IMF Economic Review (2012) 60, 193–222. doi:10.1057/imfer.2012.8

Clearing, Counterparty Risk, and Aggregate Risk

* Bruno Biais holds a Ph.D. from HEC and is Professor at the Toulouse School of Economics (FBF IDEI Chair on Investment Banking and Financial Markets & CNRS). Florian Heider is a Senior Economist in the Financial Research Division at the European Central Bank. Marie Hoerova is an Economist in the Financial Research Division of the European Central Bank. The authors thank Pierre-Olivier Gourinchas (editor), Ayhan Kose (co-editor), Stijn Claessens (guest editor), Ana Fostel (IMF ARC discussant), Iman van Lelyveld (DNB discussant), Christophe Perignon, and two anonymous referees for helpful comments on earlier drafts. This paper was prepared for the Twelfth Jacques Polak Annual Research Conference on “Monetary and Macroprudential Policies” held 10–11 November 2011, in Washington, DC. Many thanks for insightful comments to participants at the IMF Twelfth Jacques Polak Annual Research Conference, the Fifth Financial Risk International Forum in Paris, the Financial Infrastructures Conference (Tilburg University / Dutch National Bank), and the European Central Bank. The views expressed do not necessarily reflect those of the European Central Bank or the Eurosystem. Biais gratefully acknowledges the support of the European Research Council, Grant 295484, Trading and Post-trading.

Abstract

The paper studies the optimal design of clearing systems. The paper analyzes how counterparty risk should be allocated, whether traders should be fully insured against that risk, and how moral hazard affects the optimal allocation of risk. The main advantage of centralized clearing, as opposed to no or decentralized clearing, is the mutualization of risk. While mutualization fully insures idiosyncratic risk, it cannot provide insurance against aggregate risk. When the latter is significant, it is efficient that protection buyers exert effort to find robust counterparties, whose low default risk makes it possible for the clearing system to withstand aggregate shocks. When this effort is unobservable, incentive compatibility requires that protection buyers retain some exposure to counterparty risk even with centralized clearing.

JEL Classifications:

G22; G28; D82

Counterparty risk is the risk to each party of a contract that his or her counterparty will not live up to its contractual obligations. As vividly illustrated by the failure of Lehman Brothers and the near failures of AIG and Bear Stearns, counterparty risk is a real issue for investors. These episodes underscore that institutions should monitor the risk of their counterparties and strive to contract with creditworthy ones.

Clearing entities, and in particular Centralized Clearing Platforms (hereafter CCPs), can offer insurance against counterparty risk. The clearing entity interposes between the two parties. If one of them is unable to meet its obligations to the other, the clearing entity makes the payment on behalf of the defaulting party. Would the use of CCPs make markets safer? In September 2009, the G20 leaders, followed by the Dodd-Frank Wall Street Reform & Consumer Protection Act, and then the European Commission, answered yes. They proposed that all standardized OTC derivatives contracts be centrally cleared. 1

Was this the right move? More generally, how, and to what extent, can clearing improve the allocation of risk, and how should it be designed? Should it be decentralized or centralized? Should it provide full insurance against counterparty default? Is it likely to decrease or increase risk exposures? Is clearing enough to cope with counterparty risk, or should it be complemented by other risk-mitigation tools? We take an optimal contracting approach to analyze these issues and offer policy implications.

We consider a simple model in which a continuum of risk-averse agents who hold risky assets (protection buyers) faces a continuum of risk-neutral limited-liability agents (protection sellers). For example, protection buyers can be financial institutions holding a portfolio of loans and seeking insurance against the default of these loans. For simplicity we assume that the asset held by each protection buyer can take on only two values, high and low, with equal probability. The protection sellers offer to insure the protection buyers against the risk of a low value of this asset. 2 The problem is that protection sellers themselves may default. This creates counterparty risk for protection buyers and reduces the extent to which they can hedge their own risk. At some cost, protection buyers can exert effort to search for good counterparties with low default risk (“due diligence”). When deciding whether to do so, protection buyers trade off the benefits of better insurance (granted by good counterparties) and the cost of effort. If protection buyers are sufficiently risk-averse, or the search cost is low enough, then it is optimal to exert effort to find a creditworthy counterparty.

