The Network of Counterparty Risk: Analysing Correlations ...

Vahan Nanumyan, Antonios Garas, Frank Schweitzer:The Network of Counterparty Risk: Analysing Correlations in OTC Derivatives,

published in PLoS ONE 10(9), e0136638. doi: 10.1371/journal.pone.0136638

The Network of Counterparty Risk:Analysing Correlations in OTC Derivatives

Vahan Nanumyan, Antonios Garas, Frank Schweitzer1

Chair of Systems Design, ETH Zurich, Weinbergstrasse 58, 8092 Zurich, Switzerland

Abstract

Counterparty risk denotes the risk that a party defaults in a bilateral contract. Thisrisk not only depends on the two parties involved, but also on the risk from various othercontracts each of these parties holds. In rather informal markets, such as the OTC (over-the-counter) derivative market, institutions only report their aggregated quarterly risk exposure,but no details about their counterparties. Hence, little is known about the diversification ofcounterparty risk. In this paper, we reconstruct the weighted and time-dependent networkof counterparty risk in the OTC derivatives market of the United States between 1998 and2012. To proxy unknown bilateral exposures, we first study the co-occurrence patterns ofinstitutions based on their quarterly activity and ranking in the official report. The networkobtained this way is further analysed by a weighted k-core decomposition, to reveal a core-periphery structure. This allows us to compare the activity-based ranking with a topology-based ranking, to identify the most important institutions and their mutual dependencies.We also analyse correlations in these activities, to show strong similarities in the behavior ofthe core institutions. Our analysis clearly demonstrates the clustering of counterparty risk ina small set of about a dozen US banks. This not only increases the default risk of the centralinstitutions, but also the default risk of peripheral institutions which have contracts with thecentral ones. Hence, all institutions indirectly have to bear (part of) the counterparty risk ofall others, which needs to be better reflected in the price of OTC derivatives.

Introduction

After the financial crisis of 2008 the systemic risk resulting from OTC (over-the-counter)derivatives has become an important topic of public debate and scientific research. Differ-ent from exchange-traded derivatives, OTC derivatives are traded on non-regulated marketswhich have grown both in size and importance during the last decade. In December 2008 theBank for International Settlements (BIS) reported (see Semiannual OTC derivatives statisticsat http://www.bis.org) that total notional amount on outstanding OTC derivatives grew upfrom 370,178 bn USD in June 2006 to 683,725 bn USD in June 2008, i.e., it almost doubled insize in only two years.

1Corresponding author: [email protected]

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A particular worrying feature of this development results from the increasing concentration ofthe counterparty risk of OTC derivatives in the hands of only a few institutions. This trend hasnot changed after the financial crisis of 2008, on the contrary the concentration increased.

Taking the example of the US alone, in the 4th quarter of 1998 contracts totaling 331 bn USDwere signed by 422 commercial banks and trust companies which where not listed in the top25 institutions dealing with OTC derivatives. This numbers have to be compared against thecontracts totaling 32,668 bn USD (i.e., a hundred times more) signed by only the top 25 insti-tutions in the OTC derivatives market. Comparing this to the time after the financial crisis, thedifference became much bigger. In the 1st quarter of 2012 the 25 top ranked US institutions heldcontracts totaling 227,486 bn USD (i.e., almost ten times more than in 1998), whereas all otherinstitutions held contracts totaling only 496 bn USD (which is almost comparable to what washeld in 1998). Hence, we observe an extreme concentration of derivatives market where the shareof derivative contracts held by the top 25 institutions was almost 99% in 1998 and increased tomore than 99.5% in 2012.

This increasing concentration may also increase the vulnerability of the institutions involvedand can lead to cascades in case of default. Until now, no concentration of exposure againsta particular counterparty is reported by banks. The Basel Committee on Banking Supervisionreferred to this issue for the first time only in its report of March 2013 [1].

In our paper, we address the problem in a twofold way. Based on a dataset of the 25 most activeplayers in the U.S. derivative market, over a period of 14 years, we reconstruct the network ofcounterparty risk. We show that this risk generates an almost fully connected network of inter-dependence among these players, however it is skewly distributed, i.e., most of the counterpartyrisk is concentrated in only 10 mayor institutions. This implies two problems: in a fully connectednetwork, it becomes much more difficult to hedge the risk of default, because every player is acounterparty of any other. This may increase the risk of default cascades, which can be amplifiedby the particularly active counterparties. Additionally, the concentration of counterparty risk ina few institutions may exacerbate the problem of contagion and financial distress in the wholenetwork if those institutions become distressed.

OTC Derivatives

The role of derivatives

Derivatives are financial instruments, i.e., they are tradable assets. Importantly, they have nointrinsic value. Instead, their value depends on, or is derived at least partly from, the valueof other entities, denoted as the “underlying”. These can be other assets such as commodities,stocks, bonds, interest rates and currencies, but, dependent on the complexity of the financial

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product, the underlying can be almost anything that deemed to have an intrinsic value. Thisimplies that socio-psychological issues such as “confidence”, “faith” or “trust” play an importantrole in defining those values.

Formally, derivatives are specified as contracts between two parties. Such contracts define howthe value of the underlying is estimated at particular future dates and what conditions have to befulfilled for payments between these parties. Because parties do not need to own the underlying,derivatives make for an ideal instrument to speculate about the future rising or falling valueof underlyings or to hedge against the risk associated with it, provided that a counterparty iswilling to bet on this.

Trading derivatives basically means to find a counterparty for the contract. Importantly, partiescan trade derivatives in two different ways, in regulated markets specialized in trading deriva-tives (ETD, exchange-traded derivatives) or privately, without involving an exchange or otherinstitutions (OTC, over-the-counter derivatives). Although OTC markets are usually well orga-nized, they are less formal. In particular, there is no central authority which would regulate theconditions of the derivative contracts or would control the fulfillment of these conditions.

OTC derivatives are usually preferred over the exchange traded ones because taxes and otherexpenses are lower and they are much more flexible, meaning that the counterparties can agreeon very specific or unusual conditions as opposed to the limited set of derivative types designedand operated by an exchange. As a trade-off for flexibility and the possibility of higher earningsOTC derivatives bear significant additional risks as compared to the exchange traded ones.

Risk involved in OTC derivatives

Derivatives are generally used to hedge risks, but derivatives themselves are a source of risk.These are credit risk and market risk, along with liquidity, operational and legal risks [2]. Incase of OTC derivatives, credit risk is the main source of risk because of the usual absence ofa clearing house that guarantees the fulfillment of obligations between parties. Thus, the twocontracting parties are exposed to counterparty default risk, i.e., the risk that a counterparty willundergo distress, or even default prior to expiration of the contract and thus will not make thecurrent and future payments. In contrast to lending risk, to which only the party which lends isexposed, both sides involved in OTC contract are exposed to counterparty risk. To have somesort of mitigation, the parties involved in OTC derivatives are usually banks which act on theirown behalf or on behalf of their clients.

There are different ways to mitigate counterparty risk in case of default. For example, usingclose-out netting agreements allows that all contracts are netted, eliminating the possibility ofselective execution of contracts [3]. For bilateral close-out netting, which mostly applies to OTCderivatives markets, the two parties agree to net with one another, i.e., to set off gains and losses

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from all of their bilateral contracts. This differs from the case of multilateral close-out nettingwhich mostly applies to ETD, i.e., to markets where all parties’ obligations are netted together.In both cases, netting is only a procedure to follow after a default and thus does not address theemergence of counterparty risk.

It is obvious that netting decreases credit exposure, as it takes into account only the net obli-gations, thus reducing both operational and settlement risk and operational costs. In order toknow the risk, the present value of contracts, prior to their contracted termination, has to bedetermined. Outstanding contracts are marked to market, taking into account the replacementcosts, i.e., the loss suffered by the non-defaulting party in replacing the relevant contract. This as-sessment of credit exposure at a single point in time is denoted as current credit exposure (CCE).However, derivative contracts usually have considerable lifetimes and are very often character-ized by fast and large changes in credit exposure. Therefore, the potential future exposure (PFE)is used to estimate the possible CCE increase over a fixed time frame. These estimates are, ofcourse, predictions that depend on the choice of financial models and corresponding confidencelevel. The total credit exposure (TCE) is then measured as the sum of CCE and PFE, followingthe Basel I framework. In Section Correlations in risk we will use the TCE values reported byfinancial institutions to estimate correlations in their risk.

Whereas netting agreements work in the absence of clearing houses, recent developments try tomitigate counterparty risk by means of central counterparty clearing houses (CCPs) [4]. In thepresence of a CCP a bilateral contract between two counterparties is substituted by two contracts,so that the CCP stands between the two contracting parties. This allows for more transparencyand for multilateral netting, which can facilitate the reduction of both counterparty and systemicrisk. Although involvement of a CCP was previously required in contracts for credit default swaps(CDS) [5], a special class of derivatives, its broader utilization can be seen as a reaction to thefinancial crisis of 2008.

However, regulations requiring CCPs in all standardized types of OTC derivatives are either new,e.g. the US Dodd-Frank Act from 2010, or are still being developed. Therefore, their impact onOTC derivatives markets is not well known yet, both empirically and theoretically. [6] recentlyattempted to shed some light on the possible systemic effects from CCPs. They performed atheoretical investigation of cascading effects and systemic risk in different financial networkswith one or two CCPs.

One may argue that not considering the role of CCPs in OTC derivatives networks is a limitationof this paper. But one should bear in mind that we analyse data ranging from 1998 to 2012,i.e., most of the time CCP were not required, and not reflected, in the OTC data. To keep ourmethods consistent for the whole time period, we neglect the possible (but not documented)presence of CCPs. Moreover, even today it is not known whether the wide adoption of CCPs will

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succeed in making the OTC derivatives network entirely transparent. So our methods to inferundiscovered and potentially dangerous links of the network may still be needed in the future.

