements. This is then a source of poten-
                                                                                               tial divergence between the interests of agents, who we have
                                                                                               assumed to be risk-neutral, and a risk-averse policymaker
   Replacement cost loss:                                                                      with a financial stability objective, who might attach more
   1CCP/2CCP                            1.0
                                                                                               weight to the replacement cost risk-mitigation benefits of
                                    0.8                                                        margin pooling. A comparison with bilateral clearing provides
                                                                                               some insight into the relative effects of margin pooling and
                                                                                               netting. The multilateral netting result established above con-
                                    0.4                                                        tinues to hold when no margin pooling is available (i.e., ρΔp =

                                                              Position correlation = 0         ρV = 1). However, when |ρV| ¬ 1 and the correlations between
                                                              Position correlation = 0.5
                                                              Position correlation = 1         price changes or trading positions take opposite signs, the
  -1                                          0                                       1
                                                                                               margin-pooling effects on replacement cost risk captured in
                                                                   Price correlation           bilateral clearing outweigh the netting benefits of CCP clear-
                                                                                               ing. Nevertheless, even then, the benefits of CCP clearing in
 Figure 2 – Ratio of replacement cost losses under single and multi-product CCP
 clearing for alternative position and price correlations
                                                                                               total pre-settlement cost terms remain significant.
 (Benchmark: multi-product CCP)

                                                                                               16 This effect increases as |ρV| ¬ 1. With positions drawn from the same distribution,
                                                                                                  it becomes increasingly likely that the trader’s positions in each asset will be of       121
                                                                                                  similar size. This makes it more likely that, for a given correlation in price changes,
                                                                                                  sufficient margin will have been posted in respect of a position in which no loss
                                                                                                  has been incurred to offset replacement cost losses on a position suffering an
                                                                                                  adverse price shock.
      Comparing the pre-settlement risk implications of alternative clearing

      Portfolio-based margining                                                                 sets are typically only granted on positions where price-
      Finally, in this section we consider how these results might be                           change correlations are significant, stable, and justified by
      affected if margins were calculated on a portfolio basis. This                            economic relationships.
      is becoming increasingly common in bilateral clearing rela-
      tionships17, but remains limited in the CCP context. Indeed, in                           Exploring heterogeneity
      the CCP case, offsets are often granted only within distinct                              In this section, we return to a single-asset environment, but
      families of assets (under SPAN-type procedures18), in which                               introduce heterogeneity in trader types. This allows us to
      correlations tend to be more stable and predictable. In our                               investigate agents’ individual incentives to participate in par-
      simulation exercise, we assume that a bilateral trader (or a                              ticular clearing arrangements. Specifically, we would like to
      consolidated CCP) calculates margin on the basis of the port-                             explore the extent to which individual and collective prefer-
      folio variance of its outstanding positions vis-à-vis a particu-                          ences differ, and, to the extent that they do, what this might
      lar counterparty, taking into account actual trading positions                            imply for the topography of the clearing landscape. The mar-
      and the actual covariance of price changes (assumed                                       gin-setting methodology described above allows margin to be
      observed). The calculation for the two-asset case considered                              tailored according to individual credit quality. Working with
      here is given in expression (8):                                                          homogeneous trading agents in the analysis provided above,
                                                                                                this was not a relevant factor. Here, however, the results rest,
      σΔpporti = √[(σΔpk)2 . ((Vib,k) ÷ (|Vib,k|) + |Vib,l|))2 + (σΔpl)2 . ((Vib,l)             to a significant extent, on whether margin is tailored in this
      ÷ (|Vib,k| + |Vib,l|))2 + 2ρΔp ((Vim,k Vim,l) ÷ (|Vib,k| + |Vib,l|))2 . σΔpk              way. While margin will always tend to be tailored to individual
      σΔpl] (8)                                                                                 participants’ default probabilities in bilateral clearing
                                                                                                arrangements, this is rarely the case in CCP arrangements.
      The optimal margin level is then calculated as before. Our                                Baer et al. (2004) argue that this reflects several factors,
      analysis of this case leads us to Corollary 3.                                            including the potentially high cost to the CCP of intensive
                                                                                                monitoring of its members. Furthermore, the incentive to
      Corollary 3 – When margin is set on a portfolio basis, allow-                             monitor may be dampened by the fact that multilateral net-
      ing offsets to reflect diversification in an agent’s trading                              ting reduces individual agents’ risk exposures to relatively
      positions, the replacement cost risk-mitigation benefits                                  low levels. To explore agents’ individual incentives to join par-
      associated with margin pooling will be significantly dimin-                               ticular clearing arrangements, we extend our model by allow-
      ished. Total pre-settlement costs will, however, decline as                               ing agents to be of two types: high and low credit quality. We
      collateral posting requirements are reduced. This is borne                                compare cost and risk outcomes for cases in which margin is
      out by our simulations. When absolute correlations in both                                fully tailored to credit quality and cases in which a single mar-
      price changes and trading positions are low, the reduction in                             gin rate is imposed on all participating agents. We analyze
      total costs from adopting a portfolio approach is very small;                             two distinct configurations of membership: first we consider
      indeed, with zero correlation in both price changes and trad-                             unrestricted access, with all trading agents being direct mem-
      ing positions, portfolio margining reduces total pre-settle-                              bers of the clearing arrangement and then we go on to con-
      ment costs by just 2%, reflecting the fact that replacement                               sider arrangements with access restricted to high-quality
      cost losses rise 70% relative to the asset-by-asset margining                             traders only19.
      alternative. It is only when absolute price-change correla-
      tions are high that significant cost reductions are captured                              Unrestricted access
      by adopting a portfolio-based margining approach. This                                    If fully tailored margining is feasible and costless under all
      accords with observed CCP behavior: as noted, margin off-                                 three alternative clearing arrangements, it can easily be