Even when they exert effort, protection buyers remain exposed to some counterparty risk since the default probability of the protection seller is always strictly positive. In this context, how can a clearing entity offer insurance against counterparty risk and improve welfare? To clarify the economic drivers underlying this issue, we distinguish three cases. First, the risk exposures of the protection buyers are independent, and their search effort is observable and contractible (no moral hazard). Second, the risk exposure of the protection buyers has an aggregate component, but there is no moral hazard. Third, the risk exposure has an aggregate component and there is moral hazard. The optimal design as well as the usefulness of clearing arrangements vary across these three cases.

Consider the first case (no aggregate risk, no moral hazard). With decentralized clearing, there are clearing agents interposing between each pair of protection buyer and protection seller. For a fee, these clearing agents can insure protection buyers against the default of their counterparty. A clearing agent chooses a portfolio of liquid, low-return assets (cash) and illiquid, high-return assets. To be able to pay protection buyers, clearing agents must set aside liquid assets. This has an opportunity cost since the return on liquid assets is lower than on illiquid ones. Because of this cost, it is optimal to insure only partially against counterparty risk. Since they are not fully insured against counterparty risk, it is optimal for sufficiently risk-averse protection buyers to exert effort and search for creditworthy protection sellers.

With centralized clearing, the CCP interposes between all protection buyers and all protection sellers. Hence, the total insurance payment by the CCP is the sum of all the individual payments to protection buyers. Since the individual risks are independent, the law of large numbers applies and the sum of all payments is deterministic. Correspondingly, the fees levied by the CCP are exactly equal to the amount of insurance needed and it is no longer necessary to set aside liquid assets. Thus, the first benefit of mutualization via a CCP is that it avoids the opportunity cost of holding liquid assets. Since this cost is not incurred, full insurance against counterparty risk is optimal. This is the second benefit of mutualization. Also, with mutualization, the protection buyers effectively insure each other. Hence, they are not affected by the default of protection sellers. Consequently there is no need to search for good counterparties. Avoiding the search cost is the third benefit of mutualization.

Consider now the second case (aggregate risk, no moral hazard). 3 To model aggregate risk, we assume there are two equiprobable macrostates, referred to as good and bad. In the good state, the probability that each individual protection buyer’s asset value is high is greater than one half. In the bad state, it is lower than one half. 4 Conditional on the realization of the macrostate, the values of the protection buyers’ assets are i.i.d. Hence, the aggregate value of the protection buyers’ assets is larger in the good state than in the bad state. While mutualization among protection buyers continues to be useful, it cannot provide insurance against the aggregate risk. The protection sellers become valuable again, even with centralized clearing, because the resources they bring to the table are useful to insure protection buyers against aggregate risk. Correspondingly, the effort to search for good counterparties is also valuable. If protection buyers are sufficiently risk-averse, the optimal contract involves (i) effort to locate good counterparties, and (ii) full insurance thanks to the mutualization of idiosyncratic risk and transfers from protection sellers in the bad macrostate.

Finally, consider the third and most intricate case (aggregate risk and moral hazard). In this case, the CCP cannot observe whether protection buyers exert search effort to find creditworthy protection sellers or not. Should the CCP continue to promise full insurance against counterparty risk as in the second case above? If it does, then protection buyers have no incentive to incur the cost associated with the search for creditworthy counterparties. Consequently, the average amount of resources brought to the table by protection sellers would be small. Their default rate would be high in the bad macrostate and the CCP would have to pay a lot of insurance. This liability could exceed the resources of the CCP, and push it into bankruptcy. To avoid this, the CCP should not offer full insurance against counterparty risk when there is moral hazard. This risk exposure, while suboptimal in the first-best, is needed in the second-best to maintain the incentives of protection buyers to exert search effort.

