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Central Counterparty Default Waterfalls and
Systemic Loss
Mark Paddrik
Office of Financial Research
mark.paddrik@ofr.treasury.gov
Simpson Zhang
Office of the Comptroller of the Currency
simpson.zhang@occ.treas.gov
20-04 | June 18, 2020
Central Counterparty Default
Waterfalls and Systemic Loss ∗
Mark Paddrik†
Simpson Zhang‡
June 2020
Abstract
Central counterparty default waterfalls act as last lines of defense in over-the-counter markets
by managing and allocating resources to cover defaults of clearing members and clients. However,
central counterparties face competing objectives in setting up their default waterfalls. In this
paper we evaluate the trade-offs between default waterfall resiliency and central clearing, using
a unique and comprehensive dataset containing all U.S. cleared and bilateral credit default swap
positions. We evaluate the resiliency of different default waterfall designs, accounting for the
interconnectedness of payments in the system, the presence of client clearing obligations for
members, and the distribution of losses among market participants.
Keywords: central counterparty, systemic risk, default waterfall, financial networks, credit
default swaps
JEL Classification Numbers: G10, G23, G28, L14
∗We thank Celso Brunetti, Roy Cheruvelil, Ben Craig, St´ephane Cr´epey, Peter Curley, Selman Erol, Katherine Gleason, Stephen Kane, David Li, Sriram Rajan, Stacey Schreft, Stathis Tompaidis, Robert Wasserman, Jessie
Jiaxu Wang, H. Peyton Young, John Zitko and participants of the Fifth Network Science and Economics Conference, Canadian Economic Association Annual Meeting, SIAM Conference on Financial Mathematics & Engineering:
CCP Symposium, Western Finance Association Conference, Society for Economic Dynamics Meeting, 19th Annual
FDIC/JFSR Bank Research Conference, and 2019 OFR/FRBC Financial Stability Conference for their valuable comments. We would like to thank Elizabeth McKee for her excellent Helpance in aggregating CCP filings and analyzing
CCP manuals. Additionally, we would like to thank OFR’s High Performance Computing, Data, and Legal teams
for collecting and organizing the data necessary to make this project possible. The views expressed in this paper do
not necessarily reflect the views of the Office of the Comptroller of the Currency, the Office of Financial Research,
the U.S. Department of the Treasury, or any federal agency and do not establish supervisory policy, requirements, or
expectations.
†Office of Financial Research, U.S. Department of the Treasury, 714 14th St NW, Washington, DC 20220; phone:
202-927-8511; email: Mark.Paddrik@ofr.treasury.gov.
‡Office of the Comptroller of the Currency, 400 7th St SW, Washington, DC 20219; phone: 202-649-6288; email:
Simpson.Zhang@occ.treas.gov.
1
Central counterparty (CCP) clearing in over-the-counter (OTC) financial markets has grown
substantially since the 2007-09 financial crisis, from nearly nonexistent in 2007 to more than 70
percent of new interest rate derivatives and index credit default swaps volume in the United States
in 2019 (Financial Stability Oversight Council (2019)). Financial regulators have encouraged this
growth in cleared products as a way to reduce the financial stability risks posed by large counterparty failures. CCPs help to ensure the continuity of payments within these markets and reduce the
potential losses that taxpayers suffer (Financial Stability Board (2017)). They do so by performing
risk management and maintaining default waterfalls, financial resources that cover losses generated
by counterparty default.
Although default waterfalls are critical to a CCP’s risk management, there is little consensus
on the optimal structure of default waterfalls globally. After the introduction of central clearing to
numerous previously non-cleared markets, many new CCPs were created with a tremendous degree
of variation in how they source default waterfall resources. Such variations reflect the conflicting
objectives that the default waterfall must serve. As a CCP’s default waterfall is its last line of
defense in times of stress, it is important that the waterfall be resilient against market shocks.
But it is also necessary for the waterfall to account for the incentives of participants, as requiring
large contributions can be costly for clearing members and discourages clearing through the CCP
(Ghamami and Glasserman (2017)). Lower rates of central clearing could in turn decrease financial
system resilience.
Assessing the systemic risk implications of CCP default waterfall designs is difficult for financial
regulators, CCPs, and market participants alike due to the historical rarity of CCP member defaults
and the complex interrelationship of payments within both cleared and non-cleared portions of
derivatives markets (Duffie (2015); Cont (2015)).1 Spillover effects can arise through both the
cleared and non-cleared network of exposures and from fire sales of illiquid collateral, causing
greater losses in a crisis. As firms see a limited view of the overall market, they face difficulties
in accurately evaluating the extent of these spillover effects and determining the cost-benefit of
a particular default waterfall structure (Cox and Steigerwald (2017)). Although groups such as
the International Swaps and Derivatives Association (ISDA) and standard-setting bodies such as
1Kroszner (1999), Cox (2015), and Bignon and Vuillemey (2020) examine in depth a few historical examples of
large clearing member default at derivatives CCPs.
2
the Committee on Payments and Market Infrastructures (CPMI) and International Organization
of Securities Commissions (IOSCO) have written reports that qualitatively discuss the merits of
different default waterfall designs (Elliott et al. (2014); ISDA (2013); CPMI-IOSCO (2014)), there
has been limited theoretical modeling of these mechanisms or empirical testing using market data.
In this paper we evaluate the merits of existing CCP default waterfall designs through a structural modelling approach that can account for these complexities. Unlike the theoretical works
of Biais et al. (2012), Amini et al. (2015) and Wang et al. (2020) that have investigated optimal
counterparty risk exposures through trade-offs in CCP risk-sharing, we take the network of exposures as given and focus on how the CCP’s default waterfall influences financial system loss. We
calibrate this model using a unique and comprehensive dataset on U.S. credit default swap (CDS)
CCP transactions to assess the resilience of the system against large market shocks. We also assess counterfactual default waterfall structures and determine their impacts on CCP stability and
overall financial system resilience.
We examine the impact of the CCP’s default waterfall and recovery mechanisms on both total
and individual losses suffered from variation margin owed by (and to) the CCP members of a major
CDS central counterparty. We also incorporate the hundreds of clients that clear through CCP