Clustering of counterparty risk

In this paper, we discuss a particular risk involved in OTC derivatives, namely the clustering ofcounterparty risk. While counterparty risk itself is already difficult to estimate, it becomes evenmore tedious for a party to find out about the additional risk that a counterparty bears becauseof it’s involvement in other OTC derivatives. The problem is illustrated in Fig. 1. It shows nineinstitutions that have in total ten different OTC contracts. The width of the links shall indicatethe volume of these contracts, i.e., the three institutions 1, 2, 3 in the center (indicated by thedashed line) form a fully connected cluster of strongly engaged institutions. What is their implicitimpact on those institutions outside the center? Each of these has only one contract with one ofthe major institutions in the center and is likely not aware of the whole structure of the networkof OTC derivatives.

5

4

8

6 7

3

1

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Figure 1: Schematic illustration of the exposure clustering.

There is a two-step scenario to increase the risk of the different institutions: (i) Transfer of riskfrom the outer institutions to the central counterparty: Institution 4 is probably not aware thatits counterparty 1 also has contracts with institutions 5 and 6. If one of these outer institutionsdefaults, this puts an additional risk for institution 1 to default, which is likely not accountedfor in the OTC contract between 4 and 1. Additionally, institutions 4 and 5 also have a contractwhich is likely not known to institution 1. Thus, the default of either 4 or 5 increases the riskfor the remaining one, which indirectly increases the risk for institution 1 [7]. (ii) Increase ofrisk between central institutions: Because the center institutions form a fully connected cluster,if one of these undergoes distress or even defaults this immediately affects the other two coreinstitutions. This in turn affects the outer institutions.

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In conclusion, because of the strong coupling of the center institutions, which we call clusteringof counterparty risk here, all institutions indirectly have to bear (part of) the counterparty riskof all other institutions in the network. This should be priced in their OTC derivatives, buteffectively it is not because that would imply to know (a) all the links and (b) all their weightsor, in plain words, all the OTC contracts made. But, as explained above, the existence of OTCderivatives is precisely because such information should not be made publicly available. As wewill see from the data, all public information only refers to the total amount of OTC derivativesfor each institution, but not to their counterparty network.

This sets the stage for our paper. Even in the absence of official information about the networkof counterparty risk, we want to derive some insights into its structure, from a dataset describedin the following. Specifically, we want to derive a proxy for the structure of this weighted, andtime dependent, network. Further, we want to estimate correlations between OTC derivatives,i.e., infer on possible counterparties from the co-movement of the engagement of institutions.

The Network of OTC Derivatives

Activities and Ranks

In order to reconstruct the network of counterparty risk from the available dataset, we need tointroduce a few variables that are later to be mapped to specific data.

First of all, we identify each institution in the dataset by an index i = 1, ..., N , where N = 61,i.e., the total number of distinct institutions. Note that the dataset for each quarter only lists the25 best ranked institutions, which are not necessarily the same for each quarter (see also Fig. 2).Thus, during the whole period of 14 years, 61 different institutions appeared in the dataset.

At each time step t, where t is discrete and measured in quarters, up to T = 57, institutions iand j can act as counterparties, i.e., they have contracts of total volume xij(t). Importantly, thedataset neither lists the counterparties j nor the volume of their contracts, xij(t). It lists, however,the quarterly activity of each institution, ai(t) =

∑Nj=1 xij(t), i.e., the aggregated volume, given

in column 5 of Table A in Supporting Information Thus, the aim of our paper is to reconstructthe network of dependencies from this aggregated data. Note that, if an institution was not activein a particular quarter, i.e., not listed in the dataset for that period, its activity is set to zero.

To give an example, Fig. 3 shows the activity of two banks that are consistently engaged inOTC derivatives in every quarter. Impressively enough, their activities differ in about two ordersof magnitude and further show a different business strategy over time. While the quarterlyactivity of Keybank remains almost constant over 12 years, the activity of Bank of America grew

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BANK OF AMERICAJPMORGAN CHASE BANKCITIBANKHSBC BANK USAWELLS FARGO BANKWACHOVIA BANKSTATE STREET BANK&TRUST COBANK OF NEW YORKPNC BANKSUNTRAST BANKKEYBANKNATIONAL CITY BANKNORTHERN TRUST COMELLON BANKU S BANKDEUTSCHE BANK TR CO AMERICASLASALLE BANKBANK ONEFLEET NATIONAL BANKFIRST TENNESSEE BANKGOLDMAN SACHS BANK USAFIFTH THIRD BANKREGIONS BANKBRANCH BANKING&TRUST CONATIONAL CITY BANK OF INMERRILL LYNCH BANK USABANK OF NEW YORK MELLONLASALLE BANK MIDWESTUNION BANKCHASE MANHATTAN BANKMORGAN GUARANTY TR CO OF NYFIRST UNION NATIONAL BANKMORGAN STANLEY BANKCAPITAL ONERBS CITIZENSTD BANKCHASE MANHATTAN BANK USAALLY BANKHUNTINGTON NATIONAL BANKCOMERICA BANKTD BANK USAUBS BANK USABANKBOSTONFIRST NB OF CHICAGOCITIBANK SOUTH DAKOTANATIONSBANKREPUBLIC NB OF NEW YORKIRWIN UNION BANK&TRUST COCHASE BANK OF TEXASBMO HARRIS BANKBOKFBANK OF OKLAHOMALEHMAN BROTHERS COML BKCOUNTRYWIDE BANKSTANDARD CHARTERED BANK PLCFREMONT INVESTMENT&LOANCITIBANK NEVADAFLAGSTAR BANK FSBFIA CARD SERVICESGMAC BANKWOODLANDS COMMERCIAL BANK

1 5 10 15 20 25

Figure 2: Time series of the financial institutions appearing among the 25 top ranked between1998 and 2012. Color codes the rank: the darker the color the better the rank (rank 1 consideredthe highest), white indicates the absence in the ranking.

exponentially during the same period of time, clearly shown in the linear slope in the logarithmicplot. Only in 2012, after the financial crisis, this involvement was slightly reduced.

Based on the quarterly activities, ai(t), we can assign each institution i a rank ri(t) ← r[ai(t)]

with r discrete and r ∈ {1, 2, ...N} such that r[ai(t)] < r[aj(t)] if ai(t) > aj(t) for any pairi, j ∈ N . I.e., rank 1 corresponds to the institution with the highest activity value at time t, rank

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1999 2002 2005 2008 2011

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KEYBANK

Figure 3: The total derivatives notional amount of two banks which constantly appear duringthe whole period from 1998 to 2012. The difference of order of magnitude motivates to takeinto account the ranks of institutions when building their network. The linear regression slopefor log(aBoA) for the period 1999/Q3 – 2011/Q3 (bolder line) is 0.206638, which corresponds toyearly growth ratio (at(t+ 1)/ai(t)) equal to 1.229537.

2 to the one with the second highest activity, and so forth. If an institution was not active in agiven period, its rank is set to zero. Because the rank ri considers the position relative to otherinstitutions, it can change even if the activity of an institution remained constant over a certainperiod.

Fig. 2 gives an overview of how often the institutions were present in the ranking up to 25 inany of the quarters, with their ranks color coded. This matrix already indicates that there areremarkable fluctuations in the ranks of most of the institutions, except for a group of about 10institutions. Fig. 4 gives a more detailed picture by plotting the ranks of this group over time. Weobserve that there exists a smaller core group (of about 7 members) with consistently low ranks,which can be well separated from a second group with higher, and more fluctuating, ranks.

This can be also observed by looking at the ranks Ri ← r[Ai] resulting from the aggregatedactivities Ai =

∑Tt=1 ai(t). Plotting the inverse function A(R) shown in Fig. 5, we observe a

rather skew distribution of the aggregated activities with respect to the rank, with a skewnessvalue γ = 4.637150 and a Gini coefficient [8] g = 0.9558996. Moreover, the plot suggests that

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1999 2002 2005 2008 2011

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0.00 BANK OF AMERICA0.00 JPMORGAN CHASE BANK0.00 CITIBANK0.00 HSBC BANK USA0.00 WELLS FARGO BANK0.00 WACHOVIA BANK0.00 STATE STREET BANK&TR0.00 BANK OF NEW YORK0.00 PNC BANK0.00 SUNTRAST BANK0.00 KEYBANK0.25 CHASE MANHATTAN BANK

Figure 4: Changes of the ranks ri(t) of a set of banks, with the number showing their dis-tance to the core of the weighted network based on the co-occurrence and activity of financialinstitutions introduced in Temporal and aggregated networks.

the aggregated activity A follows a log-normal distribution with respect to the rank R:

A(R) =1

Rσ√

2π· exp

[−(lnR− µ)2

2σ2

]; R ≥ 1 (1)

where µ = 14.54116 is the mean value and σ = 2.865165 the standard deviation of the distribu-tion. To further compare the empirical with the log-normal distribution, Fig. A in SupportingInformation shows the Q−Q plot and gives the results of the two-sample Kolmogorov-Smirnovtest.

The inset of Fig. 5 presents the cumulative distribution P (R < Y ) =∑Y

R=1A(R). It indicatesthat about 95% of the total activity results from the seven first ranked institutions, while the 15first ranked institutions cover more than 99% of the total activity. It may be tempting to restrictthe analysis to only these 15 institutions. However, the aggregated activities do not allow to drawconclusions about the concentration of activities in certain time periods or a change of strategyin choosing counterparties, before and after the financial crisis. Therefore, we will present moredetails on the temporal activities in Section Temporal and aggregated networks.