In sum, our analysis yields the following implications. Centralized clearing is superior to decentralized clearing, since it enables the mutualization of risk. Policymakers are therefore right to promote centralized clearing. They should, however, keep in mind the limitations of centralized clearing and endeavor to mitigate their adverse consquences. In particular, while the mutualization delivered by centralized clearing reduces the exposure to idiosyncratic risk, it does not reduce the exposure to aggregate risk. Minimizing that exposure requires exerting effort to find creditworthy counterparties, robust to macroshocks, and also attracting diverse counterparties, whose default risks are not too correlated. Our analysis also underscores that centralizing clearing can reduce both the social value and the private incentives to exert the search effort. While improving the allocation of counterparty risk, the centralization of clearing might therefore increase the aggregate counterparty default rate. Finally, under the plausible assumption that the effort to find creditworthy counterparties is unobservable, there is a moral hazard problem and the CCP must be designed to maintain the incentives of protection buyers. This precludes full insurance against counterparty default. The incentive constraint is especially important when aggregate risk is significant. In particular, when aggregate risk is large, incentive compatibility requires that protection buyers retain some exposure to the idiosyncratic component of risk.

Our analysis contributes to the microprudential and the macroprudential study of clearing mechanisms. Microprudential analyses focus on one financial institution, studying its regulation, for example, to avoid excessive risk taking. Macroprudential analyses consider a population of financial institutions and focus on the equilibrium interactions between these institutions, as well as on aggregate outcomes generated by these interactions. All of these features are present in our analysis. This is because, by construction, CCPs raise macroprudential issues since they clear the trades of a population of financial institutions. Furthermore, our analysis emphasizes the interaction between the design of CCPs and the presence of aggregate risk. It underscores that when aggregate risk is significant, CCPs are useful but should not provide full insurance against counterparty risk, lest this would jeopardize the incentives of market participants to search for creditworthy counterparties.

The next section presents the institutional background. Section II reviews the literature. Section III presents the model. Section IV analyzes the case with no aggregate risk and no moral hazard. Section V turns to the case with aggregate risk and no moral hazard. Section VI examines the situation in which there is both aggregate risk and moral hazard. Section VII offers a discussion. Section VIII concludes. Proofs not given in the text are in the online appendix.

I. Institutional Background

Definition of clearing. After a transaction is agreed upon, it needs to be implemented. This typically involves the following actions:

• Determining the positions of the different counterparties (how many securities or contracts have been bought and sold and by whom, how much money should they receive or pay). This is the narrow sense of the word “clearing.”
• Transferring securities or assets (to custodians, which are financial warehouses) and settling payments. This activity is referred to as “settlement.”
• Reporting to regulators, calling margins and deposits, netting.
• Handling counterparty failures.

Understood in a broad sense, clearing refers to this whole process. The market-wide system used for clearing operations is often referred to as the “market infrastructure.”

The basic mechanism of clearing and counterparty risk. Clearing in spot markets differs somewhat from its counterpart in derivative markets. First consider the case in which A and B agree on a spot trade: B buys an asset (stock, bond, commodity) from A. against the payment of price P. The clearing entity receives the asset from A and transfers it to B (or his custodian or storage facility). The clearing entity also receives the payment of P dollars from B and transfers it to the account of A. 5

Derivative markets are more complicated because contracts are typically written over a longer maturity and are often contingent on certain events. Consider for example the case of a CDS. A sells protection to B against the default of a given bond. Before the maturity of the contract, as long as the underlying bond does not default, B must pay an insurance premium to A. Just like the payment of the price for the purchase of an asset, this payment can take place via the clearing agent. If the underlying bond defaults before the maturity of the contract, A must pay the face value of the bond to B. while B must transfer the bond to A. Thus, the clearing entity receives the bond from B and transfers it to A. and receives the cash payment of the face value from A and transfers this to the account of B .