members, which the members are responsible for in the event of their default, and examine the
impact of client defaults on systemic resiliency. client clearing losses have been highly significant
historically. For instance, clients were heavily responsible for the default of the CCP Caisse de
Liquidation des Affaires en Marchandise in 1974 (Bignon and Vuillemey (2020)). As recently as
March 2020, a large client of the CME clearing member ABN Amro defaulted and caused the
member an estimated $200 million in losses (Mourselas and Smith (2020)).
This work makes several contributions to the literature on central clearing and risk sharing.
First, we quantify how losses are allocated across a financial payment system. We do so by providing
a comprehensive measure of systemic loss and examining how losses are influenced by the scale of
market shocks and the liquidity of collateral. We find substantive spillover effects due to network
contagion that dramatically elevate losses from large shocks. Though asset fire sales can also
intensify the level of systemic losses, in line with Duarte and Eisenbach (2018), we find that current
collateral standards are high enough to prevent major liquidation losses.
Second, we analyze how different waterfall structures that vary in the proportion of losses
3
allocated to individual CCP members vs. the shared collective of all CCP members affect the
quantity of capital needed to sustain the CCP against market shocks. We compare our results with
a unique data collection on the default waterfall designs of more than 60 global derivatives CCPs.
This allows us to analyze how global variations in funded resources, including initial margins,
CCP capital, and guarantee funds, influence expected losses for market participants and the CCP’s
resilience under stress. These data provide us with a measure of the preferences of CCPs and
clearing members in selecting a default waterfall’s resource allocation.
Finally, we consider the CCP members’ responses to changes in waterfall structure. As more
default waterfall resources are required, clearing members may become more hesitant to participate
in central clearing due to the heightened costs. We estimate the resilience of the default waterfall if
participation in central clearing is also reduced. We find that the changes in central clearing participation can have a large impact on the resilience provided by requiring more waterfall resources. In
the case of more minor market shocks, requiring more waterfall resources will not counterbalance
the consequences of decreased central clearing participation. This result highlights the downward
pressure on waterfall resources that a CCP faces in periods of market calm, which is in line with
the downward trends in CCP waterfall resources in the decade following the 2008 financial crisis.
Previous papers that examined CCP default waterfall designs include Capponi et al. (2017),
which examines the CCP’s role in attracting less risky membership and the consequences for risk
sharing from allocating risk to themselves in the default waterfall. In contrast, we consider the aggregate loss to firms and counterparty externalities, similar to Acharya and Bisin (2014), Ghamami
(2015) and Ghamami and Glasserman (2017), by incorporating the impacts of several layers of
the waterfall on client clearing and non-cleared positions into our analysis. Importantly, previous
papers in this literature have not considered the full network implications of the CCP’s default
waterfall, nor have they had access to the detailed transaction-level market data that we use.
Other papers such as Huang (2019) have studied the conflicting objectives CCPs may have in
determining their waterfall structures. As commercial enterprises with profit-making incentives,
CCPs compete for the clearing business of members and their client positions (Glasserman et al.
(2016)). This is likely to drive how much and where waterfall resources are allocated, as collecting
collateral has direct short-term costs for participants and could disincentivize participation in central clearing. Our paper is complementary to these other works and helps determine the magnitude
4
of the stability benefits provided by default waterfall resources, which must be balanced against
the costs imposed on CCP members.
The rest of this paper is divided into the following sections. Section 1 provides a background
on CCP default waterfalls and how they have been implemented. Section 2 describes our CCP
payments model and how the waterfall is incorporated into it. Section 3 describes how to compute
systemic losses and individual firm losses using the model. Sections 4 presents an empirical test of
CCP waterfall resiliency using U.S. CDS market data. Section 5 presents counterfactual analysis
that considers the impact of various segments of the default waterfall. Section 6 concludes.
1 CCP Default Waterfall Structure
A CCP’s recovery plan to deal with clearing member or client defaults is known as its default
waterfall. The default waterfall provides a detailed list of resources that the CCP will use in attempting to recoup losses from clearing member defaults. While the exact rules of default waterfalls
vary across CCPs, their overall structures are similar and follow from standard industry guidelines
(ISDA (2013), ISDA (2015)). The stages of a typical default waterfall are depicted in Figure 1.
1.1 Default Waterfall Resources and Mechanisms
The first several stages of the default waterfall are present in nearly all CCPs, and they involve
widely used mechanisms. These stages are known as the funded waterfall stages because their
resources are contributed before the shock occurs. Thus the amount available to use is independent
of the shock. Since these are the first stages to be used, there is more historical precedent for them
than for the final stages, and they are thus better understood and tested.
The first stage of the default waterfall is the initial margin (IM) of the defaulting clearing
member. IM is held at the CCP in case a clearing member defaults. IM can be used when the
clearing member does not fulfill its payment obligations. The IM amount is usually set at a certain
Value-at-Risk (VaR) level, such as 99 percent, but may also have additional components, like
concentration and liquidity (Capponi et al. (2020)). IM is also collected for non-centrally cleared
transactions. However, the margin period of risk (MPOR) used in IM calculations typically differ,
with derivative CCPs typically using a 5-day MPOR while bilateral trades typically use a 10-day
5
Figure 1. Stages of CCP Default Waterfall
CCP Capital
Guarantee Fund Contribution of Defaulting M
IM of Defaulting M IM of Defaulting Client
Member Defaults Client Defaults
Guarantee Fund Contribution of Surviving Ms
Funded Resources
Assessments
VM Gains Haircutting
End-of-Waterfall Mechanisms
Note: The chart depicts the series of resources and mechanisms in the waterfall which will be accessed if previous