The available data also allows us to analyse the composition of the activities ai(t) with respect toexchange traded derivatives (ETD) and OTC derivatives. I.e., the value of the total derivatives

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32 LASALLE BANK MIDWEST33 FIRST TENNESSEE BANK34 UNION BANK35 RBS CITIZENS36 MERRILL LYNCH BANK USA37 TD BANK38 BANKBOSTON39 REPUBLIC NB OF NEW YORK40 CAPITAL ONE41 CHASE MANHATTAN BANK USA42 ALLY BANK43 TD BANK USA44 HUNTINGTON NATIONAL BANK45 UBS BANK USA46 STANDARD CHARTERED BANK PLC47 COMERICA BANK48 BOKF49 BMO HARRIS BANK50 CITIBANK SOUTH DAKOTA51 BANK OF OKLAHOMA52 COUNTRYWIDE BANK53 LEHMAN BROTHERS COML BK54 CHASE BANK OF TEXAS55 GMAC BANK56 FLAGSTAR BANK FSB57 WOODLANDS COMMERCIAL BANK58 IRWIN UNION BANK&TRUST CO59 FIA CARD SERVICES60 CITIBANK NEVADA61 FREMONT INVESTMENT&LOAN

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Figure 5: Distribution of the aggregated activity Ai over the rank Ri obtained from the wholereporting period. (inset) Cumulative sum P (R < Y ) =

∑YR=1A(R). The ceiling of the distri-

bution, which is the capacity of the market over the whole period of time is shown by the greyline, while the orange line shows the corresponding 95% percentile.

is split into ai(t) = aETDi (t) + aOTC

i (t) and Ai = AETDi + AOTC

i , respectively. Already the sheernumbers of the ai(t) and aOTC

i (t) tell that OTC derivatives make up for the vast amount ofcontracts. I.e., we should not assume that the ranks ri(t) or Ri obtained from both ETD andOTC derivatives are different from those ranks that would result from only considering the valuesof aOTC

i (t) or AOTCi . To test this hypothesis, Fig. B in the Supporting Information provides a

Q−Q plot to compare both values. We see that up to rank 15 there is no difference in the ranksobtained by these two measures, whereas between ranks 15 and 50 the difference in ranks wouldbe 1 or 2. Only for ranks above 50, the differences become remarkable. So it is reasonable to usethe ranks ri(t) and Ri in the further evaluation.

However, when analysing the counterparty risk in derivative contracts, we will make a distinctionbetween the (less risky) ETD and the more risky OTC derivatives. In fact, as Fig. 6 indicates,the importance of OTC derivatives as compared to the ETD vastly differs across institutions.The ratio AOTC

i /AETDi is below 10 for about 1/3 of all institutions, which implies that 10% or

more of the activities is in ETD. However, looking at the 15 best ranked institutions, we seefor most of them the ETD business accounts for only 2%-5% of their activity. So again, it is

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reasonable to proxy activities related to OTC derivatives by the total activities - but wheneverpossible, we will take into account the real values for OTC derivatives.

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Figure 6: Ratio AOTCi /AETD

i versus ranks Ri based on the total activity Ai.

Temporal and aggregated networks

In order to estimate the link structure of the network of counterparty risk, we first look intothe co-occurrence of any two institutions among the 25 best ranked institutions in each givenquarter. I.e., we define a link as lij(t) = 1 if for both institutions 1 ≤ {ri(t), rj(t)} ≤ 25 andlij(t) = 0, otherwise. Their co-occurrence does not necessarily imply that the two institutionsare counterparties of an OTC derivative. A ranked institution i could do all its OTC contractswith the many institutions that have ranks too high (i.e., activities too low), to be listed in thisdataset. Practically, however, this cannot be the case because, as the OCC reports verify, already99% of all OTC derivatives are held by the 25 best ranked institutions. So, the not listed oneswould make only for 1%, which cannot explain the large activities of any of the 25 best rankedinstitutions. Consequently, it is reasonable to assume that i has at least one contract with anyof the other 24 institutions, and the best ranked institutions have likely more than one.

The co-occurrence network certainly overestimates the business relations based on OTC contractsbecause it is basically a fully connected network between the 25 best ranked institutions. Further,the co-occurrence may change in each quarter. Therefore, as the next step, it is reasonable toassign weights for the links between any two institutions based on the number of quarters, they

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co-appear in the dataset. I.e., we define weights as

wij =1

T

T∑t=1

lij(t) (2)

to normalize them to the available time period. A node that has links with high weights to itsneighbors certainly represents an important institution in the OTC derivatives market. We usethe weights to define the importance of an institution asWi =

∑Nj=1wij . In the following network

figures, the size of the nodes is scaled to the normalized importance, Wi/∑

iWi.

This allows us now, based on the aggregated values, to draw in Fig. 7 a first approximation ofthe network of counterparty risk. While this figure clearly shows the important institutions withrespect to their co-occurrence, it neglects another important information, namely their rankingwhich is a proxy of their relative activity. Imagine institution i with a steady but relativelylow activity over time, just enough for frequently appearing in the network, while institution jmay have a much higher activity, but during a shorter period of time, resulting in a better, butless frequent ranking. As a result, institution i will be over-presented in the network drawn inFig. 7, while institution j will be under-represented. Such activity differences are prevalent inthe dataset as the investigations in Section Activities and Ranks show. In the example shown inFig. 3, the activity of Keybank was two to three orders of magnitude lower than the activity ofBank of America. But because KeyBank was present in the top 25 list during the whole timeperiod, it gained a similar position in the network in Fig. 7 as giants such as Bank of Americaor Citibank.

Therefore, to further improve our estimation of the network of counterparty risk, we take intoaccount the overall activity of an institution by using their ranks to assign weights to the linksof co-occurrence. I.e., instead of lij(t) = 1, we use

lij(t) = min

{1

ri(t),

1

rj(t)

}(3)

The rationale behind is to bind the weight of a link to the activity of the less active institution.To elucidate this, let us assume that institution i is a big player with rank ri(t) = 2 at time t,while j is a less important institution with rank rj(t) = 21. Because both institutions co-appearin the same quarter, each of them has links to all other institutions listed in the same time period,i.e., 24 links. For the less important institution j, 20 of these links get assigned a weight of 1/20,namely those links to institutions with better ranks. But there are 4 links to institutions with anactivity less than j and therefore with higher ranks. Those links get assigned the weights 1/22,1/23, 1/24, 1/25. I.e., for each institution, links to less active counterparties have less weight,while links to more active counterparties have the maximum weight that could occur given therank of that institution. Likewise, for institution i only one link, namely the link to the highest

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BRANCH BANKING&TRUST CO

CAPITAL ONE

CHASE BANK OF TEXAS

CHASE MANHATTAN BANK

CHASE MANHATTAN BANK USA

CITIBANK

CITIBANK NEVADA

CITIBANK SOUTH DAKOTA

COMERICA BANK

COUNTRYWIDE BANK

DEUTSCHE BANK TR CO AMERICAS

FIA CARD SERVICES

FIFTH THIRD BANK

FIRST NB OF CHICAGO

FIRST TENNESSEE BANK

FIRST UNION NATIONAL BANK

FLAGSTAR BANK FSB

FLEET NATIONAL BANK

FREMONT INVESTMENT&LOAN

GMAC BANK

GOLDMAN SACHS BANK USA

HSBC BANK USAHUNTINGTON NATIONAL BANK

IRWIN UNION BANK&TRUST CO

JPMORGAN CHASE BANK

KEYBANK

LASALLE BANK

LASALLE BANK MIDWEST

LEHMAN BROTHERS COML BK

MELLON BANK

MERRILL LYNCH BANK USA

MORGAN GUARANTY TR CO OF NY

MORGAN STANLEY BANK

NATIONAL CITY BANK

NATIONAL CITY BANK OF IN

NATIONSBANK

NORTHERN TRUST CO

PNC BANK

RBS CITIZENS

REGIONS BANK

REPUBLIC NB OF NEW YORK

STANDARD CHARTERED BANK PLC

STATE STREET BANK&TRUST CO

SUNTRAST BANK

TD BANK

TD BANK USA

UBS BANK USA

UNION BANK

U S BANK

WACHOVIA BANK

WELLS FARGO BANK

WOODLANDS COMMERCIAL BANK

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WiWiWiWiWiWiWi

10−325 10−2256.5

ρijρijρijρijρijρijρij

−1

0

1

−1

0

1

−1

Figure 7: Weighted network based on the co-occurrence of financial institutions in the top 25ranking, aggregated over all quarter years. The size of a node increases with its importance Wi,the width of the links increases with their weights wij , where lij ∈ {0, 1} (i.e., do not depend onthe ranks). The links are colored according to the non-normalized correlation coefficient (definedin Section Correlations in activities) between activities in OTC derivatives of the two banks.

ranked institution, gets a weight 1/2, whereas the 23 links to all other institutions become lessand less important as 1/3, 1/4, ..., 1/25.

The resulting network is shown as an animation (at the time of writing only supported in Adobe R©

products) in Fig. D in Supporting Information. At each time step this is a fully connectednetwork, but the weights of the links, as well as the importance of the institutions, change

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during every timestep. The animation nicely elucidates the emergence of new key players inthe OTC derivatives markets before and after the crisis, as well as the changed preferences inchoosing counterparties.

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CAPITAL ONE

CHASE BANK OF TEXAS


CHASE MANHATTAN BANK USA

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CITIBANK NEVADA


COMERICA BANK

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FIA CARD SERVICES

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KEYBANK

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MELLON BANK



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Figure 8: Weighted network based on the co-occurrence and activity of financial institutionsin the top 25 ranking, aggregated over all quarter years. The coding of size and color of nodesand links are the same as in Fig. 7, but the wij and Wi are calculated from the lij as given byEq. (3) i.e., dependent on the ranks. The time resolved network is shown in Fig. D in SupportingInformation. The aggregated network should be compared with Fig. 7 where activities are nottaken into account.

To allow a comparison with Fig. 7, we aggregate the weights of the links over time according toEq. (2), to take into account both co-occurrence and activity, and calculate the importance of aninstitution as before, Wi =

∑Nj=1wij . The resulting weighted network is then shown in Fig. 8,

which should be compared to Fig. 7. The most obvious difference is a less dense core, built up by

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a smaller number of important institutions, in Fig. 8. Tracing particular institutions, e.g. UnionBank, we see that their position becomes less influential. But the core of the network, i.e., theset of the ten most important institutions, remains the same and shall be investigated in thefollowing.