Clearing entities also typically provide insurance against the default of trading counterparties. For example, in the CDS trade described above, if the underlying bond defaults and A is bankrupt, then the clearing entity can provide the insurance instead of A. In this case, it is the clearing entity that receives the bond and pays cash to B. Such insurance is more significant in derivative markets than in spot markets: other things equal, the risk of default of one of the counterparties is greater over the long maturity of derivative contracts than during the few days or hours it takes to clear and settle a spot trade. To meet the default costs, the clearing entity must have capital and reserves.

Bilateral vs. centralized clearing. The clearing process can be bilateral and operated in a decentralized manner. In this case the trade between A and B is cleared by a “clearing broker” or “prime broker.” If on the same day there is a trade between two other institutions, C & D. it can be cleared by a different broker. In contrast, with Central Counterparty Clearing (hereafter CCC) the clearing process for several trades (between A & B as well as between C & D ) is realized within a single entity, referred to as the Central Clearing Platform (hereafter CCP). In this centralized clearing system, the CCP takes on the counterparty risk of all the trades. This implies that the CCP can be exposed to a large amount of counterparty default risk. To cope with such risk, the CCP needs relatively large capital and reserves. Such reserves can be built up by levying a fee on the brokers using its services (possibly contingent on activity levels). The CCP can also issue equity capital subscribed to by the brokers and financial institutions using its services. To the extent that the counterparty loss on a given trade is paid for by the capital and reserves of the CCP provided by all the members of the CCP, centralizing clearing leads to the mutualization of counterparty default risk.

CCC has been the prevailing model for futures and stock exchanges. A polar case is the Deutsche Börse, where the trading platform and the clearing platform are vertically integrated. In contrast, decentralized clearing is most frequent when trades are conducted in OTC markets. 6 Up to now, a large fraction of the Credit Default Swaps market has been OTC and cleared in a decentralized way. Note, however, that trading mechanisms and clearing mechanisms are distinct. Thus, it is possible to have OTC trading and CCC. In that case, the search for counterparties and the determination of the terms of trade is decentralized, while the two parties who struck a deal clear the trade in a CCP. 7

II. Literature

Similarly to the present paper, Stephens and Thompson (2011) study the case in which protection sellers can default. 8 They assume protection sellers are privately informed about their type. 9 They analyze the risk of contracting with a bad protection seller. When they extend their analysis to centralized clearing, they show that it can lead to an inefficient increase in that risk. Pirrong (2011) also warns that centralized clearing could lead to an increase in counterparty default and notes that “with asymmetric information, it is not necessarily the case that the formation of a CCP is efficient.” Similarly, Koeppl (2012). who, like us, emphasizes the mutualization benefits of CCPs, shows that they can “upset market discipline.”

While we also find that centralized clearing can increase counterparty default, we show, in contrast to Stephens and Thompson (2011). Pirrong (2011). and Koeppl (2012). that the optimal CCP is welfare improving relative to bilateral clearing. 10 This difference in conclusions stems from a difference in approaches. Instead of considering features of the CCP that are exogenously given, we take an optimal contracting approach to study the design of the optimal clearing mechanism. By construction the resulting CCP is Pareto optimal (subject to information, resource, and technology constraints). From a normative viewpoint, our contribution is thus to identify the conditions and the design under which centralized clearing brings about efficiency gains.

Acharya and Bisin (2010) and Leitner (2012) also offer insights into the optimal design of centralized clearing. As noted by Acharya and Bisin (2010). no protection buyer can control the trades of his counterparty with other investors in OTC markets. So when a protection seller contracts with an additional protection buyer, this exerts a negative externality on other protection buyers. It increases counterparty risk and generates inefficiencies in equilibrium (similar to the inefficiencies arising in the nonexclusive contracting model of Parlour and Rajan, 2001 ). Acharya and Bisin (2010) show how centralized clearing can eliminate such inefficiencies by implementing price schedules that penalize the creation of counterparty risk. Furthermore, Leitner (2012) shows how, within a central mechanism, position limits prevent agents from entering into excessive contracts. Our focus is different. In Acharya and Bisin (2010) and Leitner (2012). the benefit of centralized clearing is that it enables to control the risk exposure of protection sellers. In our analysis, the benefit of centralized clearing is the mutualization of counterparty default risk. Also, while centralized clearing makes excessive risk positions observable in Acharya and Bisin (2010) or elicitable in Leitner (2012). the benefit of centralized clearing in our analysis applies even when the effort to search for creditworthy counterparties is observable.