ones are insufficient to cover total default losses in the event of a clearing member (M) or client default. The solid
arrows depict the most common set of waterfall resource contingencies. A defaulting clearing member’s, or client’s,
obligation is first covered by their initial margin (IM). Positions of defaulting clients are the responsibility of the
associated clearing member, who has to cover any shortfalls in variation margin (VM) payments owed for those
positions. If the clearing member cannot fulfill this obligation, the clearing member may be put into default. If the
clearing member’s IM is insufficient to cover its obligations, the resources of the following stages will be used.
Source: Authors’ creation.
MPOR.
The second stage of the default waterfall is the guarantee fund contribution of the defaulting
clearing member. Guarantee fund contributions are collected from all clearing members and held
at the CCP. A clearing member’s contribution is usually proportional to its VaR, and is thus also
proportional to its IM. The CCP’s total guarantee fund amount is typically sized according to the
“Cover 2” rule, which states that the guarantee fund should cover the default of the two largest
clearing members of the CCP. However, alternative risk-based rules can also be used. We will
empirically test the resilience offered by variations in the ratio of guarantee funds to IM. The
6
guarantee fund is more versatile than IM because it can be used to cover the losses of any clearing
member, but this versatility also opens up non-defaulting clearing members to losses.
The next stage is the CCP’s own capital contribution.2 This is commonly referred to as “skin in
the game” and is intended to reduce moral hazard on the part of the CCP. CCP capital contributions
are typically small relative to the total IM or the guarantee fund, and are generally one to three times
smaller in relative magnitude, as we will discuss in the following section. The final stage of funded
resources is the loss mutualization of surviving clearing members’ guarantee fund contributions.
The guarantee fund covers the defaulted payments pro rata across each of the clearing members.
In the event that the funded resources are entirely deployed, a few different end-of-waterfall
mechanisms can be implemented either to raise fresh funds, via assessments, or reduce obligations,
via variation margin gains haircutting (VMGH). Assessments allow the CCP to request additional
funds from non-defaulting clearing members, whereas VMGH allows the CCP to temporarily reduce
the VM payments on its obligations. These mechanisms have rarely been used in practice and may
have alterations made to them to further support the CCP. For the purpose of focus, we will not
analyze these mechanisms in the main body of the text, but we do discuss and analyze them in
Appendix D.3
1.2 Empirical Comparison of CCP Default Waterfall Resources
Though CCPs use the same types of default waterfall resources and mechanisms globally, the
amount of resources collected at each stage varies significantly in practice. To highlight the differences empirically, we collected a unique data sample of default waterfall resources from the
Principles for Financial Market Infrastructures (PFMI) filings of 60 global CCPs from the fourth
quarter of 2017. Our data show a large degree of heterogeneity in how resources are allocated
along the waterfall. Particularly, there are major differences in the amount of resources CCPs have
available through their IM, guarantee funds, and CCP capital contributions.
Such differences are significant because the relative levels of IM and guarantee fund can have a
2This stage may come in one or two parts depending on the CCP. Some CCPs allow for a second part that comes
after the guarantee fund stage. We use one part in our analysis for simplicity, but having a second part would not
materially change our model.
3We compare their assessment rules, specifically the cap on assessments as a function of the guarantee fund
contribution sizes, and whether their rules permit usage of variation margin gains haircuts (VMGH) and initial
margin haircuts (IMH). Each choice of rules can have a significant effect on the size of the shock the CCP can
withstand.
7
tremendous impact on the resilience of the CCP, its clearing members, and the overall market. We
empirically test the magnitude of these effects below in Section 5 using positions-level data from a
major U.S. CCP. Additionally, though for the sake of focus we do not analyze CCP end-of-waterfall
mechanisms in the main body of the text, we do discuss and empirically analyze them in Appendix
D.
The CCP data collection is summarized in the following sequence of tables. Table I shows the
average percentage of resources for different stages of the default waterfall across CCPs grouped
by asset class. Commodity CCPs make the highest percentage of capital contributions, whereas
Interest Rate CCPs make the lowest percentage. Credit CCPs have relatively high levels of IM
and guarantee funds but low levels of capital contribution relative to other CCP asset classes. This
waterfall structure shifts the losses from the CCP onto the clearing members. The table also shows
the maximum assessment limit as a percentage of total guarantee funds.4 These values are due to
caps on assessments set by each CCP as a function of guarantee fund size.
Table I. Waterfall Resources by CCP Asset Class
Interest Rate Currency Commodity Credit Equity
Number of CCPs 13 12 16 6 13
Funded Resources
Initial Margin 79.2 73.6 77.2 77.9 81.1
Guarantee Fund 19.2 21.8 13.7 20.1 13.4
CCP Capital 1.6 4.6 9.1 2.0 5.5
End-of-Waterfall Resources
Assessments 86.5 96.9 75.8 60.2 124.9
Note: The table presents the mean percentage of funded resources collected at each stage, and the maximum assessment a CCP can make on its clearing members relative to the guarantee fund size, grouped by the asset class a CCP
clears. Looking across CCP types, initial margin makes up the majority of resources collected, ranging from 70 to 81
percent, followed by the guarantee fund with 13 to 22 percent. The CCP’s contribution is minimal, ranging from 1
to 9 percent. More generally we find that no particular asset class appears to have any unique preference in assigning
resources.
Source: CCPView Clarus Financial Technology; authors’ analysis.
Table II shows a similar summary grouped by the location of the CCP. There does not seem
to be a global consensus on the optimal waterfall design for minimizing systemic risk or ensuring
incentive compatibility for CCP members. The ratios vary dramatically across regions. Asian and
European CCPs have significantly lower percentages of IM than North American CCPs. European
CCPs have larger levels of guarantee funds, while Asian CCPs have larger CCP capital. These
4Some CCPs allow for a greater assessment amount if there are multiple clearing member defaults versus a single
clearing member default.
8
differences across regions can have an important impact on the CCP’s resilience under periods of
