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Universiteit van Amsterdam

Vrije Universiteit

JOINT DEGREE IN COMPUTATIONAL SCIENCE

The Role of Central Clearing Parties in OTC

Derivatives Markets

Author: Maarten P. Scholl

Examinator Daily Supervisor Prof. B.D. Kandhai Prof. S.A. Borovkova

Second Reader Dr. Sumit Sourabh

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Preface

Maarten P. Scholl Amsterdam March 2017

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We investigate systemic risk in OTC-derivatives markets. We are inte-rested in the methods that a Central Clearing Party can use to dampen shocks in the system. We construct a discrete event simulation of a realistic interbank system. The interbank network has two layers: loan-borrowing and interest rate swaps. Using a computing cluster we can sweep the entire parameter space and evaluate the choices available to a CCP. Additionally we investigate the efficiency of having multiple central clearing parties for different asset classes.

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Contents

List of Figures vii

List of Tables ix

List of Acronyms xi

1 Literature Review 1

1.1 Clearing . . . 2

1.1.1 Clearing Agreements . . . 2

1.1.2 Central Clearing Parties . . . 3

1.2 Over-the-Counter Derivatives . . . 4

1.3 History of Clearing . . . 4

1.3.1 Examples of CCP Intervention. . . 5

1.4 Current State of Central Clearing . . . 5

1.5 Existing Work . . . 6

1.5.1 Procyclicality . . . 6

1.5.2 Contagion. . . 6

1.5.3 Systemic Risk Measures . . . 8

1.5.4 Complex Systems . . . 9

1.6 Goals . . . 9

2 Counterparty Risk 11 2.1 Counterparty Exposure . . . 12

2.1.1 Fair Value Accounting . . . 12

2.2 Exposure Management . . . 12

2.2.1 Credit Events . . . 13

2.2.2 Interest Rate Swap (IRS) Exposure . . . 13

2.3 Collateralisation . . . 14

2.3.1 Variation Margin . . . 14

2.3.2 Initial Margin . . . 15

2.4 Simulation . . . 17

2.4.1 Value Adjustments . . . 18

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3.2.1 Risk Measures . . . 20

3.2.2 Value-at-Risk . . . 20

4 Model 23 4.1 Interest Rate Models . . . 23

4.2 Rate Curves . . . 23

4.3 Historic Data . . . 24

4.4 Applying the Model in Practice . . . 25

4.5 Simulated Term Structure. . . 26

4.6 Interbank Network . . . 27 4.7 Construction . . . 27 4.8 Clearing . . . 30 4.9 Payment Netting . . . 30 4.10 Trade Compression . . . 30 4.11 Bilateral Clearing . . . 30 4.11.1 Netting . . . 30 4.11.2 Default . . . 31 4.12 Central Clearing . . . 31 4.12.1 Novation . . . 32 4.12.2 Compression by Novation . . . 33 4.13 Portfolio Transfer . . . 33 4.14 Auction . . . 33

4.14.1 First-Price sealed-bid auctions . . . 34

4.15 Default Waterfall . . . 35

4.15.1 Loss Allocation . . . 35

4.15.2 Moral Hazard. . . 35

4.15.3 Variation Margin Haircut . . . 35

4.16 Computation . . . 37 4.17 Infrastructure . . . 37 4.17.1 Cluster . . . 37 4.18 Scaling. . . 38 5 Experiment 41 5.1 Standard Values . . . 41 5.1.1 Interbank Network . . . 41 5.2 Capitalisation . . . 43 5.3 Initial Default . . . 43 5.4 Process. . . 43 5.5 Resolution . . . 44 5.6 Results . . . 45 5.7 Experiments . . . 45 5.7.1 Parameter Sweep . . . 45

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5.7.2 CCP Survival . . . 47

5.7.3 Lending . . . 49

5.8 CCP Tools . . . 50

5.8.1 Default Fund Contribution. . . 50

5.8.2 Initial Margin (IM) Risk Measure . . . 51

5.8.3 CCP Margin Period of Risk . . . 53

5.9 CCP Competition . . . 54 5.10 Policy Recommendations . . . 54 5.11 Future Research . . . 55 5.11.1 Assets Types . . . 55 5.11.2 Competition . . . 55 5.11.3 Regulatory Arbitrage . . . 56 A Financial Markets 57 A.1 Financial Instrument Valuation . . . 57

A.1.1 Arbitrage . . . 58

A.2 Diagram . . . 58

A.3 Financial Instruments . . . 59

A.3.1 Bond . . . 59

A.3.2 Forward Rate Agreement . . . 62

A.3.3 Interest Rate Swap . . . 63

B Initial Margin Algorithm 65 B.1 Binary Heap . . . 65

B.1.1 Analysis . . . 69

C Modeling Interest Rates 73 C.1 Bootstrapping . . . 73 C.2 Nelson-Siegel Functions . . . 73 C.3 Dynamic Nelson-Siegel . . . 74 C.4 Nelson-Siegel-Svensson. . . 75 C.5 Quasi-Newton methods . . . 77 C.6 Comparison . . . 79 C.7 Dynamics . . . 80 C.7.1 State-Space Model . . . 80

D Test for Autoregressive Property 83 D.1 Dynamic Nelson-Siegel . . . 83

D.2 Dynamic Nelson-Siegel-Svensson . . . 84

E Graph Construction Algorithm 85 E.1 Components. . . 85

E.1.1 Degree Distribution . . . 85

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List of Figures

1.1 Interest Rate Product Market Share . . . 4

1.2 Survey of Clearing per Instrument end-June 2016 . . . 6

2.1 Interbank-OIS . . . 11

2.2 Failure due to Rehypothecation of Collateral. . . 14

2.3 Illustrated example of loss in case of default. . . 15

2.4 Margin Period of Risk . . . 16

2.5 Expected Exposure . . . 17

2.6 Potential Future Exposure . . . 17

3.1 Non-subadditivity of VaR . . . 21

4.1 Historic Euro par-curve. . . 24

4.2 Example of simulated term structure using the Diebold-Li model. . . 26

4.3 Sample Core Periphery Network . . . 28

4.4 Parties A and B are to exchange payments worth 3 and 2 in the same currency. . . 30

4.5 Bilateral netting. . . 30

4.6 Three parties agree to engage in multilateral netting on the payments over two IRS. . . 31

4.7 Bilateral clearing requires the involvement and consent of all parties involved. . . 31

4.8 Before novation . . . 32

4.9 Novation . . . 32

4.10 Party A already has one contract (IRS1) centrally cleared. Party A then sells a new contract (IRS2) to party B, or has an existing contract that both parties choose to backload to the Central Clearing Party (CCP). . 33

4.11 Novation: the CCP initiates new contracts between itself and parties A and B. . . 33

4.12 Novation netting: where possible, contracts between clearing members and CCP are netted. . . 33

4.13 Data Flow in Computing Infrastructure. . . 38

4.14 Strong and weak scaling of computational framework. . . 38

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5.4 Losses at different system sizes . . . 46

