For the instruction, please check the attachment below. Please give this within 24 hours. If you would like to help with this, please contact m

Questions about CVA for CCPs

This case asks you to use a contagion model to assess the risk faced by someone exposed to the default of a clearing house (or central counterparty, CCP). As background, you may want to read the articles about the risk of CCP default.

The model will make the following simplifying assumptions.

1. The clearing house has 25 members. (You are not a member. You are a client of one or more members.)

2. The clearing house defaults if 5 or more members default within a month.

3. Defaulting members are instantly replaced by new non-defaulting members so that there are always 25 members.

4. If the clearing house defaults, the recovery rate on its obligations is R = 0.10.

5. There will be no government bailout if the CCP defaults.

6. The riskless rate is zero.

Default by member firm i is governed by a Poisson process J (i) t which jumps into default with

intensity λt. The intensity process is common to all member firms, but, given λt, the Poisson jumps are independent across firms. The intensity obeys the Hawkes process,

dλt = κ(λ̄ − λt) dt + ∑ i

β dJ (i) t ,

where the sum runs over the 25 active members. Thus a default by the jth member means that

dJ (j) t = +1, which raises the risk of all the others defaulting.

We will discretize the model to intervals ∆t = 1/52, or one week, so that each member’s probability of default each week is λ1 /52 where λ1 is the intensity at the start of the week.

Our model for the mechanics of default is as follows. All clients’ positions are marked-to-market continually until CCP default, and thus they have zero value. Once default occurs, the CCP stops paying clients with winning positions. The value of these positions continues to evolve after default. We will assume that the clients’ claims on the CCP are frozen at the end of one week after a default occurs. The CCP then cancels all client positions and pays the recovery rate on the positive claims.1

Continued on next page.

1Note that your initial margin is assumed to be NOT at risk. The CCP cannot seize it to pay other clients.

� Question 1. Default clustering (or contagion) in this model is controlled by the parameter β. So accurately estimating it will have important implications.

Assume that under the physical measure we have parameters κ = 4, λ̄ == 0.01. Assume the system is currently healthy, so that λ0 = λ̄. Simulate 10

5 histories of the system for five years with β = 0.05. How many clearing house defaults do you observe? How much does the answer change if β = 0.15.

Can you think of any ways that β could be estimated from historical data?

� Question 2 (a). CVA is computed under the risk neutral measure. Assume that under this measure we have κQ = 2, λ̄Q = 0.02 and βQ = β = 0.10. Re-run your simulation for 1 year with these values, assuming λ

Q 0 = λ̄

Q. Keep track of the date of the first CCP default (if any) along each simulated path.

Now supose you have a 1-year futures position with the CCP in a commodity that is unrelated to the financial system (for example, sugar). Under the risk neutral measure, its futures price, f, obeys df/f = σ dW and σ = .20. Your position has a notional value of $1 million. Use your simulations of the CCP default times and the assumptions on default loss given above to compute the CVA (in dollars) for your futures position. Explain exactly what your algorithm is doing.

� Question 2 (b). Now suppose you have a cleared trade with the CCP which is a long position in a 5-year CDS referencing one of the member banks. So if the CCP defaults there is a probability of 1 in 5 that your CDS is triggered. Suppose the position has a notional value of $1 million and the recovery rate on the bank’s debt is R = 0.5. What is the CVA on this position? For this calculation, you may ignore the component that comes from the mark- to-market in states where the CCP defaults and the member bank does not. Again, explain clearly how you are computing the CVA.

� Question 3. This question asks you to think about the value of a “too-big-to-fail” guaran- tee that tax-payers may be providing to clearing houses. Even though the true probability (under our model) of a CCP default is very small, the gaurantee’s value is determined by the risk-neutral measure.

Mathematically, our model of CCP default exposure is very similar to the default exposure of a senior tranche of a CDO. As we have seen, the 2007-2009 financial crisis was kindled by losses in senior tranches of CDOs made up of assets whose default processes were very highly correlated. So we don’t want to make the mistake of over estimating their safety again.

What is the value of a 5-year CDS on the clearing house (with notional value of $1 million). Express your answer as a price today, not a fee payment.

2

The Office of Financial Research (OFR) Working Paper Series allows members of the OFR staff and their coauthors to disseminate preliminary research findings in a format intended to generate discussion and critical comments. Papers in the OFR Working Paper Series are works in progress and subject to revision. Views and opinions expressed are those of the authors and do not necessarily represent official positions or policy of the OFR or Treasury. Comments and suggestions for improvements are welcome and should be directed to the authors. OFR working papers may be quoted without additional permission.

Central Counterparty Default Waterfalls and Systemic Loss

Mark Paddrik Office of Financial Research [email protected]

Simpson Zhang Office of the Comptroller of the Currency [email protected]

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, Stéphane Crépey, Peter Curley, Selman Erol, Kather- ine 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 Confer- ence, 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 com- ments. We would like to thank Elizabeth McKee for her excellent assistance 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: [email protected]

‡Office of the Comptroller of the Currency, 400 7th St SW, Washington, DC 20219; phone: 202-649-6288; email: [email protected]

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 counter-

party 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 struc-

tural 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 expo-

sures 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 as-

sess 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 partic-

ipation 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 ag-

gregate 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 cen-

tral 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 at-

tempting 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 Contri- bution of Defaulting M

IM of Defaulting M IM of Defaulting Client

Member Defaults Client Defaults

Guarantee Fund Contri- bution 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 dif-

ferences 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 assess- ment 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 as- sessment 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 assess- ments, 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 co

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