market stress. Our empirical analysis in Section 5 shows that CCPs with higher IM relative to
guarantee funds and capital are less resilient to market shocks.
Table II. Waterfall Resources by Jurisdictional Region
Asia Europe North America Oceania South America
Number of CCPs 27 20 12 2 2
Funded Resources
Initial Margin 69.2 74.0 85.2 90.1 97.7
Guarantee Fund 18.7 25.3 13.5 2.2 2.2
CCP Capital 12.2 0.7 1.3 7.7 0.1
End-of-Waterfall Resources
Assessments 75.5 122.3 77.5 300.0 73.6
Note: The table presents the mean percentage of funded resources collected at each stage, and the maximum assessment a CCP can make on its clearing members relative the guarantee fund size, grouped by the continental
jurisdiction a CCP resides. Looking across CCP jurisdictions, we see wide variation in funded resources and assessments, suggestive of jurisdictional regulatory preferences influencing CCP’s default waterfall allocations.
Source: CCPView Clarus Financial Technology; authors’ analysis.
An additional dimension to the waterfall structure is the liquidity of the collateral resources
held by the CCP and used in the event of default. Although intra-firm payments are made in
cash, holding IM and guarantee fund collateral in cash alone creates significant costs for clearing
members. As a result, other forms of collateral that pay higher interest rates are typically held, or
the CCP may rely on credit lines in case of short-term delays in payments. Table III highlights the
percent of collateral and credit lines held by 30 CCPs as of the fourth quarter of 2017.
Table III. Funded Resource Collateral and Credit Lines
Mean Median Std Dev Min Max
Collateral
Secured Cash Deposits 44.3 47.5 35.0 – 100.0
Unsecured Cash Deposits 14.6 1.8 31.0 – 100.0
Repo Lent Cash/Securities 10.3 – 21.1 – 81.4
Government Securities 28.2 21.0 30.2 – 99.0
Other 2.6 – 13.5 – 74.2
Unsecured Credit Lines 8.1 – 23.4 – 121.8
Note: The table presents the percentage of collateral and liquidity resources held by 30 OTC derivative CCPs as
of the fourth quarter of 2017. The majority of CCP collateral holdings are in cash, repo, or government securities.
A small percentage of holdings are in other less liquid assets. Additionally some CCPs have unsecured credit lines,
which we present as a percentage of their total collateral holdings, that they may draw on in times of short-term
liquidity impairment.
Source: CCPView Clarus Financial Technology; authors’ analysis.
In the event of a default, non-cash collateral will need to be liquidated before payments can be
9
made, likely at a reduced price in times of market stress. These liquidation costs and the ability
to raise cash in a timely fashion are additional elements of risk that need to be considered. As
a result CCPs in general hold very high quality collateral, in cash or cash equivalents, as Table
III highlights, and require haircuts. Though CCPs may take wider forms of collateral if needed,
they generally encourage collateral delivered to be of high quality through applying steep haircuts
relative to the general market.
2 Model of CCP Default Waterfall
CCP stress can arise via many forms. For instance, a substantial shock such as the Comprehensive Capital Analysis and Review (CCAR) shock can lead to a situation where some firms owe
much more VM than they expect to receive. These VM obligations are supposed to be satisfied
within a very short time – typically within a few hours – and can put severe stress on the firms’
trading desks. This stress may prevent a firm from fulfilling all its obligations to its counterparties.
This, in turn, increases the stress on the firm’s downstream counterparties, amplifying the impact
of the shock through the network of CDS exposures. The model assumes that payments are all
made simultaneously as margin payments are made intra-day, though it can take several days or
weeks for some portfolio liquidations if necessary.
In the next two sections, we introduce a network model to account for this type of contagion,
and we show how to incorporate the different components of the CCP waterfall into the model.
2.1 Basic Setup and Payments
The setup is based on the framework of Glasserman and Young (2015), which in turn builds on
the model of Eisenberg and Noe (2001). There are N + 1 agents in the market, with 0 indexing the
CCP and i ∈ 1, …, N indexing the non-CCP firms. Each pair of counterparties i, j can have a set of
contracts between them, which we assume are in a single asset class, for instance CDS. Contracts
can represent both bilateral and centrally cleared transactions.
There are three types of non-CCP firms in our model: clearing members M, clients C, and
bilateral firms B. These firms differ in their use of central clearing. Clearing members may clear
through the CCP directly. Clients cannot clear through the CCP directly but must instead submit
10
Figure 2. Example Network of Cleared and Non-cleared Obligations
B1 M1
C1
CCP
M2
C2
B2
M3
C3
M4 B3
C4
B4
Note: Four firm types are depicted in the network: the CCP, clearing members (M), clients (C), and bilateral firms
(B). The links represent obligations, both direct (solid) and client clearing (dashed). These firms differ in their use
of central clearing. Clearing members may clear through the CCP directly. Clients cannot clear through the CCP
directly but must instead submit trades through a clearing member. Clearing members pass through the payments
received or owed from the client to the CCP, and clearing members must cover any shortfalls in these payments out
of their own funds.
Source: Authors’ creation.
trades through a clearing member. Clearing members pass through the payments received or owed
from the client to the CCP, and clearing members must cover any shortfalls in these payments out
of their own funds. We give the details of how this process works below. We denote Ck as the set
of client firms of a clearing member k. Also, we denote Mi as the set of clearing members of a
client firm i.
5 Finally, some non-members are purely bilateral firms that do not participate in any
centrally cleared transactions and instead engage only in bilateral transactions.
Given a market shock, we can calculate the variation margin (VM) payment obligations for
each individual contract. We then net all the VM payments owed on contracts between every pair
of counterparties. This produces a net VM payment that needs to be made between this pair. We
exclude client clearing trades in this summation, and will instead consider them separately next.
We write the net VM payment obligations as an obligation matrix P¯ = (¯pij )i,j∈N0
, where ¯pij is the
net amount of VM owed by node i to node j in the aftermath of the shock. We denote the indices
of the first row and column of this matrix as 0 to account for the CCP. Note that if ¯pij is positive
5
In the data, we do not observe the identity of the clearing member that a client uses, but we assume that the
client clears through the clearing member with which it has the most bilateral transactions.
11
then ¯pji is zero. Further, ¯pii = 0 for all i.