5.5 Cumulative losses to all members at different system sizes . . . 47

5.6 Mean duration of default cascade. . . 47

5.7 Individual samples for Bilateral Clearing . . . 48

5.8 Individual samples for Central Clearing . . . 48

5.9 Probability of CCP default. . . 49

5.10 Insolvencies as a result of choice for Default Fund Contribution. . . . 51

5.11 Insolvencies as a result of choice for IM Value-at-Risk level α . . . 52

5.12 Mean losses as a result of choice for IM Value-at-Risk level α . . . 52

5.13 CCP margin period of risk at 3× volatility. . . . 53

5.14 CCP margin period of risk at 10× volatility . . . 53

5.15 Mean losses to specified counterparty for different numbers of CCPs. 54 A.1 Diagramming Method of Financial Contracts . . . 59

A.2 Diagram of Zero Coupon Bond . . . 60

A.3 Diagram of Coupon-bearing Bond Contract . . . 61

A.4 FRA . . . 62

A.5 A sample swap contract. . . 63

B.1 minheap . . . 65

C.1 Nelson-Siegel τ estimation. . . . 74

C.2 Nelson-Siegel factor loading. . . 75

C.3 Nelson-Siegel τ estimation. . . . 75

C.4 Comparison of NS and NSS models on different historic cases. . . 76

C.5 Nelson-Siegel τ estimation. . . . 77

C.6 Nelson-Siegel τ estimation. . . . 79

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List of Tables

1.1 Deadline for Central Clearing Obligations. . . 5

2.1 Exposure Management of a portfolio . . . 13

4.1 Bloomberg tickers used to fit yield curve. . . 25

4.2 Default Waterfall . . . 35

5.1 Simplified Balancesheet . . . 43

5.2 Mean number of insolvencies comparing a network with interbank len-ding (first column) to a network where instead of the loans the partici-pants receive the same amount as liquid assets (100,000 samples). . . 50

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List of Acronyms

LIBOR London Interbank Offered Rate . . . .11

OIS Overnight Indexed Swap . . . .12

CSA Credit Support Annex . . . .14

G20 Group of Twenty . . . .1

EMIR European Market Infrastructure Regulation . . . .2

FRA Forward Rate Agreement . . . .63

IRS Interest Rate Swap . . . .iii

OTC Over-the-Counter . . . .2

DFC Default Fund Contribution . . . .50

CVA Credit Value-Adjustment . . . .18

FVA Funding Value-Adjustment . . . . 18

CCP Central Clearing Party . . . . vii

IM Initial Margin . . . .v

VM Variation Margin . . . .15

MtM Mark-to-Market . . . .12

VMGH Variation-Margin Gains Haircutting . . . .36

SDR Swap Data Repository . . . .41

MPI Message Passing Interface . . . . 37

VaR Value at Risk . . . .20

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Colophon

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Literature Review

1

L

ehman Brothers held a significant portfolio of subprime mortgages when the United States housing market sharply declined at the end of 2006. Throughout the next two years, the company suffered major losses and a sharp decline in share price.

On 15 September 2008 Lehman Brothers was declared to be in default, and trading in the company’s shares was halted. A portfolio consisting of mainly interest rate swaps in excess of 9 trillion notional was transferred to independent clearing house LCH.Clearnet [LCH Clearnet Group,2014]. The clearing house initially hedged the swap portfolio. Fourteen days later auctioned the portfolio among its clearing-members. The cost of handling Lehman Brothers’ default was covered entirely by the collateral posted by the company to the clearing house. For interest rate swaps, no cost was incurred to other clearing-members.

The Group of Twenty (G20), founded in 1999 to promote international financial stability, had its inaugural meeting in November 2008. The urgency of the 2007-2008 financial crisis was an important stimulus in the development of new regulation and one year later theG20gathered in Pittsburgh.

“Since the onset of the global crisis, we have developed and begun implementing sweeping reforms to tackle the root causes of the crisis and transform the system for global financial regulation. Substantial progress has been made in strengthening prudential oversight, impro-ving risk management, strengthening transparency, promoting market integrity, establishing supervisory colleges, and reinforcing internatio-nal cooperation. ”. —G20press communiqué [Financial Times,2009]

A direct outcome of the Pittsburgh summit was that the G20 would be the new permanent council for international economic cooperation. This meant that the new regulation and practices that were proposed would be highly influential on the

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rules that G20 members sought to realise in the years following. The commitment of theG20to reduce systemic risk has multiple facets: regulation, supervision and capital requirements. The proposal mentioned mechanisms to reduce systemic risk and counterparty risk in financial markets. An important type of security, over-the-counter (OTC) derivatives contracts, were mentioned specifically. Summarising, the following recommendations were a direct result of these meetings:

• All Over-the-Counter Derivative Contracts should be traded on exchanges. • These derivative contracts should be cleared through central clearing parties

(nonoptionally).

• All trades in these types of securities should be registered in a trade repository, accessible by regulatory bodies or governments.

We find direct implementation of these proposals in regulation proposed by the G20 members. In the United States a corresponding set of rules, named the

Dodd-Frank Wall Street Reform and Consumer Protection Act was signed into federal law in

2010. In the European Union a corresponding set of rules, the European Market Infrastructure Regulation (EMIR), came into force in 2012. In addition to these regulatory frameworks, the Basel Accords

1.1 Clearing

Clearing is the process that takes place during the lifetime of a trade between two

parties. Its main purpose it to reduce counterparty risk, for example by setting aside collateral for a trade. An additional benefit of clearing is the possibility to optimise payments to net obligations, reducing the overal required funds required for an institution at a given time.

Clearing can be done between two counterparties bilaterally or it can be done by an independent third party.

1.1.1 Clearing Agreements

Under rules set out by the International Swaps and Derivatives Association any Over-the-Counter (OTC) derivative transaction should be administrated using a

master agreement. This agreement covers all the terms that are applicable to the

trade, but important for our research is the optional Credit Support Annex. The agreement may also contain a Credit Support Annex that describes how the parties will manage counterparty credit risk, for example by defining collateral requirements. Counterparties agree upon and describe how they will calculate the required colla-teral amount, what type of instruments can be used for collacolla-teral (cash, bonds), and what a counterparty can do with the collateral it is holding.

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1.1. Clearing

1.1.2 Central Clearing Parties

Modern Central Clearing Parties (CCPs) are separate legal entities that provide

clearing for specific contracts in financial markets. CCPs can be commercially

inde-pendent too, but more often have strong ties to exchanges and banks as these are the venues where their customers interact. In the latter case, theCCPwill specialise in the types of contracts dealt by banks or traded on the associated exchange.

A CCP’s main purpose is to reduce counterparty risk. The CCP becomes an intermediary in cleared trades. In case of one of the original counterparties defaul-ting, the CCP will take over the portfolio of trades and associated obligations of the defaultee. The CCP will then rapidly close out this portfolio: open positions are hedged and auctioned. Losses are mutualised among clearing members. A successfulCCPis able to share losses fairly and will meet obligations to the defaul-tees original counterparties. Since all clearing members now have the same single counterparty, differences in counterparty creditworthiness no longer play a role. The exact methods and tools that a CCP can use differs per market sector. In chapter

4.8we discuss the methods we use in our simulation in detail.

Other responsibilities ofCCPs are oversight and optimisation. Since all settle-ments and paysettle-ments go through the single central counterparty nearly all transacti-ons in the market can be optimised and this can be done efficiently by the CCP. For example: payments can be netted, existing assets can be used as collateral for other trades, all decreasing funding costs for participants.

Another advantage ofCCPs is the standarisation. Not only do these aspects play a role in accounting, the costs associated with clearing a specific deal are important inputs in the traders’ strategic process. Therefore it is important that clearing rules, protocols and calculation of collateral and other costs are available and integrated with clearing members’ own information system.