Our analysis is related to Koeppl and Monnet (2010). who also consider the mutualization benefit of CCPs. But the market frictions they analyze differ from ours. They consider a bargaining process that gives rise to inefficiencies and a setting where institutions privately conduct trades, which they must be incentivized to reveal. Our focus is on optimal contracts, attaining information constrained Pareto optimality, and on trades that are observable and contractible. Unlike Koeppl and Monnet (2010). we assume that protection buyers must exert effort to screen and monitor counterparties (and we also consider the case in which this effort is unobservable). Our conclusion that, to preserve incentives, protection buyers should not be fully insured against counterparty risk is the opposite of what Koeppl and Monnet (2010) conclude. Another related paper is Carapella and Mills (2012). Focusing on information acquisition incentives, they show that by providing counterparty risk insurance (and multilateral netting), CCPs reduce counterparties’ incentives to acquire information about centrally cleared securities, making such securities less information sensitive and more liquid. They consider asymmetric information about the value of the underlying asset, while we study asymmetric information about the effort of the protection buyer to find creditworthy counterparties.

Our analysis of the mutualization benefits of CCPs also echoes the analysis of the netting benefits of CCPs by Duffie and Zhu (2011). Taking deposit constraints in different systems as given, they study which system is more economical in terms of collateral requirements. This is motivated by their observation that collateral deposits are costly. The objective of their analysis is the netting efficiency of the system. In contrast, while we also take into account the cost of deposits, we endogenize the deposits requested, and the objective in our analysis is the risk -sharing efficiency of the system. While the risk aversion of the agents and their incentive compatibility constraints play an important role in our analysis, they are absent from Duffie and Zhu (2011). 11

Finally, our analysis is also related to Diamond and Dybvig (1983) and Hellwig (1994). In Diamond and Dybvig (1983). a continuum of households can experience early or late consumption needs. Because consumption needs are i.i.d. across households, uncertainty about these idiosyncratic shocks washes out in the aggregate by the law of large numbers. Competitive banks implement the Pareto-optimal mechanism when consumption needs are observable, as they can fully mutualize the idiosyncratic liquidity risk of households. Hellwig (1994) studies aggregate interest rate risk in a Diamond and Dybvig-like setup. Efficient risk-sharing requires that households bear some of this aggregate risk, even when consumption needs are publicly observable. When such needs are privately observed, incentive compatibility constraints give an additional reason for households to be exposed to aggregate risk. Our analysis also considers risk-sharing in an environment with both idiosyncratic and aggregate shocks, and under incentive compatibility constraints, but there are substantial differences in the objects of analysis in Hellwig (1994) and in our paper: banks vs. CCP, value of assets vs. consumption needs, liquidity risk vs. counterparty risk, adverse selection vs. moral hazard.

III. The Model

There are five dates, t = 0, 1 / 4, 1 / 2, 3 / 4 and 1. A unit mass continuum of risk-averse protection buyers faces a large population of risk-neutral protection sellers. 12 The discount rate of all market participants is normalized to one and the risk-free rate to 0.

At time t = 0, each protection seller i is endowed with one unit of assets-in-place, which returns _i at t = 1. The protection sellers are heterogeneous. Some of them are solid, creditworthy institutions, which we hereafter refer to as “good.” They generate _i = R >1 with probability p and 0 otherwise. Others are more fragile, less creditworthy institutions, hereafter referred to as “bad”. They generate _i = R with probability p −δ only. 13 When protection seller i is good (resp. bad), we denote this by ξ _i = 1 (resp. ξ _i = 0), and correspondingly the probability of default of protection seller i is denoted by 1−p ( ξ _i ). The protection sellers’ positions are completely illiquid, that is, their liquidation value before time 1 is zero. All protection sellers are risk-neutral, have no initial endowment apart from the illiquid asset generating R or 0, and have limited liability.