Given the market shock, firms may only be able to satisfy part of their payment obligations due
to shortfalls in funds. We denote the actual VM payments made between firms using the realized
payment matrix P = (pij ).
Figure 3. Example of Normal and Realized Payments
Bj Ci Mk CCP0 Ml
pij ≤ p¯ij pik ≤ p¯ik pk0 ≤ p¯k0 p0l ≤ p¯0l
q
c
ik0 ≤ q¯ik0 q
m
ik0 ≤ q¯ik0
Note: The example shows the types of obligations that could occur between four types of firms, both bilateral and
client cleared. The figure helps to illustrate the dependencies that firms can have on one another, as clearing member
k’s ability to pay CCP 0 may depend on client i’s ability to fulfill its obligations. In the figure, if the realized payments
from client i, pij , pik, qc
ik0
, qm
ik0
, are less than its obligations, clearing member k and pure bilateral firm j will suffer
direct losses. Additionally, the impact of client i’s realized payments may lead to clearing member k reducing its
payments, causing potential losses to the CCP as well.
Source: Authors’ creation.
There are also client clearing transactions in the network that induce a set of corresponding
client clearing obligations. We denote the net VM client clearing obligations with a set of two
matrices Q¯ = (¯qik0, q¯0ki)i∈C,k∈M. In this notation, ¯qik0 denotes the net amount owed by client i to
the CCP through clearing with member k, and ¯q0ki denotes the net amount owed by the CCP to
client i through clearing with member k.
6 Note again that if one of these obligations is positive
then the other is zero. Because client clearing must involve a clearing member as an intermediary,
q¯ik0 is fulfilled by having client i submit a payment to clearing member k, q
c
ik0
, and that clearing
member k then submitting a payment to the CCP, q
m
ik0
. The reverse obligation ¯q0ki is fulfilled by
the CCP submitting a payment to clearing member k, q0ki, and clearing member k submitting a
payment to client i, q
m
0ki. A clearing member must pass through any payments that it receives in
the course of client clearing, even if the clearing member is in default. Therefore q
m
ik0 ≥ q
c
ik0
and
q
m
0ki ≥ q0ki. We describe how the payment values are determined in equilibrium over the next few
sections.
2.1.a Initial Margin and Capital Buffer
In most transactions, IM will be held to help cover deficiencies in VM payments. We denote
the IM that i holds from counterparty k as zki. This IM value will always be positive unless the
6The CCP does not net the transactions of a client that clears through multiple different clearing members. The
client is in effect treated as a different entity across each clearing member with which it clears.
12
counterparty k is the CCP itself as the CCP does not post IM, z0i = 0 ∀i. If counterparty k fails
to pay VM to i in a timely manner, the position will be closed out and the IM will be applied to
the shortfall in VM payments. The value of IM held is calculated on a portfolio level using a VaR
estimate based on historical look back.7
For client clearing transactions, IM will be held by the CCP for a transaction with client i
clearing through clearing member k. We denote the value of this IM by zik0. The IM is used to
cover shortfalls in payments if the client is unable to cover its obligations. The IM is then passed
through by the clearing member to the CCP to Help with the clearing member’s passthrough
obligation if necessary. The passthrough payment of clearing member k must be weakly greater
than the amount it receives, q
m
ik0 ≥ (q
c
ik0 + zik0). The CCP does not post IM for the client clearing
obligations that it owes. For a given firm i, we denote the total amount of IM that it contributes
across bilateral and client clearing obligations as zi
.
Beyond IM, firms are assumed to hold some quantity of assets on hand, which we term as capital
buffer, bi > 0. This bi
is a function of the firm’s risk management policies, non-CDS positions, or
available cash. Firms will use their capital buffers to help meet their VM obligations.
Generally collateral in the financial system can be treated as cash, particularly in the case of
cleared IM, as CCPs require IM to be in sovereign bonds or currency. As a result, if collateral zij
is seized by node j from node i, node i’s payment obligation is reduced by exactly zij . Similarly
we assume there is no liquidation cost for the capital buffer bi that is used to node i’s payment
obligations. However, in the non-cleared derivatives market, a wide range of less liquid securities,
including corporate bonds, foreign-denominated bonds, and equities are accepted as collateral, and
these types of securities are also used as collateral in repurchase agreements.
We note that our model can be adjusted to incorporate the potential consequences of collateral
illiquidity. To do so, we assume that zij and bi are held in an asset with a normalized price π.
The value of π can range from zero to one, with zero indicating a full reduction in value and one
indicating no reduction in value (i.e. cash). In turn, πzij is the reduced value of the IM and πbi
the reduced value of the capital buffer. Following the price-impact formulation used in Cifuentes
et al. (2005) and Amini et al. (2016), we posit that π is a strictly decreasing function G(1, ∆) of
7We estimate VM and IM following the formulation of Luo (2005) and applying the framework adopted in
Appendix I of Paddrik et al. (2020).
13
the total proportion of collateral asset liquidated ∆, with the first argument of G indicating the
initial price of 1. To be concrete, we set
π = G(1, ∆) = e
−λ∆ (1)
for some λ > 0 . A larger λ corresponds to a less liquid asset. Though this setting makes the
simplifying assumption that all collateral is held in a single illiquid asset, any overstatement can be
offset through a smaller value of λ. We analyze the impact of collateral illiquidity in Appendix C,
and we show that the current collateral standards are sufficient to prevent major losses. To reduce
our notation in the subsequent sections we will present the case where IM and capital buffers are
held in cash, π = 1.
2.1.b Payments for Bilateral Firms
We first derive payment equations for nodes other than the CCP. We start with the simplest
case of a bilateral firm i, and we write out the payments pij that i makes to each counterparty j
conditional on the payments that it receives from each counterparty k, pki.
The resources available to firm i are its capital buffer bi
, the payments from each counterparty
k, pki, and the IM that i holds from each counterparty k, zki. The total obligations of firm i to its
counterparties are P
k6=i
p¯ik. If this exceeds the resources of firm i, it will not be able to fully pay
its counterparties. It will thus need to reduce its payments to its counterparties proportionally. We
describe next how this reduction is implemented.
For a bilateral firm i ∈ B, we define the stress at i, si
, to be the amount by which i’s payment
obligations exceed the incoming payments from i’s counterparties and IM held:
si =