      17 A Credit Support Annex to the ISDA Master Agreement governing an OTC trade             19 In principle, any group of sufficiently homogeneous traders could populate the
122      will typically specify the terms and conditions associated with collateralization of      first tier. However, in practice, direct members are always drawn from the highest
         pre-settlement exposures.                                                                 quality group, perhaps because these are more likely to be the ‘most important’
      18 The Standard Portfolio Analysis of Risk (SPAN) margining technology, developed            players in a market.
         by the Chicago Mercantile Exchange, is widely used by CCPs around the world. The
         SPAN approach is described in detail in Millard and Polenghi (2005).
Comparing the pre-settlement risk implications of alternative clearing

shown that relative replacement cost losses and total pre-set-                           of δmargin = 5.5%, which in our setup implies coverage of
tlement costs will be as in the single asset/homogeneous                                 97.3% on all positions. This compares with coverage of 85%
agent case described above (i.e., only the netting ratio will                            on high-quality and 98.5% on low-quality agents’ exposures,
matter). And, as before, the outcome in a ringing arrange-                               when margin is fully tailored to default probability. The
ment with tailored margining will be equivalent to that of the                           benchmark for the results in the figure is the case of CCP
CCP case, but with a marked increase in the concentration of                             clearing with unrestricted access and costless fully tailored
replacement cost losses. But fully tailored margining is rarely,                         margining. Results are disaggregated into the costs and risks
if ever, observed in existing multilateral arrangements, imply-                          faced by high and low-quality agents. It is immediately clear
ing that this may either be infeasible or incentive-incompati-                           that a single margin rate places a disproportionate cost bur-
ble when monitoring/tailoring costs exist. We, therefore, con-                           den on high-quality agents: these agents are required to post
sider the implications of alternatives in which the multilater-                          a higher level of margin per-unit than would be the case
al arrangement sets a single margin rate per asset.                                      under tailored margining. Therefore, absent very high tailor-
                                                                                         ing costs, and other ancillary benefits to subsidizing the par-
Unrestricted access – single margin level                                                ticipation of low-quality counterparties, high-quality agents
In this subsection we consider cases in which a single margin                            would strongly favor full tailoring in any multilateral arrange-
level per asset is set on the basis of the mean default proba-                           ment.
bility of members, δmargin. This probability is assumed observ-
able at no cost. Figure 3 presents simulation results for a case                         Restricted access
with 20 agents, split equally between high and low-quality                               Given the adverse selection effect observed above, it is like-
agents, with default probabilities δh = 1%, and δl = 10%,                                ly that, if a multilateral arrangement with tailored margining
respectively. Margin in this case is, therefore, set on the basis                        is not feasible, traders with high credit quality will wish to
                                                                                         exclude agents of significantly lower credit quality from any
                                                                                         multilateral arrangement. A restricted access arrangement
  Benchmark: CCP with
  tailored margining                                                          Ratio
                                                                                         may then emerge, in which objectively determined access
                                                                                         criteria are set, which allow only traders with sufficiently
  Position matrices evaluated: 2,500        Replacement cost loss
  Default scenarios: 2,500                  High credit quality – CCP          0.96      high credit quality to participate directly. With membership
  Number of agents: 20                      High credit quality – Ringing      0.92      restricted in this way, it would be possible to set a single
  (10 high quality, 10 low quality)         Low credit quality – CCP           0.87
  Default probability:                      Low credit quality – Ringing       0.92      margin rate that was acceptable to all direct members, allow-
  - High credit quality: 1%                                                              ing margin tailoring costs to be avoided. With access thus
    (coverage: 97.3%)                       Total pre-settlement cost
  - Low credit quality: 10%                 High credit quality – CCP           1.58
                                                                                         restricted, a tiered arrangement would emerge where direct
    (coverage: 97.3%)                       High credit quality – Ringing       1.57     members clear on behalf of a body of second-tier indirect
                                            Low credit quality – CCP           0.88
                                            Low credit quality – Ringing       0.89