Central clearing has been criticised for extra collateral requirements and loss mutualisation. Opponents cite a potential moral hazard [Pirrong, 2011]: since losses in case of a default are shared among all clearing members, yet the potential upside is not, it may be tempting to initiate risky trades.

In an environment were clearing is optional, a CCPs services may be sought only by participants who feel they are in a weak position, or know more about the riskiness of a particular trade. This is particularly risky in a scenario when there are multipleCCPs competing in the same market segment. OneCCP may develop a negative reputation as a result of a clients.

For these reasons a CCPs policies need to be carefully balanced: it can only provide financial system stability if it finds a good midpoint between building a large buffer and setting attractive requirements for clients.

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1.2 Over-the-Counter Derivatives

OTCderivates are securities traded outside of formal exchanges. They can be traded in a dealer network or can be created ad-hoc between two parties. Contracts need not necessarily be standardised and can be customised to the requirements of either party. Depending on how common a type of contract is, they still often are quoted and traded electronically. We subdivide the OTC derivatives market into three major categories: foreign-exchange contracts, interest rate contracts and equity-linked contracts. Both by amounts outstanding and gross market value the interest rate market is by far the largest[Bank for International Settlements,2016]. In this category,IRS-contracts represent the largest share of the market. In figure1.2 we see that the overal size of theOTC interst rate derivative market fluctuates from time to time. Survey N ot io na l O ut st an di ng

FRA Swap Option

Survey G ro ss M ar ke t V al ue

FRA Swap Option

Figure 1.1: Interest rate product market share. Left: notional amount per contract. Right: gross market value per contract. (Bank of International Settlement Semiannual Report 2016)

1.3 History of Clearing

Clearinghouses originated with European banks to facilitate the settlement of claims and payments. In London bankers organised at Lombard Street to voluntarily clear payments as early as 1775 [Jevons,1875]. Clearing of contracts more complex than simple claims was not used until much later. In the late 1800s the only exchange to offer clearing was the London Stock Exchange [Lalor et al.,1881]. Offered as a

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1.4. Current State of Central Clearing

service by exchanges, the clearinghouses sought to simplify the settlement process of common exchange-traded contract types. Historically, clearing has always seen op-position from market participants. With the clearinghouse orCCPbeing the only counterparty to all clearing members, those members with high creditworthiness can no longer benefit from this reputation. The adoption of clearing therefore has always been a consequence of regulation. For example, the London Metal Exchange did not offer clearing until the Financial Services Act of 1986 [Parliament of the United Kingdom,1986].

1.3.1 Examples of CCP Intervention

The independent clearinghouse LCH.Clearnet registers seven major defaults of clearing members since 1990LCH Clearnet Group[2014]. In all cases, the default was resolved with collateral held by theCCP. CatastrophicCCP failures are rare. Three cases of CCP insolvency are mentioned in [Wendt,2015]. In all cases the failure coincided with one or more clearing member defaults. In the case of the Hong Kong Futures Guarantee Corporation the market crash of 1987 plays a role, in the two other cases confounding factors are not clear. Whether or not the clearing parties adapted their risk management appropriately, or whether this would make any difference at all in the case of a market crash is a topic of heated debate [Alloway,

2011].

1.4 Current State of Central Clearing

Central Clearing has rapidly evolved since the 2009 summit in Pittsburgh [ Doman-ski et al.,2015]. In Europe,EMIRhas come into effect. Despite original intentions of making central clearing mandatory in OTC-derivatives markets as early as end-2012 Financial Times[2009], the initial deadline for EMIR was mid-2015. The deadlines have been postponed once in March 2015. As can be seen in 1.4, large trades (Category 1) are already cleared as of writing (March 2017).

IRS CDS

EUR, GBP, USD, YEN NOK, PLN, SEK Index CDS Category 1 21 June 2016 9 February 2017 9 February 2017 Category 2 21 December 2016 9 August 2017 9 August 2017 Category 3 21 June 2017 9 February 2018 9 February 2018 Category 4 21 December 2018 9 August 2019 9 May 2019

Table 1.1: Deadline for Central Clearing Obligations.

At the end of 2016, the majority of interest rate products are cleared through central parties [Bank for International Settlements, 2016]. In figure 1.4 we find that roughly 80% ofIRSare cleared through central counterparties. We expect the remaining share of the market to rapidly move to central clearing as deadlines for mandatory clearing are near.

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FRA IRS IRO MCDS SCDS FX EQ Instrument 0.0% 20.0% 40.0% 60.0% 80.0% 100.0% Sh are

Central Counterparties Other Financial Institutions Reporting Dealers Non-Financial Customers

Figure 1.2: Types of counterparties, percentage of notional outstanding at end-June 2016.

1.5 Existing Work

As discussed in Examples of CCP Intervention, over the past four decades only a handful of events have tested the effectiveness of central clearing. Complicating the discussion is that even after the events, with all information available, there does not appear to be a consensus over what properCCPpolicy would be.

1.5.1 Procyclicality

Procyclicality in policy refers to interaction, most importantly positive feedback,

be-tween regulation and economic fluctuations. In existing work several possible me-chanisms have been revealed that amplify external shocks to the financial system. This means that these mechanisms by themselves are not studied as the source of a crisis. Rather, we accept that the source of a crisis is hard to identify, more so to predict, and we treat it as an exogenous (external) shock. We should then focus on the mechanisms that potentially dampen or amplify these negative events.

1.5.2 Contagion

In a complex system, a crisis is defined by a system-wide degradation of function, and most if not all participants experience negative effects. Therefore we can in

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1.5. Existing Work

our analysis not focus on a single default; we must look at the spread of negative effects throughout the system. The mechanisms by which shocks (negative effects) spread through the system are studied as as models of contagion[Allen and Gale,

2000]. Intermediation by CCPs makes them the central participant in an OTC-derivatives market. The advisory to theG20pose that central clearing can improve the stability of the system by damping shocks. However, it is possible that to protect against a shock that exceeds theCCPresources, these same central parties that make a financial system more resilient become sources of instability. As a consequence, financial networks may be “robust-yet-fragile” [Haldane,2009].

[Barker et al.,2016] extensively simulates the different asset classes that make up the balance sheet of a large US bank. Modeling the feedback of defaults using different classes of stochastic processes they try to estimate losses given a shock to volatility of these processes. They assume the CCP remains operational throughout the entire simulation and hence do not model the underlying interbank network structure, both aspects we want to investigate in this work.

1.5.2.1 Margin

In the 1974 case of French Caisse de Liquidation, [Hills et al.,1999] and [Dodd,

2010] claim that default could have been prevented if it had adjusted margin requi-rements (increase) to market volatility. In the context of margin policy, there are some concerns about raising margin Financial Stability Board[2009] in response to increasing volatility. Raising margins may lead to additional defaults. A study on risk measures and margin computation methods in [Murphy et al.,2014] shows that risk measures that are sensitive to recent increases in volatility show strong procyclical effects, contradicting the recommendations discussed before. This is confirmed in the work of [Brunnermeier and Pedersen, 2008] who show in an analytical framework that increased margins lead to liquidity drying up. It becomes clear that there is not a simple answer. The Basel requirements and their revisions (II and III respectively) are compared inAymanns et al.[2016]. The results show that depending on exogenous shocks and the type of banks described, different policies may be optimal: they identify three regions consisting of respectively an unconditionally stable region, a locally unstable region with chaotic behaviour and an unstable region. Applying rules set forth in the Basel II accord for leverage puts the system in the locally unstable region.