X
k6=i,0
p¯ik
| {z }
Obligations
−


X
k6=i,0
((pki + zki) ∧ p¯ki) + bi


| {z }
Resources







+
. (2)
Let ¯pi =
P
j6=i
p¯ij be the total payment obligations of i to all other nodes. In the following
definitions, we restrict attention to the nodes i in the system such that ¯pi > 0. The others do not
7
In general, x ∧ y denotes the minimum of two real numbers x and y.
14
have payment obligations and thus do not transmit payment shortfalls. In the CDS market that we
consider, such firms would be buyers of CDS protection (not sellers) and under our CCAR shock
they would not have VM obligations. Shortfall and payment equations are thus not necessary for
such nodes.
We can use these VM payment obligations to define the relative liability of node i to node j as
aij = ¯pij/p¯i
. (3)
We assume that the stress of firm i is transmitted to i’s counterparties pro rata the size of its
payment obligations. We can now define the payment functions for bilateral firms. Given any input
vector p ∈ R
2n+2 such that 0 ≤ pij ≤ p¯ij for all 0 ≤ i, j ≤ n, the payment functions pij (p) for a
bilateral firm i are given by:
pij = ¯pij − aijsi
. (4)
2.1.c Payments for Client Firms
Now we define the payments for client firms. Client firms have similar payment functions as
bilateral firms, but they also have client clearing transactions with the CCP. Recall that for these
transactions, clients need to form a contract with a clearing member, which then intermediates
transactions with the CCP. If the client owes money to the CCP, the client pays the clearing
member , which then passes the payment onto the CCP. If the client is owed money by the CCP,
the CCP will pay the clearing member, which then passes the payment onto the client. Clients also
post IM to cover shortfalls in their payments. However, the CCP does not post IM for the client.
The total resources of a client firm i are given by the sum of its payments received from bilateral
and client clearing transactions along with its capital buffer. The total obligations of client i are
given by the sum of its bilateral and client clearing obligations. If this amount exceeds the resources
of firm i, it will not be able to pay its counterparties in full and will instead pass on partial payments.
For a client firm i ∈ C, we define the stress at i, si
, to be the amount by which i’s payment
obligations exceed the incoming payments from i’s counterparties and IM held:
15
si =







X
k6=i,0
p¯ik +
X
k∈Mi
q¯ik0
| {z }
Obligations
−


X
k6=i,0
((pki + zki) ∧ p¯ki) + X
k∈Mi
q
m
0ki + bi


| {z }
Resources







+
. (5)
Unlike bilateral firms, clients will also have client clearing payment obligations. When the client
faces stress, we assume that these payments are reduced pro rata the total payment obligations
owed by the client across all types of transactions.
Denote ¯p
g
i =
P
k6=i
p¯ik +
P
k∈Mi
q¯ik0 as the sum over all payment obligations for client i. We
use these combined payment obligations to derive client i’s relative payment liability to different
firms.
aik = ¯pik/p¯
g
i
∀k 6= i, (6)
a
c
ik0 = ¯qik0/p¯
g
i
∀k ∈ Mi
. (7)
The stress of client i is transmitted to i’s counterparties pro rata the size of its combined
payment obligations. Given any vector p ∈ R
2n+2 such that 0 ≤ pik ≤ p¯ik for all 0 ≤ i, k ≤ n, the
payment functions pik(p), qc
ik0
(p) for a client firm i are given by:
pik = ¯pik − aiksi
, (8)
q
c
ik0 = ¯qik0 − a
c
ik0
si
. (9)
2.1.d Payments for Clearing Members
Now we define the payments for clearing members. Clearing members may engage in bilateral
trades, centrally cleared trades, and client clearing trades. Each of these three types of trades will
entail different obligations and resources for the clearing member. The total obligations of clearing
member k to its counterparties are given by P
i6=k
p¯ki +
P
i∈Ck
(¯q0ki + ¯qik0). If this amount exceeds
the resources of clearing member k, it will not be able to pay its counterparties in full.
Member k’s stress is given by:
16
sk =
X
i6=k
p¯ki +
X
i∈Ck
(¯q0ki + ¯qik0)
| {z }
Obligations
−


X
i6=k
((pik + zik) ∧ p¯ik) + X
i∈Ck
((q
c
ik0 + zik0) ∧ q¯ik0) + q0ki) + bk


| {z }
Resources
+
. (10)
The way that a clearing member k passes on stress is special because for centrally cleared
transactions it must pass through at least the amount that was given to it by a client i for the
CCP, ((q
c
ik0 + zik0) ∧ q¯ik0), or the CCP for a client i, q0ki. If these amounts are sufficient to cover
the original obligations, ¯qik0 and ¯q0ki respectively, then the clearing member will make the payment
in full. However, if the amount received by the clearing member is less than the obligation, the
clearing member must cover the remainder out of its own funds or be in default. If the clearing
member is under stress, then any remaining obligations will be cut pro rata based on the clearing
member’s stress.
Define ¯p
r
k =
P
i6=k
p¯ki +
P
i∈Mk
(¯q0ki − q0ki + [¯qik0 − q
c
ik0 − zik0]
+) as the sum of the remaining
payments over all entities. Because the passthrough payments must always be made, we deduct
them in determining the clearing member’s relative liability.
aki = ¯pik/p¯
r
i ∀k 6= i, (11)
a
m
0ki = (¯q0ki − q0ki)/p¯
r
i ∀i ∈ Ck, (12)
a
m
ik0 = [¯qik0 − q
c
ik0 − zik0]
+/p¯
r
i ∀i ∈ Ck. (13)
The stress of clearing member k is transmitted to k’s counterparties pro rata the size of its
remaining payment obligations. We can now define the payment functions for clearing member k.
pki = ¯pki − akisk ∀i 6= k, (14)
q
m
0ki = ¯q0ki − a
m
0kisk ∀i ∈ Ck, (15)
q
m
ik0 = ¯qik0 − a
m
ik0
sk ∀i ∈ Ck (16)
We have defined the payment functions for all entities other than the CCP. We will define the
CCP’s equilibrium payment functions and received payments in the next section. In equilibrium,
17
the payments received by a firm and the payments made by a firm must be balanced. Firms that
are under stress will cut their payments pro rata, while unstressed firms will make their payments
in full. The equilibrium payment vector accounts for contagion effects from one firm failing to pay
its counterparties and propagating stress further down the network. Such contagion effects have
the potential to be very large, as shown in Paddrik et al. (2020).
2.2 CCP Default Waterfall
In this section, we derive the CCP’s payment function from the funded stages. Recall that the
CCP is indexed as node 0. The CCP’s payment obligations are given by P
k∈M