Core-periphery structure

So far, we have used the following information to describe counterparty relations: (i) Aggregatedmeasures derived from the aggregated co-occurrence lij in the ranking of the 25 top players in theOTC market, in particular the weights wij and the importance Wi. The results are concludedin the network of Fig. 7. (ii) Temporal measures derived from the ranking ri(t), in particularthe temporal co-occurrence lij(t). The results are concluded in the animated network of Fig. Din Supporting Information, with the time-aggregated network shown in Fig. 8. While the lattercan be seen as the most refined network of counterparty risk, the characterization of both nodesand links is still based on the activity ai(t) of the respective institution, i.e., it is derived from asingle scalar measure. So, the question is whether the reconstruction of the aggregated temporalnetwork would allow us to add another dimension to characterize institutions, based on topologicalinformation.

Already a visual inspection of Figs. 7 and 8 verifies that the network is rather heterogeneous withrespect to its density. We can easily detect a core of larger (i.e., more active) and more denselyconnected nodes which can be distinguished from a periphery of nodes that are smaller (i.e., lessactive) and less densely connected. In fact, peripheral nodes are mostly connected towards thecore and much less to other peripheral nodes. The core of the network is depicted in Fig. 9 andgives a good impression of the fully connected network, albeit with links of different weights.

Whether institutions can be found in the core or in the periphery of the network certainly relatesto their importance in the OTC market. In order to quantify the topological information encodedin the network structure, we use the weighted K core analysis, which is an established methodto assign an importance value to nodes. In the first step, for the time aggregated network shownin Fig. 8, each node gets assigned a weighted degree ki [9]:

ki =

kαi ki∑

j

wij

β

1α+β

,

where ki is the degree of node i, i.e., its number of links to neighboring nodes, and∑ki

j wij isthe sum over all its link weights as defined in Eqn. (2) with the weighted lij given by Eqn. (3).The exponents α and β are used to weight the two different contributions, i.e., number of linksversus weight of links. In our analysis we used α = 0 and β = 1, i.e., we focused only on the

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Figure 9: The core of the aggregated weighted temporal network presented in Fig.8. For thecoding see the legend in Fig.8.

weights since the network is almost fully connected and the node degree does not give us anyinformation.

In the second step, we follow a pruning procedure to recursively remove all nodes with degreek ≤ K from the network, where K = 1, 2, ..... I.e., first all nodes with k ≤ 1 are removed, whichmay leave the network with other nodes that now have k ≤ 1 simply because some of theirneighbors were removed. So the procedure continues with removing these nodes, too, unless nonodes with k ≤ 1 are left. Then all nodes removed during this step get assigned to a core K = 1,and the procedure continues to successively remove all nodes with degree k ≤ 2 and assign themto a core K = 2, etc. The procedure stops at a certain high core value, K, when all nodes areremoved. The higher the K-core a node is assigned to, the more it belongs to the “core” of the

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network and the more important it is, from a topological perspective. Evidently, nodes assignedto a core with low K value are much less integrated in the network. This does not refer simplyto the number of neighbors, but also to non-local properties such as the number of neighbors oftheir neighbors, because the K-core decomposition also takes these into account. That means,the K-core a node is assigned to reflects is position in the network much better than simplemeasures such as the degree (i.e., the number of neighbors), alone.

The results of the weighted K-core analysis are shown in the left side of Fig. C in SupportingInformation, where the K value is normalized to 1. Based on their K value, institutions canbe ranked such that the higher the K value (i.e., the better the integration in the network),the better the rank. This topological ranking does not necessarily coincides with the rankingRi obtained from the aggregated activity Ai which is shown on the right side of Fig. C inSupporting Information, for comparison. This indicates that structural measures based on thenetwork topology indeed provide information different from the temporal measures based on themarket activities of the institutions. But, comparing the left and the right sides with respect tothe color coding, we observe that only in a few cases institutions have considerably different levelsof importance dependent on the measurement. It would be worth looking at these in a case-by-case study, to find out which importance measure better reflects their overall performance in thefinancial market.

We note that, for consistency, we have used the ranking obtained from the weighted K-coreanalysis to sort the different institutions in the figures, in particular in Fig. 2 where their presencein the dataset is given, and in Figs. 11 and 12 where the correlations in activities and in risk arepresented.

Correlations

Correlation measures

So far, we have analysed the co-occurrence of financial institutions in the set of the 25 bestranked institutions, weighted by their ranks. These ranks were based on their activities, i.e.,total derivatives. As a result, we could reconstruct the weighted network of counterparty riskwhich also reflects the importance of the nodes. This network was reconstructed (a) on a timeresolution of one quarter year, to show the dynamics of the network (Fig. D in SupportingInformation), and (b) on the time aggregated level (Fig. 8).

To further analyse the mutual dependence between the best ranked institutions, we now calcu-late different correlations. The network of counterparty risk has revealed how the co-occurrencechanges over time. But will the OTC derivatives of institution i increase, or decrease, if the same

17/36




measure of institution j increases? Answering this question allows some more refined conclusionsabout the dependence between these institutions.

The simplest measure is the Pearson correlation coefficient ρ, which points to a linear de-pendence between two variables. As explained above, for each institution i we have a datasetai = {ai(1), ai(2), ..., ai(T )} available which contains up to T entries about its quarterly activityai(t) measured by means of its total derivatives. We recall that some of these entries are zerowhenever institution i was not listed among the best 25 ranked. Let us define the mean valueand the standard deviation of each of these samples as:

ai =1

T

T∑t=1

ai(t) ; sai =

√√√√ 1

T − 1

T∑t=1

[ai(t)− ai

]2. (4)

The Pearson correlation coefficient with respect to the variable a is then defined as

ρaij =1

T − 1

T∑t=1

[ai(t)− ai

sai

][aj(t)− aj

saj

]. (5)

Values of ρ can be between -1 and +1. The latter indicates that the relation between activitiesai and aj can be perfectly described by a linear relationship, where ai increases as aj increases.-1, on the other hand, indicates a perfect linear relationship where ai decreases as aj increases,and vice versa. Zero would indicate that there are no linear dependencies detected in the data.Eq. (5) also shows that, in case of a positive correlation, if ai(k) > ai then also aj(k) > aj formost of the time, and if ai(k) < ai then also aj(k) < aj for most of the time, i.e., the activitiesof both institutions are mostly above (or below) their respective average, at the same time.

Correlations in activities

We first discuss the results for the most active institutions, i.e., those appearing among the 25best ranked institutions with respect to their total derivatives in every quarter. Interestingly,this applies only to 8 out of the 61 listed institutions. Fig. 10 shows the correlation matrix forthese institutions, their activities proxied by the total notional amount of derivative contracts aslisted in column 5 of Table A in Supporting Information.

There are two observations to be made: (i) the correlations between any two of these institutionsare always positive and often even close to 1, (ii) Keybank is a noticeable exception. This can beexplained by the combination of two effects: The first one is the vastly growing market in OTCderivative during the observation period which resulted in the growth of OTC derivatives for thesecore institutions. Thus, the observed correlations could, in principle, be caused by the underlyingmarket dynamics rather than by the mutual interaction. However, taking into account that the

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−0.5 0 0.5

ρij

Figure 10: Correlation matrix of the reported total derivatives of the institutions appearing intop 25 commercial banks, savings associations or trust companies in derivatives during the wholeperiod from 1998 to 2012.

10 best ranked institutions already account for 95% of the OTC derivatives market, there is littleroom for the assumption that their growth is based on OTC derivative contracts with institutionsthat do not belong to the core of 10, or to the 25 best ranked institutions. In conclusion, theseeight institutions increased their OTC derivatives activities by repeatedly choosing the samecore institutions as counterparties. The low correlations for Keybank could result both from theabsence of growth (see Fig. 3), while all others were growing, and from choosing counterpartiesfrom outside the set of core banks.

If we wish to extend this correlation analysis to the whole set of 61 institutions, it would generatea number of artifacts which should be avoided. We discuss them here, first, to motivate our ownapproach presented afterward. As already shown in Fig. 2, most of these institutions were notpresent in the ranking of the best 25, for some longer or shorter period. So, one could limitthe correlation analysis to those quarters where the two institutions were indeed present in theranking. I.e., if institution i appeared at times t1, t2, t3, t4 and while institution j appeared attimes t2, t4, t5, t6, the correlation coefficient for them is computed using only the observations at

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times t2 and t4 where both were present. The Pearson correlation coefficient based on pairwiseavailable observations with respect to the variable a is then defined as

ρaij =1

#[Ti ∩ Tj ]− 1

∑t∈Ti∩Tj

[ai(t)− ai

sai

][aj(t)− aj

saj

](6)

Ti and Tj are subsets of {1, 2, ..., T}, comprising the time steps when the institutions i and j

appeared in the ranking among the top 25, and #[Ti] and #[Ti] are the numbers of these timesteps. Ti ∩ Tj then defines the subset of timesteps where both institutions i and j appearedtogether, and #[Ti ∩ Tj ] gives the respective number of those time steps. Consequently, theaverage activity ai and the standard deviation sai are also calculated only for the subset Ti:

ai =1

#[Ti]∑t∈Ti

ai(t) ; sai =

√1

#[Ti]− 1

∑t∈Ti

[ai(t)− ai

]2 (7)

The results of this analysis are shown in Fig. E in Supporting Information. We observe that, inaddition to the strong correlations in the core of those institutions always present, there are a lotof strongly anti-correlated activities (indicated by rich red) among the low ranked institutionswhich need to be interpreted, both with respect to the correlation and to the magnitude. Westart with the latter.

Defining the Pearson correlation coefficient according to Eqn. (6) has the drawback that thecorrelation coefficients for different institutions are no longer normalized to the same number ofobservations, T , as in Eq. (5) and thus cannot be compared. Precisely, the correlations betweenBank of America and Citibank, which were both present in the ranking for T = 57 quarters willget the same weight as the correlations between Citibank Nevada and Chase Manhattan BankUSA which were present together only two times.