1.5.2.2 Leverage

The ratio of debt to equity used to finance a banks activities in trading is referred to as leverage. Using leverage a firm can finance more activities with the consequence that both potential returns and losses are greater. When collateral requirements are suddenly increased there is a need for selling off assets in order to stay solvent. These collateral requirements, as a function of the activities of the firm, will also increase with leverage. In [Morris and Shin,2008] various mechanisms are described that

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lead to fire-sales, among others include deposits, repurchase agreements, equities. The authors take a system perspective and use a simplified balance sheet to show net-work effects. This netnet-work effect is illustrated using examples of assets being moved around multiple times, under rehypothecation or using repurchase agreements. The role of the structure of the interbank network however is not discussed. Regulation on leverage has been thoroughly researched in [Poledna et al., 2013]. Using an agent-based model, the authors show that regulation on leverage reduces overall systemic risk but increases volatility in the market.

1.5.2.3 Interconnectedness

One of the first investigations of the role of interconnectedness in the financial systems is [Allen and Gale, 2000]. The authors describe how contagion spreads from link to link in an equilibrium model of contagion. Their results show that a dense (complete) structure is more robust than a sparse (incomplete) structure.

A model that describes contagion as a phase-change in the system rather than a continuous process is found in [Acemoglu et al.,2015]. Their results amend the results from [Allen and Gale,2000]: they show that for very large shocks a more densely connected system is more likely to transmit shocks and therefore makes for a more fragile financial system. This is different from the observations for small and medium sized shocks and therefore illustrates a phase-change in the system. A specialisation of this phenomenon is described in Markose et al. [2010]. In a heterogeneous network model, that is a network some classes of participants are better connected than others, it is shown that very central participants are immune to shocks from outside: they are “too big to fail”. Inversely, those participants not central to the system are at risk of incurring large losses if one of these central participants suffers an internal failure. [Poledna et al.,2015] argue that systemic risk arises from multiple layers in the financial system interacting with each other. Using established risk measures (Debt-Rank, described in the following section1.5.3) on an extensive dataset from the Mexican interbank system it is shown that focusing on a single layer of the network can lead the observer to underestimate systemic risk.

1.5.3 Systemic Risk Measures

Measures used to identify the most central participants in a network have been used to describe this as mentioned before, but for financial networks custom metrics exist:

DebtRank [Battiston et al.,2012] is a modified network centrality measure that not

only captures the connectedness of a participant but also its leverage ratio (1.5.2.2). This measure is used to identify identify vulnerable participants, identify participants that are likely to spread risk throughout the system and can be used as an early warning sign (indicator) for future crises.

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1.6. Goals

1.5.4 Complex Systems

A bottom-up view is offered by studying the exact mechanism by which risk is trans-ferred at a microscopic level. As participants react to changes in their environment, they initiate new trades and this too changes the system. We find here a recursion: each new trade may be followed by other participants reacting and initiating new trades.

Models in complex systems that illustrate the buildup and release of stress in a system start decidedly with [Bak et al., 1987]. In their model a certain stress level, often described as a grain of sand, accumulates on a point in a lattice as if it is continuously dropped there. When the stress reaches a certain level, this point “topples” and sends stress to its neighbouring points. The buildup and release of stress in this system is likened to the phenomenon of an avalanche. A more advanced model that takes the form of a game and works on arbitrary topologies (networks) is found in [Briggs, 1999]. Most importantly, by varying one of the elementary rules of the game the author identifies three different regions for the behavior of the system. In the two boundary cases the avalanches in the system are guaranteed to stop after a finite number of steps, in the other they are guaranteed to go on respectively. In the third case, without altering the rules, it is possible to choose an initial configuration such that either can happen, and this depends on the network topology.

1.6 Goals

This work is related to the work of [Borovkova and Mouttalibi,2013] which com-pared bilateral clearing agreements and stylized central clearing agreements on dif-ferent network topologies. We take into account their findings relating to different models of the interbank network and use this to construct a realistic interbank system in chapter4.6, additionally using the model described inin ’t Veld and van Lelyveld[2014].

We decide to focus on the IRS as it represents the largest share of the OTC

Derivatives Market. Moreover, there is evidence that other major classes of de-rivatives such as the Credit Default Swap as investigated in [Leduc et al., 2016] can make markets more resilient. As there is a need to explain several financial instruments that are similar to or a possible building block of anIRS, we introduce these elementary instruments in chapterA. Additionally we use interbank lending as a second layer in the interbank network as a possible amplifier of systemic risk.

The goal of this work is to investigate the tools a CCPhas available to reduce credit risk and evaluate the actions aCCPcan take.

We want to test the efficiency of aCCPclearing multiple contracts and the case where multipleCCPs are competing.

The different tools available to aCCP, most notably margin requirements and default funds, are to be assessed. This is done using an agent-based network model.

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We apply external shocks to the system by increasing volatility of interest rates, the same interest rates that are used to price the interbankIRScontracts. This has the added benefit of being able to test the system under various market conditions. The models parameters are calibrated on the financial system in the euro-zone (section

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Counterparty Risk

2

In the previous section we have used an interest rate r to discount transactions in a financial instrument. This interest too exists as product in the market and is offered by different institutions. Banks offer short-term loans and the averaged offered rate is quoted daily in for example the London Interbank Offered Rate (LIBOR)-index. The shortest term provided is often the overnight rate. In some countries such as the OIS the rate is set entirely by the central bank, whereas in other countries the central bank operates in the market along with other participants. Governments are often seen as more creditworthy than public companies (potentially operating in those countries). We therefore expect the market to price in these credit risks in the offered rates. [Thornton,2009] argues that in the financial crisis of 2007-2008, the spread between the rates offered interbank and the OIS-indexed swap was an indicator of the sudden rise of credit risk. This is illustrated in figure2.

Figure 2.1: The spread between overnight indexed swap (OIS) rates and rates offered interbank (LIBOR) [Thornton,2009]

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Since both the Overnight Indexed Swap (OIS) andLIBORrates are indices and therefore an aggregate of all participants in the market, this doesn’t give enough to manage the exposure to a specific counterparty. The rates here are the rates that are agreed upon before entering anIRS, and once these are set we can no longer adjust them to changes in counterparty creditworthiness or changes in the market.

2.1 Counterparty Exposure

The exposure to a counterparty is the combined value of all contracts and their respective cashflows with this counterparty. Assuming that all these contracts are liquidly traded, the exposure can be expressed as the sum of all contracts valued at market prices. We will use this assumption in the following section, but note that this is not generally true: when a counterparty defaults on a contract that is not liquidly traded, it can be difficult to replace that contract. For most plain interest rate swaps this is no issue, but for customised contracts, swaps for uncommon maturity, and swaps for thinly traded currencies this can be the case.

2.1.1 Fair Value Accounting

Accounting rules dictate the methods that are to be used to determine the value of an existing contract.