                                                                                         participants of lower credit quality. Each indirect participant
                                                                                         clears through a single direct member, who commits to hon-
                                                                                         oring that participant’s obligations as if they were its own.
                                            High credit quality – CCP           1.0
                                            High credit quality – Ringing       3.6      By taking responsibility for margin payments associated with
                                            Low credit quality – CCP            1.0      the positions of a second-tier participant, a direct member
                                            Low credit quality – Ringing        3.5
                                                                                         essentially provides insurance to other members of the mul-
                                                                                         tilateral arrangement against that participant’s counterpar-
  Figure 3 – Unrestricted access/single margin rate: ratio of replacement cost losses,
  total costs, and concentration under alternative clearing arrangements – disaggre-     ty credit risk20. Tiered arrangements preserve multilateral
  gated results                                                                          netting for all trades, while still ensuring that the CCP or ring

20 Here we assume that direct members do not provide insurance to indirect partici-        any additional contributions required from survivors to cover losses incurred by
   pants against default of their counterparty; hence under a tiered ringing arrange-      the CCP. In practice only direct members would be called upon to make additional   123
   ment second-tier members would remain exposed to any counterparty credit risk           default fund contributions where a CCP faced losses. However, we assume direct
   associated with their positions vis-à-vis direct members of the ring, while under a     members pass through the portion of these expected costs associated with sec-
   tiered CCP arrangement second-tier members remain exposed to their share of             ond-tier members’ positions.
            Comparing the pre-settlement risk implications of alternative clearing

            can operate with a single margin rate. Furthermore, to the                                monitoring CCP benchmark. However when disaggregating
            extent that it is difficult and costly for a CCP or a ring clear-                         the results by agent type, significant differences emerge.
            ing house to monitor and effect tailored margining for lower-
            quality agents (on whom there may be limited public infor-                                In the tiered CCP, pre-settlement costs exceed the unrestrict-
            mation), such an arrangement has the effect of delegating                                 ed access/full-tailoring benchmark for high-quality agents,
            monitoring of second-tier participants, and associated mar-                               but they are still lower than cases where there is unrestricted
            gin setting, to direct members.                                                           membership and a single margin rate. As direct members
                                                                                                      take responsibility for the default of their second-tier partici-
            Restricted access with tiering – single margin level                                      pants in both tiered arrangements, losses fall disproportion-
            In Figure 4, we present simulation results for tiered multilat-                           ately on direct members; hence, a significant increase in con-
            eral arrangements, assuming that direct and indirect mem-                                 centration of losses is observed. This effect is particularly
            bers carry the rights and obligations described above. We                                 marked in the CCP case, where we assume that second-tier
            again assume equal numbers of high and low-quality agents,                                members can only incur losses when the CCP calls for addi-
            with only high credit quality agents gaining access to the                                tional margin. Similar effects may be observed in the case of
            arrangements as direct members, and each clearing for one                                 the tiered ringing arrangement. However, in this case,
            low-quality indirect member . It is immediately clear that                                because direct members do not provide counterparty credit
            these tiered arrangements have, in aggregate, the same                                    insurance to the second tier, costs and risks are shared more
            replacement cost loss and total cost implications as the full                             evenly between the two types of agent. These results reflect
                                                                                                      the essential fact that, under CCP clearing, the counterparty
                                                                                                      to a second-tier member’s trades is the CCP, while in the ring-
             Benchmark: CCP with
             tailored margining                                                              Ratio
                                                                                                      ing case, direct counterparty risk is preserved.