The second drawback results from the time lapse between the co-appearance. While the timest4 and t6 in the above example may still be relatively close, the interval between t4 and t56would be much longer and, because of the unknown intermediate values, interpretations aboutthe correlated move of both institutions become highly speculative.

In contrast to the above example, in which the two intermediaries appear only in a few quarters,but yet co-appear twice, some pairs of intermediaries which are important both by means oflong term presence and good rankings, never appeared together, for example Goldman Sachs andBank of New York, and, as a consequence, the Pearson correlation coefficient is not even definedfor them, which is yet another drawback.

One could argue that these drawbacks disappear if we simply keep the normalization T , as inEqs. (4)(5), and instead assign an activity ai(t) = 0 whenever an institution i is not present inthe ranking. While there is no evidence that the activity was indeed zero, the error produced

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this way is certainly small because of the very skew distribution of activities shown in Fig. 5, andboth the mean and the standard deviation of the activity are not substantially affected. But itbecomes a problem when there is indeed no data because the institution does not exist in certainquarters, e.g. because of mergers and acquisitions, as in the case of Chase Manhattan Bank andJPMorgan Chase Bank.

Additionally, by proceeding like this we would generate another artifact, namely generatingartificial correlations between those institutions that are often not in the rankings and, in theworst case, never co-appear. It is in fact the absence of data that generates their correlations,artificially. Taking again the example of Goldman Sachs and Bank of New York, these twoinstitutions would then appear anti-correlated while, in fact, no correlation was defined for them.Thus, solving the above mentioned drawbacks this way would generate yet a different one.

Consequently, we will go with the correlations defined on the pairwise co-appearance, Eqn. (6),but we compensate for the different normalization by multiplying the correlation coefficientsρaij with the weights wij defined in Eq. (2) with lij = 1, which is the relative number of co-appearances. This implies that the correlations between two institutions that rarely co-appearedin the ranking are scaled down. Precisely, after this correction, the weights wij define the boundsof the values of the correlation coefficients, which are different for each pair of institution, namely[−wij ,+wij ] instead of [−1,+1]. These weighted correlation coefficients shall be interpreted dif-ferently from the conventional correlation coefficients in that a close-to-zero coefficient no longermeans that the variables are uncorrelated, but that there is no significant correlation because ofthe low weight.

The resulting correlation matrix is shown in Fig. 11. Compared to the non-scaled Fig. E inSupporting Information, both the correlated and the anti-correlated activities loose importancefor institutions with higher ranks, because the co-appearance in the ranking is rather sparse.But still, it is obvious that the correlated activities are concentrated in the core, while the anti-correlated activities can be mostly found in the periphery. Keeping in mind the exponentialgrowth of the derivative volume of some of the key players, as shown in Fig. 3, it means that theOTC market acted rather heterogeneous. Most banks with high ranks, i.e., key players, increasedtheir activities in a growing market. Banks with lower ranks, such as First National Bank ofChicago or RBS Citizens, have either reduced their overall OTC exposure or have concentratedtheir activities towards only mayor institutions, avoiding other low ranked institutions.

Correlations in risk

So far, we have only analysed correlations in activities, i.e., the correlated increase or decrease inOTC derivatives volumes between any two institutions. We found that the correlated behaviorwas the dominating one which, together with a vastly growing OTC market, implies that most

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−0.5 0 0.5

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WOODLANDS COMMERCIAL BANKGMAC BANKFIA CARD SERVICESFLAGSTAR BANK FSBCITIBANK NEVADAFREMONT INVESTMENT&LOANSTANDARD CHARTERED BANK PLCCOUNTRYWIDE BANKLEHMAN BROTHERS COML BKBANK OF OKLAHOMABOKFBMO HARRIS BANKCHASE BANK OF TEXASIRWIN UNION BANK&TRUST COREPUBLIC NB OF NEW YORKNATIONSBANKCITIBANK SOUTH DAKOTAFIRST NB OF CHICAGOBANKBOSTONUBS BANK USATD BANK USACOMERICA BANKHUNTINGTON NATIONAL BANKALLY BANKCHASE MANHATTAN BANK USATD BANKRBS CITIZENSCAPITAL ONEMORGAN STANLEY BANKFIRST UNION NATIONAL BANKMORGAN GUARANTY TR CO OF NYCHASE MANHATTAN BANKUNION BANKLASALLE BANK MIDWESTBANK OF NEW YORK MELLONMERRILL LYNCH BANK USANATIONAL CITY BANK OF INBRANCH BANKING&TRUST COREGIONS BANKFIFTH THIRD BANKGOLDMAN SACHS BANK USAFIRST TENNESSEE BANKFLEET NATIONAL BANKBANK ONELASALLE BANKDEUTSCHE BANK TR CO AMERICASU S BANKMELLON BANKNORTHERN TRUST CONATIONAL CITY BANKKEYBANKSUNTRAST BANKPNC BANKBANK OF NEW YORKSTATE STREET BANK&TRUST COWACHOVIA BANKWELLS FARGO BANKHSBC BANK USACITIBANKJPMORGAN CHASE BANKBANK OF AMERICA

Figure 11: non-normalized Pearson correlation coefficients ρij (based on pairwise availabledata), scaled by wij with lij = 1.

institutions increased their involvement. The question remains what this would mean for the riskof the counterparties,

We already mentioned in Section Risk involved in OTC derivatives that credit risk is the mainsource of risk for banking institutions. To estimate the total credit exposure (TCE), we sum uptheir current credit exposure (CCE) and their potential future exposure (PFE) as explained inSection Risk involved in OTC derivatives. This data has been made available in “Table 4” of theOCC reports for each quarter year (see Table B in Supporting Information) and is used for oursubsequent correlation analysis. “Table 4” lists, for each of the 25 first ranked institutions, the

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bilaterally netted current credit exposure and the bilaterally netted potential future exposure andthe sum of both, TCE=CCE+PFE, as reported by the institutions themselves. Looking at Q1of 2012, we first notice that, for the high ranked institutions (according to their activity in OTCderivatives), the potential future exposure exceeds considerably the current exposure, which isgenerally not the case for the lower ranked institutions. The question whether this observationis related to the financial crisis of 2008 is addressed further below.

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(b) Total credit exposure

Figure 12: Non-normalized Pearson correlation coefficients ρCCEij and ρTCE

ij (based on pairwiseavailable data), scaled by wij with lij = 1.

We can now define a correlation coefficient ρTCEij based on Eq. (6) by just replacing the values of

the activities ai(t) by TCEi(t), and for ρCCEij accordingly. Following the argumentation above, we

weight these correlations again by the weights wij . The results are shown in Fig. 12. Both figureparts indicate that, at least for the subset of banks which are the closest to the core accordingto the core-periphery decomposition, the credit exposures are highly positively correlated. Thisindicates that the core of the network consists of institutions which are very strongly interdepen-dent. This can become a reason for systemic instability, as the credit exposures and the connectedrisks cannot be well diversified.

The correlation pattern for the risk resembles the one found for the activities, Fig. 11. We haveto note, however, that a large correlation coefficient ρaij is a good indicator of a long-term activity

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between institutions i and j, but a large correlation coefficient ρTCEij does not allow us to derive

such a conclusion.

Up to this point the analysis was based on the whole available period of time (1998 – 2012). Itis interesting to repeat the correlation analysis of risk for the time before and after the financialcrisis, separately. We avoid to discuss the precise mapping of “before” and “after” and havechosen Q4 of 2008 to divide the time series into two periods. In Q4 of 2008 Goldman Sachsentered the ranking of the OCC, for the first time, right after the collapse of Lehman Brotherson 15 September, 2008.

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WOODLANDS COMMERCIAL BANKGMAC BANKFIA CARD SERVICESFLAGSTAR BANK FSBCITIBANK NEVADAFREMONT INVESTMENT&LOANSTANDARD CHARTERED BANK PLCCOUNTRYWIDE BANKLEHMAN BROTHERS COML BKBANK OF OKLAHOMABOKFBMO HARRIS BANKCHASE BANK OF TEXASIRWIN UNION BANK&TRUST COREPUBLIC NB OF NEW YORKNATIONSBANKFIRST NB OF CHICAGOBANKBOSTONCITIBANK SOUTH DAKOTAUBS BANK USATD BANK USAHUNTINGTON NATIONAL BANKCOMERICA BANKALLY BANKCHASE MANHATTAN BANK USATD BANKCAPITAL ONERBS CITIZENSMORGAN STANLEY BANKFIRST UNION NATIONAL BANKMORGAN GUARANTY TR CO OF NYCHASE MANHATTAN BANKUNION BANKLASALLE BANK MIDWESTBANK OF NEW YORK MELLONNATIONAL CITY BANK OF INMERRILL LYNCH BANK USABRANCH BANKING&TRUST COFIFTH THIRD BANKREGIONS BANKGOLDMAN SACHS BANK USAFIRST TENNESSEE BANKFLEET NATIONAL BANKBANK ONELASALLE BANKDEUTSCHE BANK TR CO AMERICASU S BANKMELLON BANKNORTHERN TRUST CONATIONAL CITY BANKKEYBANKSUNTRAST BANKPNC BANKBANK OF NEW YORKSTATE STREET BANK&TRUST COWACHOVIA BANKWELLS FARGO BANKHSBC BANK USACITIBANKJPMORGAN CHASE BANKBANK OF AMERICA

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(a) Total credit exposure before 2008 Q4

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WOODLANDS COMMERCIAL BANKGMAC BANKFIA CARD SERVICESFLAGSTAR BANK FSBCITIBANK NEVADAFREMONT INVESTMENT&LOANSTANDARD CHARTERED BANK PLCCOUNTRYWIDE BANKLEHMAN BROTHERS COML BKBANK OF OKLAHOMABOKFBMO HARRIS BANKCHASE BANK OF TEXASIRWIN UNION BANK&TRUST COREPUBLIC NB OF NEW YORKNATIONSBANKFIRST NB OF CHICAGOBANKBOSTONCITIBANK SOUTH DAKOTAUBS BANK USATD BANK USAHUNTINGTON NATIONAL BANKCOMERICA BANKALLY BANKCHASE MANHATTAN BANK USATD BANKCAPITAL ONERBS CITIZENSMORGAN STANLEY BANKFIRST UNION NATIONAL BANKMORGAN GUARANTY TR CO OF NYCHASE MANHATTAN BANKUNION BANKLASALLE BANK MIDWESTBANK OF NEW YORK MELLONNATIONAL CITY BANK OF INMERRILL LYNCH BANK USABRANCH BANKING&TRUST COFIFTH THIRD BANKREGIONS BANKGOLDMAN SACHS BANK USAFIRST TENNESSEE BANKFLEET NATIONAL BANKBANK ONELASALLE BANKDEUTSCHE BANK TR CO AMERICASU S BANKMELLON BANKNORTHERN TRUST CONATIONAL CITY BANKKEYBANKSUNTRAST BANKPNC BANKBANK OF NEW YORKSTATE STREET BANK&TRUST COWACHOVIA BANKWELLS FARGO BANKHSBC BANK USACITIBANKJPMORGAN CHASE BANKBANK OF AMERICA

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ρij

(b) Total credit exposure after 2008 Q4

Figure 13: Correlations in total credit exposure (a) before and (b) after the financial crisis of2008 Q4.