Mark-to-Market Valuation Setting the valuation equal to the latest price observed in the market is referred to as Mark-to-Market (MtM) valuation. Depending on data available to those executing the trade, one can use the best quoted price, the midpoint between quoted bid and ask or the latest price at which a transaction occurred. A potential risk here is that the prices as observed in the market may not hold true for the size of the portfolio we are considering. [Haldane,2011]

Mark-to-Model Valuation For illiquid instruments, the best quotes or the latest price may not be accurate enough. For custom instruments they may not event exist. In these situations, counterparties will agree on a model and parameters.

2.2 Exposure Management

A bank will keep daily or even live records of its exposure to each of its counterparties. Additional information such as changes in credit rating or news on the counterparty are monitored.

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2.2. Exposure Management

2.2.1 Credit Events

Several different events can cause the counterparty to default on a contract. The most prominent reasons for default are:

• Failure to Pay or Deliver • Breach of Agreement • Credit Support Default

2.2.2

IRS

Exposure

When anIRSswap trade is executed at market rate, Vf ix = Vf loatand the value is

zero for both parties. As times passes the accounting value changes. Whenever the value is positive, we have exposure to the counterparty as replacing the contract after counterparty default will cost us. Note, that asIRScontracts are typically executed at fair value, we need to purchase a newIRSand additionally a bond that makes up for the difference in fixed rate: the difference between the current market rate and the fixed rate of the contract we lost. Whenever the value of theIRSis negative, our exposure is zero: replacing the contract with a fixed rate equal to or more favourable than the previous contract will cost us nothing.

Day Portfolio Value Profit-and-Loss Exposure

0 0.00 0.00 1 -0.05 -0.05 0.00 2 -0.55 -0.50 0.00 3 0.45 +1.00 0.45 4 -0.25 -0.69 0.00 5 0.17 +0.42 0.17 6 1.75 +1.58 1.75 7 2.40 +0.65 2.40 8 1.80 -0.60 1.80 9 1.47 -0.33 1.47 10 2.62 +1.15 2.62

Table 2.1: Example portfolio value and Profit-and-Loss (differences). The values in this example are used in figures and

In table2.2.2we have an example realisation of anIRStrade that will be used in the following examples on collateralisation.

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2.3 Collateralisation

In order to secure the contract, we may ask our counterparty to post collateral assets (often cash and bonds) to cover the exposure. As discussed in chapter1, the exact rules are set in the Credit Support Annex (CSA)-agreement part of the master agreement of a derivative. Collateral is transferred in margin payments. Clearing members hold margin accounts where they keep margin payments received from counterparties. Collateral can be used by the counterparties for other activities, this is called rehypothecation. It is important that margin payments received from one counterparty are not reused to pay margin calls elsewhere. In figure2.3why this is the case: A B C IR S2 IRS 1 IRS3 C 1 C2 C3

Figure 2.2: Failure due to Rehypothecation of Collateral. Participant A received collateral from participant C over IRS1. Participant A posts this amount to B for a

similar contract it has with B. Unbeknownst to A, participant B too rehypothecates the same margin amount back to C. Should C default, neither A or B are protected

well: only 1

3 of collateral required is available in the system, and it is currently tied

up with the defaulting participant.

2.3.1 Variation Margin

Variation margin payments are calculated over differences in portfolio value at a

certain frequency. Between two counterparties, the variation in accounting value for all trades is aggregated and the variation margin payments are netted.

Suppose a trade we have with a counterparty goes in our favor, and this trade contributes significantly to their decline until they go into default. The more fre-quent we exchange variation margin, the lower the expected losses (equal to the expected difference over one margin period).

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2.3. Collateralisation

Figure 2.3: Illustrated example of loss in case of default. On t = 0 the counterparty defaults and the principal incurs losses equal to the change in value of the portfolio since the previous collateral transfer.

2.3.2 Initial Margin

In the case of a counterparty default, we most likely need to re-hedge our positions. We can repurchase the lost contract in the market, or we may need to sell of some positions. Either way, we need some time to re-hedge. The time we expect to need to close the portfolio is called the Margin Period of Risk. In figure2.3.2we see the relation between the initial loss (the loss incurred by the counterparty failing to pay Variation Margin (VM)). During the period thereafter we are still susceptible to market risk and therefore we also incur an additional loss.

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Figure 2.4: Margin Period of Risk. On top of the initial loss, initial margin is used to cover the losses incurred in the period after the counterparty default.

To cover the costs that are incurred during this period an additional IM is charged. This amount can be computed over a portfolio or netting set. Inside such a set, anti-correlated trades will reduce the variance of the set and therefore reduce the initial margin amount. Outside of these sets however, IMis never netted. Under the Basel III Accord IM becomes mandatory in any OTC-derivative transaction above a treshold [Basel Committee on Banking Supervision,2013].

Suppose we expect we need 5 businessdays to close a portfolio, we would com-pute Initial Margin as a function of the worst losses we expect during a 5 businessday period. This can be done empirically using historic data or using models and simu-lation. In chapter3we discuss a fast method to compute empiricalIM.

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2.4. Simulation

2.4 Simulation

Figure 2.5: EEis the mean exposure taken accross all simulated paths.

Figure 2.6: (Below) ThePFEis often computed as the 95% or 99% quantile of all simulated paths (here the 99% quantile is used). Note that the potential exposure is five fold that of the mean (expected) exposure.

Based on simulation we can build a model of the expected exposure we might have during a trade. Suppose we become the receiver on a 0.5M 5-Year swap: we exchange the difference between a fixed rate of 1% and the reference rate (6-Month Euribor) twice per year. Suppose we have enough historic data or a model of the floating rate (chapter 4), we can simulate many different realisations the floating rate can take in a 5-Year span. We want to simulate these paths in their entirety (day-by-day) as the payments exchanged on the swap depend on the rate near the

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different fixing dates. In figure2.4 we see the expected and potential exposures for this portfolio of a single receiver swap.

2.4.1 Value Adjustments

Using simulation we can tailor our contract to a specific counterparty. These adjus-tments to the price fall under the umbrella of value-adjusadjus-tments [Green,2015]. We may adjust the price based on what their credit rating is; we could such a rating from an external credit rating agency or by doing fundamental analysis (Credit Value-Adjustment (CVA)). Similarly we can price in the cost of allocating cash or bonds if we expect to post large amounts of collateral (Funding Value-Adjustment (FVA)). Although these adjustments are widely used in practice, they are out of scope for our simulation as it would require is to introduce many more variables: credit ratings, funding rates for the aforementioned value-adjustments.

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Initial Margin Calculation

3

Initial Margin (IM) is an additional post of collateral intended to cover the cost of

closing out a position in case of default. It is different from Variation Margin in that it is calculated for an entire set of trades and can not be netted.

3.1 Variants

Initial Margin is a function of the historic performance of the portfolio. Different variations and implementations exist: Value-at-Risk or Expected Shortfall are often used as risk measures. A central clearing party will use a combination of recent market data, historical stress-scenarios and optionally simulated scenarios in order to determine Initial Margin (A. Green: “XVA”). Different weighing schemes may be used, for example inverse exponential weighting to assign more weight to recent changes in the market.

In chapter 4 we will develop a model for interest rates and derive its variance. We could directly use the analytical expression for the variance in our IM calculation. However, we will not do this for several reasons.

Firstly, this is not how it works in practice: we can not assume the central clearing party to have perfect knowledge of the processes and parameters driving profits and losses, instead it must work with empirical data. Secondly, developing a framework for simulation in software, we want to develop a method that is as general as possible. Should we ever want to change our interest rate model to a process that has no easy analytical solution for variance, or maybe if we want to use historic rates we would have to rewrite our Initial Margin calculation.