             Position matrices evaluated: 2,500          Replacement cost loss
             Default scenarios: 2,500                    All agents – tiered CCP               1.0    Agents’ preferences among alternative
             Number of agents: 20                        All agents – tiered ring              1.0    multilateral clearing arrangements
             (10 high quality, 10 low quality)           High credit quality – tiered CCP      1.4
             Default probability:                        High credit quality – tiered ring      1.3   We can use the results above to examine which clearing
             - High credit quality: 1%                   Low credit quality – tiered CCP       0.6    arrangement might ultimately emerge. A thorough treatment
               (coverage: 85%)                           Low credit quality – tiered ring      0.6
             - Low credit quality: 10%
                                                                                                      of this question would require a more sophisticated analysis
               (coverage: 98.5%)                         Total pre-settlement cost                    of monitoring costs and incentives, as well as costs associat-
             Tiering: Only high credit quality           All agents – tiered CCP                  1
                                                                                                      ed with margin tailoring, which is beyond the scope of this
             agents are direct members of the            All agents – tiered ring                 1
             CCP/ring                                    High credit quality – tiered CCP      1.11   analysis. Nevertheless, the indicative results presented here
                                                         High credit quality – tiered ring      1.1
                                                                                                      may constitute a useful starting point for any future analysis
                                                         Low credit quality – tiered CCP     0.94
                                                         Low credit quality – tiered ring    0.94     of this question.

                                                         All agents – tiered CCP               3.5    We define γ as the cost per member that agents incur if mar-
                                                         All agents – tiered ring              5.9    gin requirements are tailored to individual members’ default
                                                         High credit quality – tiered CCP      3.9
                                                         High credit quality – tiered ring     4.9
                                                                                                      probabilities. γ can be interpreted as comprising the costs of
                                                         Low credit quality – tiered CCP       0.6    intensive monitoring of agents plus the cost of installing and
                                                         Low credit quality – tiered ring       2.1
                                                                                                      operating the technology required to apply margin on a tai-
             Figure 4 – Tiered membership/single margin rate: ratio of replacement cost losses,       lored basis by participant, rather than by contract. We assume
             total costs and concentration under alternative clearing arrangements                    that, under a tiered arrangement, it is costless to set an objec-

                                                                                                      21 This is the most diversified tiering arrangement possible. In practice, tiering is like-
124 – The                 journal of financial transformation                                            ly to be more concentrated, with some first-tier members acting for several sec-
                                                                                                         ond-tier members, and other first-tier members only clearing on their own behalf.
Comparing the pre-settlement risk implications of alternative clearing