The results of our analysis before and after Q4 of 2008 are shown in Fig. 13. Comparing thetwo parts of the figure, we make two observations: (i) All listed banks follow a similar behaviorbefore and after the crisis. But after the crisis the correlations became more homogeneous andnon-negative even between low-to-low ranked and low-to-high ranked institutions. (ii) Exceptonly few banks, the key players in the core did not change. Therefore, the OTC derivativesmarket structurally remained the same despite its vast growth.

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Conclusions

Our investigation reveals the hidden network structure behind the OTC market in the UnitedStates, and the network evolution from 1998 to 2012. For this, we use publicly available data fromthe [1] reports, which contains aggregated numbers about the activities of financial institutions,measured by the volume of their different derivatives.

We focus on two different aspects: (i) co-occurrence patterns of institutions, which take intoaccount their ranks and activities to reconstruct the network of counterparty risk. This networkwas further analysed using of a weighted k-core method, to reveal its core-periphery structure.This allowed us to compare the topology-based ranking with the activity-based ranking, and toidentify the most important institutions and their mutual relations. (ii) correlation patters, toreveal dependencies in activities, and the subsequent counterparty risks of any two institutions.Our findings, namely an emergence of a pronounced core and the higher correlations in creditexposure associated with it, hint at increasing counterparty and systemic risk in OTC derivativesmarket.

One could argue that the list of the few top institutions with the highest counterparty risk isnot really surprising and financial experts would have known this anyway. But the point of ourinvestigation is to present a formal, yet simple approach, to decompose their known aggregatedactivities into unknown bilateral exposures. Only this allows us to reveal the hidden network, andto estimate the systemic risk. Counterparty risk is not just the sum of individual risks, but canbe amplified over the network of dependencies. Precisely, the failure of single institutions, evenin the periphery of the OTC network, can lead to the collapse of the whole system because ofdistress and load distributed over the network [11].

Such considerations do not only enhance our understanding of systemic risk, they also allow todevelop more refined risk measures, and a more realistic pricing of OTC contracts. This networkperspective is missing in existing investigations [12, 13] on systemic risk in OTC derivativesmarkets. It moves the focus from discussing netting procedures after a default to the moreimportant question of how systemic risk emerges, i.e., what happens before a default.

To conclude, our investigations contribute to the ongoing debate about the impact of the OTCderivatives market on the stability of the financial markets. We support the position that OTCderivatives increase financial instability, because they generate a hidden network of dependenciesthat at the end increase the chance of failure cascades. This has not become obvious becauseof the bilateral nature of counterparty risk and the lack of transparency in OTC markets. Butour simple and practical method allows to at least estimate this hidden network of additionaldependencies and to better estimate, and price, the risk resulting from these. It particularlypoints to the limitations in diversifying risk in such markets and the need to implement further

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regulations, as already proposed by the European Market Infrastructure Regulation (EMIR)under the Basel III umbrella BCBS (2011).

Acknowledgments

The authors thank Stefano Battiston and Paolo Tasca for discussions, and Michelangelo Puliga forpointing us to the dataset. We acknowledge financial support from the Project CR12I1_127000OTC Derivatives and Systemic Risk in Financial Networks financed by the Swiss National Sci-ence Foundation.

References

[1] Basel Committee on Banking Supervision. Supervisory framework for measuring and con-trolling large exposures; 2013.

[2] Waldman AR. OTC Derivatives & (and) Systemic Risk: Innovative Finance or the Danceinto the Abyss. Am UL Rev. 1993;43:1023.

[3] Hendricks D. Netting agreements and the credit exposures of OTC derivatives portfolios.Federal Reserve Bank of New York Quarterly Review, Spring. 1994;.

[4] Cecchetti SG, Gyntelberg J, Hollanders M. Central counterparties for over-the-counterderivatives. BIS Quarterly Review. 2009;2009:45–58.

[5] Kaushik R, Battiston S. Credit Default Swaps Drawup Networks: Too Interconnected to BeStable? PLoS ONE. 2013 07;8:e61815.

[6] Feng X, Hu H, Pritsker M. Network effects, cascades and CCP interoperability. InternationalJournal of Modern Physics C. 2013;.

[7] Tasca P, Mavrodiev P, Schweitzer F. Quantifying the impact of leveraging and diversificationon systemic risk. Journal of Financial Stability. 2014;15:43 – 52.

[8] Gini C. Concentration and dependency ratios. Rivista di Politica Economica. 1997;87:769–789.

[9] Garas A, Schweitzer F, Havlin S. A k -shell decomposition method for weighted networks.New Journal of Physics. 2012;14:083030.

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[10] Office of the Comptroller of the Currency. Quarterly Report on Bank Deriva-tives Activities; 2012. Available from: http://www.occ.gov/topics/capital-markets/financial-markets/trading/derivatives/derivatives-quarterly-report.html.

[11] Burkholz R, Garas A, Schweitzer F. How Damage Diversification Can Reduce SystemicRisk. ETH Risk Center WP series, arXiv:150300925. 2015;.

[12] Miguel A, Singh M. Counterparty Risk in the Over-the-Counter Derivative market. Inter-national Monetary Fund; 2008.

[13] Singh MM. Collateral, netting and systemic risk in the OTC derivatives market. Interna-tional Monetary Fund; 2010.

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http://www.occ.gov/topics/capital-markets/financial-markets/trading/derivatives/derivatives-quarterly-report.html




Supporting Information

Appendix 1: Data Availability and Processing

Our quantitative analysis is based on a dataset derived from the quarterly reports on derivativesof the Office of the Comptroller of the Currency (OCC).

These reports contain, for each quarter, different tables with derivatives data of the top 25 USnational insured commercial banks and trust companies. A typical “Table 1” from the first quarterof 2012 [1] is shown in Tab. A in the Appendix. The unit for all numbers is 1 million US dollars.

The first column contains the ranks and the second column the name of the institution. Thedata used for the ranking can be found in the fifth column, labeled Total derivatives. It gives aproxy for the activity of an institution. The most active one is assigned rank 1 and referred toas the “highest ranked” (or best ranked) in the following. In the second set of columns, “Table1” of these reports further presents the composition of the derivatives contracts into exchangetraded derivatives (ETD) (futures contracts, option contracts) and Over-The-Counter (OTC)traded derivatives (forwards, swaps, options and credit derivatives). In the last column, foreignexchange spots are reported but not included in the sum of total derivatives.

Below the list of the ranked institutions, Tab. A reports three important rows: (a) the sum of thederivative contracts for the top 25 ranked institutions, (b) the sum of the derivative contracts ofall other reporting institutions (with the number of these stated in the reports until 2007/Q1and (c) the sum of (a) and (b) referring to the whole market.

Such Tables are available for each quarter between 1998/Q4 and 2012/Q4, i.e., for 57 quarters.

The full OCC quarterly reports on derivatives are available on the OCC website [1] in PDFand raw data is available in XML format. In order to obtain the data on credit exposures fromderivative contracts, the latter was chosen and processed with the XML package of R statisticalenvironment. A technical problem was met and solved at this stage. The XML parser would notprocess random rows of the data. Inconsistencies in the structure of XML were the source of theproblem and were found by manually checking the problematic rows. In the these rows one ortwo excessive empty data nodes were present, after deletion of which the whole available datawas parsed. No XML file is published by OCC for the 2008 Q3, so the PDF file of the report wasprocessed to obtain data and add it the rest of the dataset.

The next step after obtaining the data on credit exposures was merging it with the originaldataset on notional amounts of derivative contracts. A technical hurdle was in matching differenttypesetting of the names of some institutions (e.g. extra spaces). At this stage few missing entriesin the original dataset were found and fixed.

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The raw data was combined into a CSV table and included 17 columns with the data from thementioned two tables of the OCC reports. The chosen time range corresponded to 57 quarters,with 25 entries for every one summing up to 1425 rows in the table. Every row included thetime-stamp, name of the institution, its rank, state, total assets, total derivatives, total amountsof 7 types of derivatives, bilaterally netted current credit exposure, potential future exposure,total credit exposure from all contracts and total credit exposure to capital ratio (the last inpercents).

The number of unique combinations of name and state in the raw dataset was 93, but the stateswere left out of consideration. Thus in the present analysis two actors with the same namebut from different states were considered to be the same actor. The technical legitimacy of thisassumption is based on the fact that no two actors with the same name but from different statessimultaneously appeared in the reports. Checking the legal validity of the assumption is not inthe scope of this analysis.