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3.2 Online Algorithm

Our CCP will determine Initial Margin from the W most recent updates in the market. In essence, for every portfolio of trades the CCP is tracking, we keep a W sized sliding window. Every step in the simulation, we remove the oldest update, replace it with a new mark-to-market value of the portfolio, and calculate IM. The exact implementation of the algorithm can be found in the appendix.

3.2.1 Risk Measures

In order to adequately determineIMwe need a risk measure ρ(X) that, given an observed or simulated profit-and-loss distribution (X), tells us how much margin we should set aside.

3.2.2 Value-at-Risk

Value at Risk (VaR) is a common risk measure. The VaR at confidence level α is defined as:

VaRα(X) =inf{x ∈ R : P (X + x < 0) ≤ 1 − α}

=inf{x ∈ R : 1 − FX(−x) ≥ α}

(Value at Risk) In essence, theVaRat level α is equal to negative the quantile at (100%− α). 3.2.2.1 Criticism of VaR as a Risk Measure

[Artzner et al.,1998] defines four criteria for coherent risk measures.

Subadditivity : ρ(X) + ρ(Y )≤ ρ(X + Y ). A combination of two (or more) risky instruments in a portfolio should have a risk measure at least as high as the sum of risk measures of the constituents of the portfolio.

Translation Invariance ρ(X + n) = ρ(X) − n. Shifting the profit-and-loss distribution should equally shift the risk measure.

Positive Homogeneity ∀λ ≥ 0, ρ(λX) = λρ(X). Increasing the position size should increase the risk measure by the same scale.

Monotonicity X ≥ Y =⇒ ρ(X) ≤ ρ(Y ) For all possible realisations X, Y where

X ≥ Y , the risk measure maintains the ordering.

We will show by example thatVaRis not a coherent risk measure for the process that we use in our simulation.

In section ?? we will show that our chosen process is a stationary Gaussian process, and the expected distribution of differences is normal. However, as part

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3.2. Online Algorithm

of the experiments we increase the volatility during the simulation. This means that when we look at the history of generated interest rates during the simulation, we might observe the results from two distinct distributions:

Generalising to a more easily describable distributions, suppose we have to

inde-pendent and identically distributed variables X and Y that are distributed as follows:

=N (0, 1) +

{

0 (1− p)

N (0, 10) p (3.1)

Figure 3.1: Non-subadditivity of VaR. The parameter p refers to the probability of the rare event as described in equation3.1.

For particular values of p in equation 3.1 we find that subadditivity property is violated. In practice this means that using VaR as a risk measure exposes to a problem: in some scenarios the combination of several trades will have a lower expected exposure than the sum of all exposures of the trades measured indepen-dantly. The usage of VaR as a portfolio risk measure has therefore been widely criticised. Most notably [Taleb,1997] argues that V aR can be abused by traders as it is not a coherent risk measure. Traders and risk managers may combine and split up packages of trades at will in order to get the most favourable risk measure, because this risk measure determines their collateral requirements.

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Model

4

4.1 Interest Rate Models

We are interested in modeling the dynamics of interest rates for two reasons. Firstly, we want to generate realistic price dynamics for our interest rate swap contracts at different maturities. Secondly we need a mechanism to exert an exogenous shock on the system.

4.2 Rate Curves

The relation between the time to maturity T and a generic (annualised) rate r(t) form a rate curve. Since financial products have different structures there are diffe-rent curves for each product. For example, in the context of fixed income products such as bonds curve is often referred to as the yield curve, as the offered rates represent the return on the bond with maturity T as an investment. For interest rate swaps there is the swap-curve that represents the rate that makes the net present value of the swap zero. Note that since these product are different by nature and have different cashflows (structure), at a given time we may have multiple distinct rates (despite there being no arbitrage opportunities). In order to convert between the rates, we need an interest rate to discount a single future cashflow as we did with the zero rate in equationAccrual. However, there are no products which ofter this zero-coupon bond and we can not observe this rate directly. We must therefore construct this curve ourselves using the available rate curves of other products in a process called bootstrapping. Given the rates for our selection of products we let a solver find the zero rates. We chose the QuantLibFirth[2004] to help us with this, as it already contains the functionality to solve these types of systems.

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4.3 Historic Data

Figure 4.1: Historic Euro par-curve.

We construct a par curve for each day between 1999-04-01 and 2016-12-21. We construct a curve with tenors ranging from overnight out to 60 years. Because we do not have swap rates for all these tenors, and because the selection of swap maturity has changed throughout the years we must use different products to bootstrap our curve. The most important rates are the EONIA (Euro OverNight Index Average) fixings ranging from overnight to 6 months. Because we are going to use regression to fit a curve model, we can use rates that are indicative but do not actually represent tradeable contracts. For 7 to 11 months, 1 year and 1.5 years we use the Bloomberg Compound rates (EUSWG-EUSWK, EUSA1, EUSA1F); these rates are based on estimates from the Bloomberg trading platform. The remainder from 1 year to 60 years are all tradeableIRSs. The tickers used and the associated year fraction can be seen in table4.3.

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4.4. Applying the Model in Practice

Ticker year fraction Ticker year fraction

EONIA Index 1/360 EUSA8 Curncy 08.00

EUR001W Index 00.02 EUSA9 Curncy 09.00

EUR001M Index 00.08 EUSA10 Curncy 10.00

EUR002M Index 00.17 EUSA11 Curncy 11.00

EUR003M Index 00.25 EUSA12 Curncy 12.00

EUR004M Index 00.33 EUSA13 Curncy 13.00

EUR005M Index 00.42 EUSA14 Curncy 14.00

EUR006M Index 00.50 EUSA15 Curncy 15.00

EUSWG Curncy 00.58 EUSA16 Curncy 16.00

EUSWH Curncy 00.67 EUSA17 Curncy 17.00

EUSWI Curncy 00.75 EUSA18 Curncy 18.00

EUSWJ Curncy 00.83 EUSA19 Curncy 19.00

EUSWK Curncy 00.92 EUSA20 Curncy 20.00

EUSA1 Curncy 01.00 EUSA25 Curncy 25.00

EUSA1F Curncy 01.50 EUSA30 Curncy 30.00

EUSA2 Curncy 02.00 EUSA35 Curncy 35.00

EUSA3 Curncy 03.00 EUSA40 Curncy 40.00

EUSA4 Curncy 04.00 EUSA45 Curncy 45.00

EUSA5 Curncy 05.00 EUSA50 Curncy 50.00

EUSA6 Curncy 06.00 EUSA55 Curncy 55.00

EUSA7 Curncy 07.00 EUSA60 Curncy 60.00

Table 4.1: Tickers (Bloomberg) and year fraction used. The rates up to and including 6 months (EON IA through EU R006M are European Central Bank daily fixed interest rates. For 7 to 11 months, 1 year and 1.5 years we use the Bloomberg Compound rates (EU SW G− EUSW K, EUSA1, EUSA1F ). The remainder, starting from 2 up to and including 60 years are based on tradeable IRS.