p¯0k +
P
i∈Ck
q¯0ki
.
The resources that the CCP has available come from the CCP’s default waterfall and the VM payments it receives. As described in the introduction, the funded layers of the CCP default waterfall
consist of the following stages: IM of defaulting clearing members, guarantee fund contributions of
defaulting clearing members, CCP capital, and guarantee fund contributions of surviving clearing
members.
IM is the first stage used in the default waterfall. It is used to cover shortfalls in the payments of
clearing member obligations, including a clearing member’s client clearing obligations. zk0 denotes
the IM collected by the CCP from clearing member k. Including IM, the CCP receives total
resources from clearing member k of:

pk0 +
X
i∈Ck
q
m
ik0 + zk0

∧

p¯k0 +
X
i∈Ck
q¯ik0

. (17)
The next several stages of the default waterfall utilize the guarantee fund of the CCP. Funds
are first taken from contributions of the defaulting clearing members. If that is insufficient to cover
the CCP stress, funds are next taken from the CCP’s capital contribution b0, and then from the
remaining guarantee fund contributions of all the clearing members.
We define some notation to describe the guarantee fund. Let γ be the total size of the CCP’s
guarantee fund. We assume that each clearing member k contributes an amount γk to the guarantee
fund. Thus the total guarantee fund is given by the following equation:
γ =
X
k∈M
γk. (18)
18
The guarantee fund contributions γk are computed by examining the riskiness of the portfolio
of each clearing member. We approximate the contribution γk by using the proportion of IM of
clearing member k held by the CCP , as zk0 is a reflection of the relative amount of risk clearing
member k contributes to the total portfolio of the CCP.8
γk = γP
zk0
j∈M zj0
(19)
In section 1.2 we will present a survey of the default waterfall sizes of real-world CCPs. There
exists a large degree of variation in guarantee fund sizing, as CCPs follow different rules such as
Cover 1 or Cover 2 (CPMI-IOSCO (2012)). We examine the resiliency and trade-offs of these
different rules in our empirical tests.
The CCP also provides its own capital contribution to cover losses, which we denote by b0. This
capital contribution is used after the guarantee fund of defaulting clearing members and before the
guarantee fund of non-defaulting clearing members.
The CCP prefunds the first four stages of the default waterfall. The amount that is available is
thus fixed and independent of the market shock. In addition, implementing these stages does not
create additional stress for the network.9
The remaining CCP stress after the funded waterfall layers, denoted s0, is given by the following
equation:
s0 ≡


X
k∈M

p¯0k +
X
i∈Ck
q¯0ki − (pk0 +
X
i∈Ck
q
m
ik0 + zk0) ∧ (¯pk0 +
X
i∈Ck
q¯ik0)