tively determined access criterion to exclude low credit quali-                       Conclusion
ty agents. Furthermore, consistent with our earlier analysis of                       In this paper, we quantify the benefits of moving from bilat-
bilateral relationships, we assume that direct members can                            eral to multilateral clearing arrangements and show how
monitor indirect members costlessly. Under these assump-                              these depend on the number of agents involved in trading
tions we obtain the following expressions for each agent’s                            assets. We also identify a difference in the risk implications of
total expected pre-settlement costs, where TCFull denotes the                         multilateral ringing and CCP arrangements due to the greater
total pre-settlement cost, excluding monitoring/tailoring                             concentration of losses in the ringing case. We show that
costs, where clearing takes place through a CCP with fully tai-                       margin-pooling benefits exist where multiple assets are
lored margin. The results show that in all cases agents will be                       cleared through the same clearing arrangement, with these
indifferent between CCP and ringing arrangements. As                                  benefits exploitable through the consolidation of CCPs. The
observed in the previous sections, the only difference between                        scale of any risk reduction available through margin pooling
these arrangements is that replacement cost losses are more                           will depend, however, on the variances and covariances of
concentrated under a ringing arrangement.                                             both price changes and trading positions in these assets, and
                                                                                      also on whether margin is set on an asset-by-asset or portfo-
For high credit quality agents, an arrangement with unre-                             lio basis. Indeed, we show that portfolio-based margining can
stricted access and a single margin rate will always be domi-                         erode the replacement cost risk-reduction benefits of margin
nated by a tiered arrangement. The relative attractiveness of                         pooling, though we note that a CCP would not typically
the tiered and fully tailored arrangements will depend on the                         extend portfolio-based margining beyond products with high
scale of monitoring/margin-tailoring costs. In this regard, if                        and stable absolute price-change correlations.
the inequality in (9) holds, a high-quality agent’s favored
arrangement will be one in which membership of the multilat-                          Throughout the paper, we highlight areas in which the pure
eral netting arrangement is restricted: γ >0.11 TCFull (9). For                       total cost-driven choices of risk-neutral agents may differ
low-quality agents, an unrestricted clearing arrangement                              from those of a risk-averse policymaker. In the context of tier-
with a single margin rate is, for all γ, the lowest cost alterna-                     ing, for example, we note that high-quality agents may have a
tive; followed by a restricted arrangement with tiering. While                        strong incentive to restrict access to a CCP or ringing
high and low-quality agents’ preferences do not fully coin-                           arrangement, while a risk-averse policymaker might wish to
cide, the non-cooperative equilibrium here will, for all γ, be                        exploit the full mutualization benefits of unrestricted CCP
the emergence of a tiered arrangement.                                                membership.

                                         Total pre-settlement costs                   • Baer, H. L., V. G. France, and J. T. Moser, 2004, “Opportunity cost and prudentiality:
                                                                                        an analysis of collateral decisions in bilateral and multilateral settings,” Research in
                                   CCP clearing                Ring clearing            Finance, 21, 201-27
                                                                                      • BIS, 1998, “OTC derivatives: settlement procedures and counterparty risk manage-
 Clearing arrangement      High credit    Low credit     High credit    Low credit
                                                                                        ment,” Bank for International Settlements
 Unrestricted/                                                                        • BIS, 2003, “A glossary of terms used in payments and settlement systems,” Bank for
 tailored margining        TCFull + γ     TCFull + γ     TCFull + γ     TCFull + γ      International Settlements
 Unrestricted/                                                                        • BIS, 2004, “Recommendations for central counterparties,” Bank for International
 single margin rate        1.58 TCFull    0.88 TCFull    1.57 TCFull    0.89 TCFull     Settlements
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 single margin rate        1.11 TCFull    0.94 TCFull    1.10 TCFull    0.94 TCFull     derivatives,” Bank for International Settlements
                                                                                      • Counterparty Risk Management Policy Group II, 2005, “Towards greater financial
                                                                                        stability: a private sector perspective,”
 Figure 5 – Comparison of total pre-settlement costs for agent i under alternative
                                                                                      • Devriese, J., and J. Mitchell, 2005, “Liquidity risk in securities settlement,” National
 clearing arrangements, assuming a cost to performing tailored margining
                                                                                        Bank of Belgium Working Paper no. 72

            Comparing the pre-settlement risk implications of alternative clearing

            • Elsinger, H., A. Lehar, and M. Summer, 2006, ‘Using market information for banking
              system risk assessment,” International Journal of Central Banking, 2:1, 137-65
            • Geithner, T. F., 2004, “Challenges facing the global payments system,” remarks
              made at the SIBOS 2004 Atlanta conference
            • Hills, B., D. Rule, S. Parkinson, and C. Young, 1999, “Central counterparty clearing
              houses and financial stability,” Bank of England Financial Stability Review, 6, 122-34
            • Koeppl, T., and C. Monnet, 2005, “Central counterparties,” Queen’s University
              Ontario, mimeo
            • Kroszner, R. S., 1999, “Can the financial markets privately regulate risk?: The devel-
              opment of derivatives clearinghouses and recent over-the-counter innovations,”
              Journal of Money, Credit and Banking, 31, 596-618
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              and the risk of contagion,” Bank of England Working Paper no. 230

126 – The                   journal of financial transformation

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