At time t = 0, each protection buyer j is endowed with an asset whose random final value _j realizes at time t = 1. We assume that _j can take on two values: with probability 1 / 2 and θ otherwise. The asset owned by the protection buyer can be thought of as a loan portfolio, and θ can be interpreted as occurring when the loans are only partially repaid. We assume that R − θ = Δ θ. which implies that when protection sellers do not default, they can fully insure protection buyers against their risk . We also assume that all exogenous random variables are independent.

Because the protection buyers are risk-averse while the protection sellers are risk-neutral, there are potential gains from trade. But to reap these gains from trade, protection buyers must contact protection sellers. At time t = 1 / 4, protection buyer j can choose to exert effort (e _j = 1) and devote resources to finding a good counterparty. This involves searching for counterparties, screening them, and checking their risk exposure and financial solidity. 14 Denote the corresponding cost by B. Matches occur at time t = 1 / 2. When exerting effort, a protection buyer finds a good protection seller with probability one. Alternatively, protection buyer j may choose not to exert costly effort (e _j = 0). In this case, he finds a bad protection seller with probability one. 15 The preferences of the protection buyers are quasi-linear, that is, there exists a concave utility function u such that the utility of protection buyer j with consumption x is u (x )−e _j B .

Ex ante, the types of protection sellers are unobservable. At time t = 1 / 2, however, protection buyer j observes the type of protection seller i with whom he is matched.

At time 3 / 4, aggregate macroeconomic uncertainty is resolved. But for simplicity and clarity, we assume until Section V that there is no aggregate risk and hence we postpone the exposition of how we model this risk until then. We relax this assumption in Section V and study how the introduction of aggregate risk alters the economics of clearing and risk-sharing in our framework.

Our model starts at time t = 0, when a market infrastructure is put in place. We consider three possibilities: bilateral trade between a protection buyer and a protection seller (no clearing), trilateral trade with a clearing agent (decentralized clearing), or multilateral contracting with a CCP (centralized clearing). Figure 1 summarizes the sequence of event V_S .

Sequence of Events

Full figure and legend (33K )

For simplicity, but without affecting the results qualitatively, we assume that the protection buyer has all the bargaining power. Thus, contracts are designed to maximize the protection buyers’ expected utility, subject to the participation, feasibility and incentive constraints spelled out below.

At time 1, the realizations of _i . _j and are observable and contractible. Until Section VI, we assume for simplicity and clarity that the effort e _j of protection buyers is observable and contractible. Thus, the optimal clearing arrangement we characterize until Section VI implements the first-best, subject to the limited liability and search constraints. In Section VI, we introduce moral hazard and analyze the information-constrained optimal clearing arrangement that implements the second-best.

IV. Idiosyncratic Risk and Observable Effort

In this section, we study optimal risk-sharing contracts when protection buyers’ efforts are observable and they are only exposed to idiosyncratic risk. We first characterize the optimal bilateral contract between a protection buyer and a protection seller without a clearing agent. We then consider trilateral contracting between the two parties and a single clearing agent. We conclude the section with the analysis of the optimal multilateral contract with a CCP.

Bilateral Contracting Without Clearing Agent

The contract, offered at time t = 1 / 2 once a match has been made, spells out the transfer τ from the protection seller to the protection buyer. 16 When τ is positive, the protection seller pays the protection buyer. When τ is negative, the protection buyer pays the protection seller. The transfer τ is contingent on the value of the assets of the protection buyer (_j ) and the protection seller ( _i ). Figure 2 depicts the bilateral relations, and transfers τ, in the market without clearing. Only two (representative) pairs of protection buyers and protection sellers are depicted, but the same structure applies to all matches. The protection seller has limited liability, hence τ is such that