 − γ − b0


+
. (20)
The CCP’s stress is zero if it can cover its payment obligations without using up its own capital
b0 and the guarantee fund contributions of all clearing members γ. Only after the guarantee fund
is fully used up (in the fourth stage) will the CCP stress be greater than zero. After the guarantee
fund is used up, the CCP passes on this level of stress to its counterparties by cutting its payments
pro rata. In Appendix D, we analyze the impact of including the end-of-waterfall mechanisms to
8
γ reflects the expected loss to the CCP if the two largest clearing members were to default, after accounting for
the clearing members beyond their zk0. For the purposes of this model, we use public disclosures of γ, discussed in
Section 4.1.
9Clearing members must eventually replenish the IM and guarantee fund contributions that are used, but this
will usually come later. The PFMI regulations require that the IM and guarantee fund payments be replenished by
the start of the next business day to ensure compliance with the cover two rule.
19
cover the remaining stress.
Given the CCP’s stress s0, we define the combined payment obligations for the CCP to derive
its payments. We let ¯p
g
0 =
P
i6=0 p¯ki +
P
k∈M q¯0ki.
We use these combined payment obligations to derive the CCP’s relative payment liability to
different firms.
a0k = ¯p0k/p¯
g
0
, (21)
a0ki = ¯q0ki/p¯
g
0
. (22)
p0k = ¯p0k − a0ks0 ∀k ∈ M, (23)
q0ki = ¯q0ki − a0kis0 ∀k ∈ M. (24)
Similar to other firms, the CCP prorates its outgoing payments proportionally based on its level
of stress.
2.3 Existence of Payment Equilibrium
In this section, we prove that a payment equilibrium will exist for any default waterfall design
in the financial system we have proposed. Compared with the classical network model of Eisenberg
and Noe (2001), our model features the additional complexities of IM, client clearing obligations,
and CCP default waterfall obligations. However, we show in the following theorem that a maximal
payment equilibrium still exists for our model. A maximal payment equilibrium refers to an equilibrium with the largest value of payments made by all the firms. We will focus on the analysis of
the maximal payment equilibrium for our model in the empirical section of the paper. We state
our existence result in the following theorem.
THEOREM 1. A maximal payment equilibrium exists for the financial clearing system.
Proof. To prove the existence theorem, we build on the results obtained in Paddrik et al. (2020).
Proposition 1 of that paper guarantees existence of a greatest fixed point for a function that is
upper-semicontinuous, monotone, and order-preserving on a bounded lattice. To apply this result
to our model, we start by showing that our payment functions satisfy these properties. The payment
20
functions in our model are given by Equation (4) for purely bilateral firm payments, Equations (8)-
(9) for client payments, Equations (14)-(16) for clearing members, and Equations (23)-(24) for the
CCP. We define the mapping function Φ(p, q) as the set of all the p and q payment functions for
all firms in our model.
First, we note that all of the payment functions are continuous, and thus upper-semicontinuous.
To show that the payment vectors are also monotone and order preserving, note that all the payment
functions are decreasing in the amount of stress at each entity. We therefore need to show that
lower payments received will increase the stress in each of these equations. For the non-CCP
equations, this is straightforward to see directly from the definitions of stresses: Equation (2) for
purely bilateral firms, Equation (5) for the clients, and Equation (10) for the clearing members.
Stress at the CCP is given in Equation (20), which also shows that it is also a decreasing function of
payments. Since each individual payment function is upper-semicontinuous, monotone, and order
preserving, the function Φ(p, q) satisfies these properties as well.
Since the function Φ(p, q) is upper-semicontinuous, monotone and order preserving, we can
apply Proposition 1 in Paddrik et al. (2020) to show that starting from ¯p and ¯q, the sequence of
payment vectors will converge to the greatest fixed point payment vector. Therefore a maximal
payment equilibrium will exist.
In the empirical applications, we will compute the maximal equilibrium by choosing values of the
capital buffers {b0, b1…, bn} and then recursively computing a fixed point of this system by taking
the limit of the sequence (p
1
, q1
) = Φ(¯p, q¯),(p
2
, q2
) = Φ(p
1
, q1
), …,(p
n+1, qn+1) = Φ(p
n
, qn
),… The
resulting fixed point is a maximal equilibrium of the network model. In Appendix A, we describe
this fictitious algorithm in more detail and how it is used to calculate the equilibrium payment
vector in the empirical settings. Finally, we note that both our existence result and our fictitious
algorithm can be extended in a straightforward way to cover collateral illiquidity.10
10In the case where πzij and πbi are held in an illiquid asset, rather than cash, and the asset follows the priceimpact function given in Equation (1), finding the greatest fixed point for the clearing payments and the illiquid asset
value may require further iterations of the fictitious algorithm. However, a greatest fixed point is guaranteed to exist
given the monotonicity of π by Tarski’s fixed point theorem (1955), as applied in Cifuentes et al. (2005), Elliott et al.
(2014), Gofman (2017), and Amini et al. (2016).
21
3 Measuring Losses
A social planner concerned with financial system risk must select a desirable default waterfall
design by assessing the consequences of different waterfall structures on overall system losses and
how those losses are distributed. We use systemic loss, defined as the total of bankruptcy losses
that creditors suffer, which follows the interpretation applied in Eisenberg and Noe (2001) and
Glasserman and Young (2015). However, unlike the measures used in these works, which consider
only the shortfall of payments, we also consider bankruptcy costs resulting from client clearing and
the CCP’s default waterfall. Clearing members are responsible for defaulted client obligations and
clearing members’ default resources are used by the CCP to cover defaulting member obligations.
Thus clearing members can become creditors to the defaulted firms as if they were directly receiving
payments.11 Systemic loss captures the overall level of payment disruption to the system felt across
all firm types.
We next discuss how losses are calculated among the individual participant types. Then we
describe how total systemic losses can be derived in our model. This measure will allow us to later
empirically measure the social welfare implications of different default waterfall structures.
3.1 Losses for Different Types of Firms
We now write out the total losses for the different types of firms. For each firm x, we denote
the loss as lx. These loss equations will be used in the empirical section to compute the amount of
losses suffered by individual market participants based on different shock sizes and default waterfall
structures.12
For a purely bilateral firm i, losses given a payment equilibrium are composed only of bilateral
losses. These bilateral losses are equal to the difference in expected payments versus received
payments plus IM in bilateral transactions.
li =
X
k6=i
[¯pki − (pki + zki)]+
| {z }
bilateral
, ∀i ∈ B. (25)
11An example of this bankruptcy cost on clearing members can be seen in the default of a clearing member of
Nasdaq OMX CCP in late 2018, which caused clearing members to become creditors to the order of €107 million.
12In Appendix B we provide a detailed description of the different types of losses in our model.
22
For a client firm j, losses given a payment equilibrium are composed of bilateral plus client
clearing losses, which occur when clients do not receive their full obligations in client clearing
transactions.
lj =
X
k6=j
[¯pkj − (pkj + zkj )]+
| {z }
bilateral
+
X
k∈Mj

q¯0kj − q
m
0kj
| {z }
client clearing
, ∀j ∈ C. (26)
For a clearing member k, losses given a payment equilibrium are composed of bilateral and
direct clearing, client clearing, and waterfall losses, which occur when waterfall contributions are
used to cover obligations of a separate defaulting clearing member. We denote the waterfall losses
by ˆγk, and we show how they can be computed in Appendix B.
lk =
X
i6=k
[¯pik − (pik + zik)]+
| {z }
bilateral and cleared
+
X
i∈Ck

[¯qik0 − (q
c
ik0 + zik0)]+ + ¯q0ki − q0ki
| {z }
client clearing
+ ˆγk
|{z}
waterfall
,
∀k ∈ M. (27)
3.2 Losses for the CCP
We now describe the losses of the CCP, which may be different from the losses of other types
of firms. The CCP’s losses can come from two channels. First, the CCP has a capital contribution
of b0 that it could lose if used in the default waterfall. We denote the amount used in equilibrium
by ˆb0, which is equal to the amount the CCP needs to cover in excess of received payments, IM,
and own default fund contributions of defaulting clearing members:
ˆb0 = min


X
k∈M

p¯0k +
X
i∈Ck
q¯0ki − (pk0 +
X
i∈Ck
q
m
ik0 + zk0 + γk) ∧ (¯pk0 +
X
i∈Ck
q¯ik0)

, b0

 (28)
The CCP can also suffer losses from payment shortfalls that exceed its total waterfall resources
(IM, guarantee fund, and capital contribution). Since the CCP has a balanced book, the remaining
shortfall in the payments it receives after using its default waterfall is equal to the equilibrium

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