The number of entries differing by the name of the institution was 82 in the raw data. The nameswere processed and their number reduced to 61. The conditions for merging two similar nameswere the absence of simultaneous appearance in the reports, similar ranks and orders of reportednumbers. Again, legal aspects for merging these data were not considered. The main source ofambiguity in names were “NA” and “NATIONAL ASSN” endings. These were dropped and so, forexample, “KEYBANK NA” and “KEYBANK NATIONAL ASSN” became “KEYBANK”. Othermore specific changes in the names are presented in the list below (in bold is the chosen name).

CAPITAL ONENames in the original data were CAPITAL ONE BANK and CAPITAL ONE NATIONAL ASSN

DEUTSCHE BANK TR CO AMERICASBANKERS TRUST CO was renamed to DEUTSCHE BANK TR CO AMERICAS in April of 2002

MELLON BANKMELLON was misspelled MELLONG

SUNTRUST BANKThe bank was reporting as SUNTRUST BANK ATLANTA before 2000

UNION BANKThe bank was reporting as UNION BANK OF CALIFORNIA until the 3rd quarter of 2008

BANKBOSTONIn the report from 1998 Q4 the name was BANKBOSTON CORPORATION

BANK OF AMERICABANK OF AMERICA was BANK OF AMERICA NT&SA until the mid 1999.

FIRST TENNESSEEThe bank was misspelled as FIRST TENESSE in one entry

BMO HARRIS BANKThe bank appeared as HARRIS TRUST&SAVINGS BANK

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STANDARD FEDERAL BANK changed its name after being acquired by LaSalle Corp. in 2005

As described above, some banks which changed their names in the considered time period weregiven the latest name for the whole time period, as in the present analysis the institutionsare distinguished by name. Assigning unique ID numbers to the institutions would make thepresentation of the results more abstract and less understandable.

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Appendix 2: Activities and ranks

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109

1010

Figure A: Quantile-quantile plot of the aggregated activity Ai versus the fitted log-normaldistribution, µ=14.54116, σ=2.865165. In order to check if log-normal distribution is a goodcandidate to describe the aggregated total derivatives distribution, 10000 Kolmogorov-Smirnovtwo-sample tests were made for Ai against synthetic samples, from which 9856 tests werepositive for p-value equal to 0.10.

●

●

●

●●

●

●

●●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●●

●

0 10 20 30 40 50 60

010

2030

4050

60

R_i based on OTC+EXCH

R_i

bas

ed o

n O

TC

Figure B: Ranks Ri based on the total activity Ai versus Ranks ROTCi based on the activity

resulting from OTC derivatives AOTCi

31/36




BANK OF AMERICAJPMORGAN CHASE BANK

CITIBANKHSBC BANK USA

WELLS FARGO BANKWACHOVIA BANK

STATE STREET BANK&TRUST COBANK OF NEW YORK

PNC BANKSUNTRAST BANK

KEYBANKNATIONAL CITY BANKNORTHERN TRUST CO

MELLON BANKU S BANK

DEUTSCHE BANK TR CO AMERICASLASALLE BANK

BANK ONEFLEET NATIONAL BANK

FIRST TENNESSEE BANKGOLDMAN SACHS BANK USA

REGIONS BANKFIFTH THIRD BANK

BRANCH BANKING&TRUST COMERRILL LYNCH BANK USANATIONAL CITY BANK OF IN

BANK OF NEW YORK MELLONLASALLE BANK MIDWEST

UNION BANKCHASE MANHATTAN BANK

MORGAN GUARANTY TR CO OF NYFIRST UNION NATIONAL BANK

MORGAN STANLEY BANKRBS CITIZENSCAPITAL ONE

TD BANKCHASE MANHATTAN BANK USA

ALLY BANKCOMERICA BANK

HUNTINGTON NATIONAL BANKTD BANK USA

UBS BANK USACITIBANK SOUTH DAKOTA

BANKBOSTONFIRST NB OF CHICAGO

NATIONSBANKREPUBLIC NB OF NEW YORK

IRWIN UNION BANK&TRUST COCHASE BANK OF TEXAS

BMO HARRIS BANKBOKF

BANK OF OKLAHOMALEHMAN BROTHERS COML BK

COUNTRYWIDE BANKSTANDARD CHARTERED BANK PLC

FREMONT INVESTMENT&LOANCITIBANK NEVADA

FLAGSTAR BANK FSBFIA CARD SERVICES

GMAC BANKWOODLANDS COMMERCIAL BANK

0.000.000.000.000.000.000.000.000.000.000.000.000.030.030.030.030.060.060.060.100.130.130.130.130.130.130.160.190.230.260.260.290.320.350.350.390.420.450.480.520.520.550.580.580.580.610.650.680.710.740.770.810.840.870.900.940.970.971.001.001.00

21

3

6

98

10

12

1817

24

2122

2526

15

29

13

19

33

4

27

3031

36

28

11

32

34

5

7

16

14

35

40

37

4142

47

4443

45

50

38

23

20

39

58

54

4948

51

5352

46

6160

56

59

55

57

BANK OF AMERICAJPMORGAN CHASE BANK

CITIBANK

HSBC BANK USA

WELLS FARGO BANKWACHOVIA BANK


BANK OF NEW YORK

PNC BANKSUNTRAST BANK

KEYBANK

NATIONAL CITY BANKNORTHERN TRUST CO

MELLON BANKU S BANK


LASALLE BANK

BANK ONE

FLEET NATIONAL BANK



REGIONS BANK

FIFTH THIRD BANKBRANCH BANKING&TRUST CO





UNION BANK




MORGAN STANLEY BANK

RBS CITIZENS

CAPITAL ONE

TD BANK

CHASE MANHATTAN BANK USAALLY BANK

COMERICA BANK

HUNTINGTON NATIONAL BANKTD BANK USA

UBS BANK USA


BANKBOSTON

FIRST NB OF CHICAGO

NATIONSBANK



CHASE BANK OF TEXAS

BMO HARRIS BANKBOKF

BANK OF OKLAHOMA

LEHMAN BROTHERS COML BKCOUNTRYWIDE BANK


FREMONT INVESTMENT&LOANCITIBANK NEVADA

FLAGSTAR BANK FSB

FIA CARD SERVICES

GMAC BANK


weighted k−core R

Figure C: Comparison of the weighted k-core (left column) and Ri (right column) rankings.Better ranks are on the top. Links connect the same institution in two rankings. The colorsrepresent k-core ranking, orange changes to green as the distance from core increases.

32/36




Appendix 3: OTC network evolution

Figure D: Animation showing the evolution of the financial institutions’ network over time. Aninstitution is present in the network at certain time step if it is in the top 25 commercial banks,savings associations or trust companies in derivatives. The network of these 25 institutions isconsidered fully connected, with the weight of a link being proportional to the inverse of thelowest rank of its end nodes. The size and color of a node represents the significance of the nodein terms of the sums of the weights of its links.