4.4 Applying the Model in Practice

The exact development of the model is described in appendix C. Using the yield curve generated by this model, we can price swaps with arbitrary start dates and end dates. As the simulation steps from day to day, we can find the zero rates at arbitrary points in the future since the Nelson-Siegel is defined everywhere in the domain from overnight to 60 years, not just at the points where we have a quotes. We will see however in the results in chapter5.6that the typical simulation only lasts for a small number of steps, typically less than 50. During this time, the effect of the payments coming closer and closer on the curve is negligible. Therefore we can simplify the pricing of the derivatives in the simulation. Rather than computing arbitrary points on the curve, we assume fixed and floating payments of equal frequency and only compute the points at specified intervals (yearly). This way, we can use the

annuity formulaA.3.3from chapterA. For example, a swap with a tenor of 10 years,

this only requires a summation over 10 elements. The alternative is to compute a portfolio of hedges against the same curve; for every payment at tenor t we hedge with a swap with maturity t. This results in n swaps that need to be priced which

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would take n + (n− 1) + (n − 2) . . . + 2 + 1 = n(n2−1) =O(n2)steps. In practice

the most common swap tenors are 5,10,2,3,4 years [DTCC SDR]. The additional accuracy provided by the Svensson term in figureC.6, which introduced a second bump with a peak at 6 months, therefore provides little extra accuracy since the points between overnight and 1 year will not be used in pricing the swaps. It seems prudent therefore to use the simpler Nelson-Siegel model. Should the simulation be expanded to use more accurate pricing of payments over the short end of the curve (overnight to 1 year), the Nelson-Siegel-Svensson model and the aforementioned computation of a portfolio of hedges should again be employed.

4.5 Simulated Term Structure

Using the mean-reverting process we can now simulate our term structure. The final step is then to build the swap curve from these rates. Using the parameters obtained for the Nelson-Siegel (NS)-model in appendix A.1 we generate a sample that is displayed in figure4.5.

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4.6. Interbank Network

4.6 Interbank Network

A detailed study on the structure of the Dutch Interbank System can be found in

in ’t Veld and van Lelyveld[2014]. The authors are able to fit a core-periphery to data made available by the Dutch regulator. These types of datasets are not available to the general public and may still by anonimised by the reporting institutes. From anonimised data, the ensemble networks structure may still be reconstructed using techniques such as [Squartini et al.,2016].

The Centre and periphery structure was first described by Raúl Prebisch [Prebisch,

1950]. These types of structures arise in economic systems as a consequence of specialisation and can be reinforced by regulation. We model the interbank network as a discrete core-periphery structure. The core-periphery model is used to describe two types of vertices: those vertices in the well-connected core and the only sparsely connected periphery.

Given a required system size V = Vcore+ Vperipheryand a Markov

connectivity-matrix C, we want to construct a connected graph that represents the interbank network. A perfect core-periphery has three properties:

1. The core of the network is completely connected

2. Periphery vertices are connected to a minimum of one and strictly less than all core vertices.

3. There are no edges between periphery vertices.

When we use this model for real-world networks that are not idealised

core-periphery graphs and calculate the connection probabilities, we may introduce an

error term ϵ to denote the occurrence of violations of property (3). The independent probability by which periphery vertices are connected to the core is denoted with p.

C = (C P C 1 p P p ϵ ) (4.1)

4.7 Construction

We need to generate one random core-periphery network for every sample we ge-nerate. This can be costly: the number of edges to generate can grow rapidly (quadratically) with the number of vertices in the graph. In a complete directed graph (all edges realised) there are V (V − 1) = O(V2) edges; we do not allow

self-loops. A naive implementation enumerates all possible vertex pairs (vi, vj and

decides probabilistically to accept or reject an edge between these vertices. This would take exactly V (V − 1) steps. We aim to reduce the number of operations below this to construct the graph as a core-periphery graph does not have near this

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C C C C C C P P P P P P P P P P P P P P P P P P P P P P P P P P P P P P P P P P −1.00 −0.75 −0.50 −0.25 0.00 0.25 0.50 0.75 1.00 Exposure / Normalised

Figure 4.3: A sample core-periphery network. Note that although the graph is a directed multigraph, Vertex size represents sum of all notionals of contracts held. Edge thickness represents the notional of that specific contract.

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4.7. Construction

amount of edges. The expected number of edges for the core-periphery graph is given by:

E [|V |] = VC(VC− 1) + pVCVP + ϵVP(VP − 1) Expected number of edges

From equationExpected number of edgeswe find that when the core is small and the connection probability p is low, the graph will be sparse, and we can save time constructing the graph if we manage to only evaluate the pairs that will make up an edge in the final graph.

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4.8 Clearing

The term clearing covers all efforts to resolve obligations between counterparties with the main goal of reducing counterparty risk. Clearing services are offered by entities tied to exchanges or other financial services providers. These services are offered for the entire lifetime of the trade: from trade execution to settlement.

4.9 Payment Netting

If traded contracts contain the obligation to pay in a specific period, the payments may be netted such that only the differences needs to be transferred. The required amount of funds is reduced, leading to lower funding costs.

4.10

Trade Compression

When contracts have a similar structure they can often be combined. The contrac-tual obligations can be netted when the timing coincides. Whether the contracts are offsetting and can be reduced, or conversely are combined into a larger single contract, trade compression has the additional benefit of reducing administrative over-head.

4.11

Bilateral Clearing

Bilateral clearing is the default method of clearing in our simulation. Counterparties agree on an accounting method (such asMtM) and make frequent collateral pay-ments. Payments over multiple contracts between the same two parties are netted.

4.11.1 Netting

A B

3 2

Figure 4.4: Parties A and B are to exchange payments worth 3 and 2 in the same currency.

A 1 B

Figure 4.5: Bilateral netting of two payments, with net payment (A, B) = 3− 2 = 1.

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4.12. Central Clearing

4.11.1.1 Multilateral Netting

Bilateral clearing can be performed with more than two parties in so-called

clearing-rings. A B C IR S 1 IRS 2

Figure 4.6: Three parties agree to engage in multilateral netting on the payments over twoIRS.

A

B IRS1 C

Figure 4.7: Bilateral clearing requires the involvement and consent of all parties involved.

4.11.2 Default

A counterparty goes into default when it can not make a complete margin pay-ment for all contracts. In the short term, this means that all contracts where the counterparty in default needs to post collateral are torn up. The principal to the contract incurs a loss equal to the cost to immediately replace the contract minus the collateral it holds. The more frequent (and recent) collateral payments were made before default, the closer the collateral amount held by the principal will be to the replacement cost.

4.12

Central Clearing

With central clearing all clearing operations can be handled by the central clearing party. For our simulation we will assume that theCCPwill optimally compress all trades and net all payments.

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4.12.1 Novation

CCP

A IRS B

Figure 4.8: Party A sells a new contract (IRS2) to party B, or has an existing contract that both parties choose to backload to theCCP.

CCP A B IR S 2 IRS 2

Figure 4.9: Novation: theCCPinitiates new contracts between itself and parties A and B.

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4.13. Portfolio Transfer

4.12.2 Compression by Novation

CCP A B IRS 1 IRS2

Figure 4.10: Party A already has one contract (IRS1) centrally cleared. Party A then sells a new contract (IRS2) to party B, or has an existing contract that both

parties choose to backload to theCCP.

CCP A B IR S 2 IRS 1 IRS 2

Figure 4.11: Novation: theCCPinitiates new contracts between itself and parties A and B. CCP A B net(I RS 1, I RS 2) IR S 2

Figure 4.12: Novation netting: where possible, contracts between clearing members andCCPare netted.