33/36




Appendix 4: CorrelationsW

OO

DLA

ND

S C

OM

ME

RC

IAL

BA

NK

GM

AC

BA

NK

FIA

CA

RD

SE

RV

ICE

SF

LAG

STA

R B

AN

K F

SB

CIT

IBA

NK

NE

VA

DA

FR

EM

ON

T IN

VE

ST

ME

NT

&LO

AN

STA

ND

AR

D C

HA

RT

ER

ED

BA

NK

PLC

CO

UN

TR

YW

IDE

BA

NK

LEH

MA

N B

RO

TH

ER

S C

OM

L B

KB

AN

K O

F O

KLA

HO

MA

BO

KF

BM

O H

AR

RIS

BA

NK

CH

AS

E B

AN

K O

F T

EX

AS

IRW

IN U

NIO

N B

AN

K&

TR

US

T C

OR

EP

UB

LIC

NB

OF

NE

W Y

OR

KN

ATIO

NS

BA

NK

CIT

IBA

NK

SO

UT

H D

AK

OTA

FIR

ST

NB

OF

CH

ICA

GO

BA

NK

BO

STO

NU

BS

BA

NK

US

AT

D B

AN

K U

SA

CO

ME

RIC

A B

AN

KH

UN

TIN

GTO

N N

ATIO

NA

L B

AN

KA

LLY

BA

NK

CH

AS

E M

AN

HAT

TAN

BA

NK

US

AT

D B

AN

KR

BS

CIT

IZE

NS

CA

PIT

AL

ON

EM

OR

GA

N S

TAN

LEY

BA

NK

FIR

ST

UN

ION

NAT

ION

AL

BA

NK

MO

RG

AN

GU

AR

AN

TY

TR

CO

OF

NY

CH

AS

E M

AN

HAT

TAN

BA

NK

UN

ION

BA

NK

LAS

ALL

E B

AN

K M

IDW

ES

TB

AN

K O

F N

EW

YO

RK

ME

LLO

NM

ER

RIL

L LY

NC

H B

AN

K U

SA

NAT

ION

AL

CIT

Y B

AN

K O

F IN

BR

AN

CH

BA

NK

ING

&T

RU

ST

CO

RE

GIO

NS

BA

NK

FIF

TH

TH

IRD

BA

NK

GO

LDM

AN

SA

CH

S B

AN

K U

SA

FIR

ST

TE

NN

ES

SE

E B

AN

KF

LEE

T N

ATIO

NA

L B

AN

KB

AN

K O

NE

LAS

ALL

E B

AN

KD

EU

TS

CH

E B

AN

K T

R C

O A

ME

RIC

AS

U S

BA

NK

ME

LLO

N B

AN

KN

OR

TH

ER

N T

RU

ST

CO

NAT

ION

AL

CIT

Y B

AN

KK

EY

BA

NK

SU

NT

RA

ST

BA

NK

PN

C B

AN

KB

AN

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F N

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YO

RK

STA

TE

ST

RE

ET

BA

NK

&T

RU

ST

CO

WA

CH

OV

IA B

AN

KW

ELL

S F

AR

GO

BA

NK

HS

BC

BA

NK

US

AC

ITIB

AN

KJP

MO

RG

AN

CH

AS

E B

AN

KB

AN

K O

F A

ME

RIC

A


−1 −0.5 0 0.5 1Value

Color Key

WO

OD

LAN

DS

CO

MM

ER

CIA

L B

AN

KG

MA

C B

AN

KF

IA C

AR

D S

ER

VIC

ES

FLA

GS

TAR

BA

NK

FS

BC

ITIB

AN

K N

EV

AD

AF

RE

MO

NT

INV

ES

TM

EN

T&

LOA

NS

TAN

DA

RD

CH

AR

TE

RE

D B

AN

K P

LCC

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NT

RY

WID

E B

AN

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HM

AN

BR

OT

HE

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CO

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BK

BA

NK

OF

OK

LAH

OM

AB

OK

FB

MO

HA

RR

IS B

AN

KC

HA

SE

BA

NK

OF

TE

XA

SIR

WIN

UN

ION

BA

NK

&T

RU

ST

CO

RE

PU

BLI

C N

B O

F N

EW

YO

RK

NAT

ION

SB

AN

KC

ITIB

AN

K S

OU

TH

DA

KO

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IRS

T N

B O

F C

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AG

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AN

KB

OS

TON

UB

S B

AN

K U

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TD

BA

NK

US

AC

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ICA

BA

NK

HU

NT

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TON

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ION

AL

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NK

ALL

Y B

AN

KC

HA

SE

MA

NH

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N B

AN

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SA

TD

BA

NK

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EN

SC

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L O

NE

MO

RG

AN

STA

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AN

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T U

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N N

ATIO

NA

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AN

KM

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GA

N G

UA

RA

NT

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R C

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F N

YC

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SE

MA

NH

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N B

AN

KU

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N B

AN

KLA

SA

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BA

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MID

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NE

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ON

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BA

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US

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L C

ITY

BA

NK

OF

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RA

NC

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AN

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TR

US

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OR

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AN

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BA

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ER

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AN

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BA

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AN

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TR

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AN

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OF

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ICA


−1 −0.5 0 0.5 1Value

Color Key

Figure E: Based on only pairwise available observations.

Appendix 5: Tables

References

[1] Office of the Comptroller of the Currency. Quarterly Report on Bank Deriva-tives Activities; 2012. Available from: http://www.occ.gov/topics/capital-markets/financial-markets/trading/derivatives/derivatives-quarterly-report.html.

34/36






Tab

leA

:“Tab

le1”

from

theOCC

repo

rtforthefirst

quarterof

2012

.T

AB

LE 1

TO

TA

LT

OT

AL

TO

TA

LT

OT

AL

TO

TA

LT

OT

AL

CR

ED

ITT

OT

AL

TO

TA

LF

UT

UR

ES

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SF

OR

WA

RD

SS

WA

PS

OP

TIO

NS

DE

RIV

AT

IVE

SS

PO

TR

AN

KB

AN

K N

AM

ES

TA

TE

AS

SE

TS

DE

RIV

AT

IVE

S(E

XC

H T

R)

(EX

CH

TR

)(O

TC

)(O

TC

)(O

TC

)(O

TC

)F

X1

JPM

OR

GA

N C

HA

SE

BA

NK

NA

OH

$1,8

42,7

35$7

1,47

8,76

0$1

,060

,040

$1,8

27,7

75$1

1,96

1,45

4$4

1,14

4,14

0$9

,319

,495

$6,1

65,8

56$7

57,9

932

CIT

IBA

NK

NA

TIO

NA

L A

SS

NS

D1,

312,

764

51,8

94,3

4450

7,78

682

2,54

06,

807,

970

31,7

89,5

588,

896,

057

3,07

0,43

31,

076,

482

3B

AN

K O

F A

ME

RIC

A N

AN

C1,

448,

262

46,3

61,6

941,

927,

382

227,

302

9,39

7,46

428

,199

,752

3,04

7,47

43,

562,

320

362,

281

4G

OLD

MA

N S

AC

HS

BA

NK

US

AN

Y10

1,92

742

,821

,356

781,

471

921,

796

3,51

9,08

629

,590

,057

7,48

0,14

952

8,79

74,

549

5H

SB

C B

AN

K U

SA

NA

TIO

NA

L A

SS

NV

A20

6,80

94,

466,

896

91,9

9153

,997

884,

122

2,65

9,87

917

7,88

659

9,02

283

,373

6W

ELL

S F

AR

GO

BA

NK

NA

SD

1,18

1,81

73,

778,

395

211,

442

50,2

2993

1,11

52,

076,

755

434,

044

74,8

1017

,124

7M

OR

GA

N S

TAN

LEY

BA

NK

NA

UT

67,6

512,

566,

841

7,12

20

440,

668

1,32

7,23

776

8,64

723

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99,4

018

BA

NK

OF

NE

W Y

OR

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NY

229,

715

1,37

2,89

818

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28,9

2538

4,85

569

7,48

624

3,29

927

058

,257

9S

TATE

STR

EE

T B

AN

K&

TRU

ST

CO

MA

183,

994

957,

264

52,1

570

796,

707

42,7

9665

,509

9538

,744

10P

NC

BA

NK

NA

TIO

NA

L A

SS

ND

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7,76

639

1,93

461

,575

32,4

0023

,519

236,

009

34,7

603,

671

2,10

511

SU

NTR

US

T B

AN

KG

A17

2,28

926

9,98

925

,561

12,7

4618

,666

162,

293

46,4

334,

289

216

12N

OR

THE

RN

TR

US

T C

OIL

91,3

4124

2,64

40

023

2,73

19,

748

104

6118

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EG

ION

S B

AN

KA

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4,71

315

0,05

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936

065

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75,6

432,

843

711

8514

STA

ND

AR

D C

HA

RTE

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AN

K P

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118,

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00

111,

586

2,73

64,

155

04,

964

15U

S B

AN

K N

ATI

ON

AL

AS

SN

OH

330,

227

113,

174

990

5,72

046

,588

47,1

949,

899

2,78

31,

104

16K

EY

BA

NK

NA

TIO

NA

L A

SS

NO

H84

,839

84,3

463,

283

018

,224

54,1

695,

286

3,38

21,

086

17F

IFT

H T

HIR

D B

AN

KO

H11

4,40

271

,188

177

016

,072

31,8

2021

,937

1,18

255

818

TD B

AN

K N

ATI

ON

AL

AS

SN

DE

193,

074

69,7

020

08,

544

57,8

011,

474

1,88

25

19B

RA

NC

H B

AN

KIN

G&

TRU

ST

CO

NC

169,

026

69,0

9288

60

15,6

4937

,229

15,3

280

4220

UN

ION

BA

NK

NA

TIO

NA

L A

SS

NC

A91

,576

56,6

944,

539

02,

765

34,9

5114

,439

064

521

RB

S C

ITIZ

EN

S N

ATI

ON

AL

AS

SN

RI

106,

242

37,5

850

07,

362

27,5

381,

818

868

6022

BO

KF

NA

TIO

NA

L A

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,734

30,3

3958

31,

004

22,9

823,

290

2,48

00

2823

CA

PIT

AL

ON

E N

ATI

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AL

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133,

000

28,9

3510

50

931

27,2

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653

1124

BM

O H

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089

923

,729

2,66

416

184

25H

UN

TIN

GTO

N N

ATI

ON

AL

BA

NK

OH

55,5

8526

,509

300

1,49

422

,160

2,33

549

01

TOP

25

CO

MM

ER

CIA

L B

AN

KS

, SA

s &

TC

s W

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DE

RIV

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S$8

,691

,082

$227

,486

,417

$4,7

60,1

20$3

,984

,435

$35,

717,

375

$138

,381

,175

$30,

598,

555

$14,

044,

757

$2,5

27,5

06O

THE

R C

OM

ME

RC

IAL

BA

NK

S, S

As

& T

Cs

WIT

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ER

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3,50

3,86

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6,05

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7,15

411

6,02

428

9,72

266

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6,80

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973

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L C

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BA

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S, S

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& T

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12,1

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7,98

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74,

770,

271

3,99

1,59

035

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138,

670,

897

30,6

64,7

5214

,051

,558

2,53

1,47

8

Not

e: B

efor

e th

e fir

st q

uart

er o

f 199

5 to

tal d

eriv

ativ

es in

clud

ed s

pot f

orei

gn e

xcha

nge.

Beg

inni

ng in

the

first

qua

rter

, 199

5, s

pot f

orei

gn e

xcha

nge

was

rep

orte

d se

para

tely

.N

ote:

Num

bers

may

not

add

due

to r

ound

ing.

Dat

a so

urce

: C

all R

epor

ts, s

ched

ule

RC

-L

NO

TIO

NA

L A

MO

UN

T O

F D

ER

IVA

TIV

E C

ON

TR

AC

TS

Not

e: C

redi

t der

ivat

ives

hav

e be

en in

clud

ed in

the

sum

of t

otal

der

ivat

ives

. C

redi

t der

ivat

ives

hav

e be

en in

clud

ed a

s an

"ov

er th

e co

unte

r" c

ateg

ory,

alth

ough

the

Cal

l Rep

ort d

oes

not d

iffer

entia

te b

y m

arke

t cur

rent

ly.

TO

P 2

5 C

OM

ME

RC

IAL

BA

NK

S,

SA

VIN

GS

AS

SO

CIA

TIO

NS

AN

D T

RU

ST

CO

MP

AN

IES

IN

DE

RIV

AT

IVE

SM

AR

CH

31

, 2

01

2,

$ M

ILL

ION

S

35/36




Tab

leB

:“Tab

le4”

from

theOCC

repo

rtforthefirst

quarterof

2012

.T

AB

LE 4

BIL

AT

ER

AL

LY

TO

TA

L C

RE

DIT

(%)

TO

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31

, 2

01

2,

$ M

ILL

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S

36/36


The Network of Counterparty Risk: Analysing Correlations ...

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