4.13

Portfolio Transfer

When a participant defaults under central clearing rules, trades under central clea-ring agreements are transferred to the respectiveCCPs.

4.14

Auction

After transfer to the CCP the portfolio needs to be closed. The CCP still has obligations to the original counterparty of the defaulting clearing member (before

novation). If it is not able to transfer the portfolio of the defaulting clearing member

it will have a remaining exposure. TheCCPhas several tools to close the portfolio: • Selling the portfolio whole or in part by means of an auction.

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• Assign healthy clearing members to take over (part) of the portfolio.

• Voluntary tear-up of the contracts over which theCCPhas remaining expo-sure, paying a settlement to the affected counterparty International Swaps and Derivatives Association[2013].

It is expected that the revenue from the auction is lower than the CCP: since the CCP must close its positions as soon as possible, and there is little demand for a (previously) very risky portfolio, it is willing to let go of the contracts at prices below market value. CCPs may have mechanisms to motivative clearing members to take part in the auction, making it more likely that the auction will be successful and the CCP is able to close the portfolio. For example, it may allocate losses on those clearing members not making competitive bids.

4.14.1 First-Price sealed-bid auctions

In a First-Price sealed-bid auction, all participants submit a single bid and the lot is awarded to the highest bidder. Note that in the case of financial contracts, the estimated value of the contracts can be negative and therefore the auctioneer (CCP) will make an additional payment.

We can not model all the motivations that may contribute to a specific bid. Rather, we assume all participants V , whose total exposure can be reduced by pur-chasing the contract, drive the bid closer toMtMvaluation with ratio (11+1|V |).

Input: Contract c, currency i, clearing members V

Output: Clearing member to take the contract, Allocation of losses

I :=

for v ∈ V do

if |exposure(v, i) + c| ≤ |exposure(v, i)| then

I := I ∪ v end end if |I| > 1 then bid:= (1 1 1+|V |)PM tM winner:= selectRandom(I) lossAllocation := max(0,PM tM−bid)

|V |−1

return winner, lossAllocation else

Forcefully transfer the contract to one of the participants assignee:= selectRandom(V )

lossAllocation := PM tM

|V |

return assignee, lossAllocation end

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4.15. Default Waterfall

4.15

Default Waterfall

A Default Waterfall describes a recovery plan when losses are incurred as a result of one or more defaults. More formally it is a protocol which describes how losses to aCCPare mutualised among its clearing members. It also describes

Default Waterfall

Initial Margin (defaultee)

Default Fund Contribution defaultee CCP Capital and Reserves

Default fund

Powers of assesment

Table 4.2: A generic default waterfall for a CCP. Central clearing parties may have different implementations for different products and markets. Loss Allocation

Methods include all methods that can be used after the fact to recover the losses the

CCPmade during the closing process.

Table 4.15 describes a generic default waterfall. A CCP active in multiple markets and instruments may have different variations for each product. Variations include different maximum claims on CCPCapital and Reserves, separate default funds for different products, and different choices for loss allocation.

4.15.1 Loss Allocation

When all prefunded resources (collateral and default fund) are exhausted, theCCP

can still continue its services for the affected products. It has multiple tools to recapitalise the fund and resume services at a later time. A Central party may do this by mutualising the losses among their healthy (remaining) members.

4.15.2 Moral Hazard

A possible consequence of high loss mutualisation is the occurrence of moral hazard. When clearing members still obtain the full upside of a trade when it goes their way, and can share the losses with all clearing members when the trade goes wrong, they are tempted to initiate more risky trades.

4.15.3 Variation Margin Haircut

To this end, aCCPmay apply haircuts to future variation margin payments in the market sectors affected by previous defaults. Typically this is applied only to those clearing members who have accumulated (net received) variation margin since the original clearing member defaulted. This way, only those members active in this

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market will share the cost of the default. Moreover, as haircuts are announced in advance and members may have time to reduce their activity in these markets, it is argued this may dampen a volatile market. This is referred to as Variation-Margin

Gains Haircutting (VMGH). There is evidence from empirical data that suggest

Lewandowska and Glaser [2017] however that VMGH does not make clearing members consistently drop these assets from their portfolios. In our model we do not incorporate Variation-Margin Gains Haircutting (VMGH) as we are only interested in directed consequences of a default cascade and the method by which theCCPrecapitalises its fund is out of scope.

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4.16. Computation

4.16

Computation

The rules for clearing and the resulting changes in the interbank system are not easily described analytically. In our experiments we observe complex behaviour: the system is sensitive to its initial conditions. A single realisation from a model of interest rates will not tell us enough to make an informed decision on which method of clearing leads to better stability. This chaotic behaviour also cautions us when we want to evaluate an exact scenario. Should we want to compare methods of clearing for an actual interbank system on which we have data, we need to be careful asses our ability to model the current state.

As with the exact realisation of interest rates, we assume other dynamics in the system such as the result of an auction or the exact sequence in which participants are declared insolvent to be subject to randomness. For these reasons, if we want to make a distinction between the two methods of clearing we should be comparing the loss distributions between two large populations of random samples. Depending on the type of analysis we are doing we would then compare mean, variance or quantiles of the simulated loss distributions.

4.17

Infrastructure

Since the required samples are all independent, we can easily distribute our com-putational task across multiple processors. In determining the type of hardware suitable for these computations we need to take into account the following aspects. Initial testing revealed that the time to compute a sample has high variance. The simulation itself has highly branching logic as a result of all the different rules for clearing and payments. Thirdly, a single simulation has relatively few data: the largest datastructures are the adjacency matrix of the interbank network and the historic performances of portfolios. Both these datastructures sizes are dependent on the size of the system, and with tests in the range of 20 ≤ N ≤ 400 these are quite small. For these reasons we choose to target the CPU rather than targeting the GPU.

4.17.1 Cluster

Our cluster consists of two servers each with two CPU sockets for a combined 40 processor cores and 128GB of memory. The four CPUs support simultaneous

multithreading and therefore we run up to 80 simulations in parallel. Figure4.17.1

shows the data flow

The machines are connected using Infiband QDR high performance networking. The communication between workers is facilitated by Message Passing Interface (MPI) and automatically uses in-memory communication or the high performance network.

(54)

Storage consists of a high-throughput Non-Volatile Memory Express drive loca-ted in one of the machines. Simulation results are stored in a simple record format and can be immediately used in analysis. The same machine hosts a Jupyter No-tebook webserver, a programming environment to write data-analysis in a various programming languages, that can be accessed from outside the cluster.

Communication

Scheduler Storage Analysis

Worker Worker

task complete result

task result task result

Figure 4.13: Data Flow in computing infrastructure. The worker processes are located on different physical machines.

4.18

Scaling

Figure 4.14: Strong and weak scaling of computational framework. Left: (Strong Scaling) for a fixed problem size, the mean time per sample for a varying number of process threads. Right: (Weak Scaling) for a fixed number of process threads, the mean computation time for increasing numbers of samples.

The cluster has 40 physical cores and uses symmetric multiprocessing to run an additional 40 threads in parallel with low overhead. This explains in part the increase of computational time for 64 threads seen in the Strong Scaling plot in figure5.1.1.1.

(55)

4.18. Scaling

Another contributing factor is the increased intensity of communication when more threads run in parallel.

(56)

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