Back Matter
Author: Ms. Li Lin1 and Jay Surti2
  • 1 https://isni.org/isni/0000000404811396, International Monetary Fund
  • | 2 https://isni.org/isni/0000000404811396, International Monetary Fund

Appendix I. List of CMs at SwapClear, ICE Clear Credit and ICE Clear Europe

Table A1.

Consolidated List of CMs at SwapClear

Source: LCH.Clearnet
Table A2.

List of CMs at ICE Clear

Sources: ICE Clear Credit and ICE Clear Europe.

Appendix II. Modeling Credit Spreads

The residuals of the standardized returns of 30 cleared CDS contracts do not follow a normal distribution nor can their behavior be adequately described by a t–distribution owing to fat-tails. This is so for those contracts where the time series of daily returns exhibits zero variance for long periods of time. This is seen; for e.g., in the time series of daily returns on CDS contracts on two SN obligors, Valero Energy and Verizon (Figure 10).

Figure 10.
Figure 10.

Comparing Daily Returns on CDS on Two SN Obligors

Citation: IMF Working Papers 2013, 003; 10.5089/9781475535501.001.A999

Source: Authors’ calculations.

Consequently, it is reasonable to fit them with a GARCH model with time varying conditional variance. While searching for an appropriate family of distributions to fit the time series of daily returns of such contracts, we must bear in mind that for a substantially long time, the variance of daily returns for such time series can be zero with the standardized residuals exhibiting extreme values as is the case with the CDS of Verizon Communications (Figure 11).

Figure 11.
Figure 11.

Comparing Standardized Residuals on CDS on Two SN Obligors

Citation: IMF Working Papers 2013, 003; 10.5089/9781475535501.001.A999

Source: Authors’ calculations.

In the literature, a mixture of the Pareto distribution—in the tails—and a kernel smoothed interior is used to fit the residuals as this captures extreme values (Figure 12).

Figure 12.
Figure 12.

Fitting Residuals Using a Mixed Paretotail and Kernel Smoothed Interior

Citation: IMF Working Papers 2013, 003; 10.5089/9781475535501.001.A999

Source: Authors’ calculations.

In order to fit a copula, the margins of the residuals have to follow a uniform distribution.31 This is difficult to reconcile with fitting of a mixed Paretotail distribution, of time series such as the Verizon CDS. Whereas the random numbers generated from the copula will have uniform margins, about 99 percent of the margins generated from the mixed Paretotail distribution are concentrated in the region [0.5. 0.7] (Figure 13). Applying the uniformly distributed margin simulated from the copula to the fitted Paretotail distribution (Figure 12) leads to a larger proportion of the simulated residuals staying in the upper and lower 10 percent quantile. Therefore, the simulated data will put a larger weight on the tails, which strongly contradicts with the pattern of real data, which is concentrated in the [0.5, 0.7] range.

Figure 13.
Figure 13.

Residual Margins from Simulated (Copula) and Real (Paretotail) Data

Citation: IMF Working Papers 2013, 003; 10.5089/9781475535501.001.A999

Source: Authors’ calculations.

Consequently, we use a non-parametric distribution that generates margins of the residuals closer to the uniformly distributed margins simulated by the copula (Figure 14). This is especially so for the tail wherein the weights, either from the simulated data or from the real data are close. Therefore, the simulated margins will no longer lead to a larger number of tailed residuals than in the real data. While the distribution of the margins under the non-parametric distribution still does not follow the uniform distribution in the range [0.3, 0.7], where the real data is concentrated in the [0.5, 0.55] range and the simulated data are uniformly distributed. However, this does not result in large discrepancies between the simulated and real data because—following figure 13—the values in the [0.3, 0.7] range are close to zero.

Figure 14.
Figure 14.

Residual Margins from Simulated and Real (Non-parametric) Data

Citation: IMF Working Papers 2013, 003; 10.5089/9781475535501.001.A999

Source: Authors’ calculations.

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1

The authors thank Aditya Narain for his support to the project. Helpful discussions with, and useful comments from Rory Cunningham, Jennifer Elliott, Michaela Erbenova, Asif Godall, Stan Ivanov, Ulrich Karl, Laura Kodres, Juri Marcucci, Bruno Momont, Kevin Sheppard, Nobu Sugimoto, Froukelien Wendt, Nicholas Vause, Philip Whitehurst, and Mark Zelmer are gratefully acknowledged. The usual disclaimer applies.

2

This section is based on Scarlata et. al. (2012).

4

See IMF (2010) or Scarlata et. al. (2012) for overviews of the risk management frameworks. Internationally agreed principles for sound risk management by CCPs, that describe the essential elements of their risk management framework, are contained in the Committee on Payments and Settlements Systems and the International Organization of Securities Commissions (2012).

5

An exception is a liquidity backstop provided by the central bank, albeit in order to prove adequate, this may, in some circumstances, require forbearance with regard to collateral eligibility and valuation. This takes us into the realm of too-big-to-fail problems that, while important, are not directly relevant to this paper.

6

The legal relationship between the CCP, the CMs and their clients will vary across jurisdictions. Annex A details the current membership of SwapClear and ICE Clear.

7

We only aim at providing a brief and heuristic description of pre-funded risk buffers in this section. A formal introduction to these concepts can be found in Gregory (2012).

8

This is a summary derived from LCH.Clearnet (2012a). Detailed documentation of SwapClear’s margin methodology was unavailable to the authors owing to its proprietary nature.

9

Here, a worst-case loss to the CCP is to be understood as the maximum decrease in the market value of the contract from the CM’s perspective.

10

This is a summary drawn from InterContinental Exchange (2012b, 2012c). See also InterContinental Exchange (2012a). As in the case of SwapClear, detailed documentation was unavailable owing to its proprietary nature.

11

A Cover k charge is one where the size of the DF is set to equal the sum of the CCP’s k largest unmargined exposures—at a chosen confidence level—across all its CMs.

12

The Basel 2.5 market risk capital rules are described BCBS (2011).

13

ES is defined to be the expected loss conditional on losses being in excess of VaR.

14

Large global banks, particularly those belonging to the Group of 14 dealers (G-14), typically have multiple affiliates of their group on the list of SwapClear CMs. Conversations with dealers indicate the resulting capital efficiency—owing to lower risk charges on exposures to qualifying CCPs relative to intra-group exposures under a consolidated CM model—as the primary motivation. Our institution-level, CM data on the other hand, is assembled from group-level filings—form FR-9-YC for U.S. bank holding companies, and U.S. SEC Form 20-F or annual consolidated financial statements for others. Group level notional positions already embed netting of intra-group exposures, and to this extent, the share of notional positions allocated through our assembled aggregated data to the G-14 dealers may deviate from, and understate, the real allocation. One such example that we are aware of, is of Goldman Sachs through additional data available publicly through the financial statements of its U.K. licensed subsidiary, Goldman Sachs International.

15

We obtain information on the share of each category of OTC interest rate derivatives in the total cleared notional from Trioptima whose data release for end-2011 reveals the shares of Basis Swaps, OIS, IRS and forward rate agreements (FRAs) in the global cleared notional to be three, 14, 82, and one percent respectively. The broad definition of swaps, covering the first three categories, had a share of 99 percent. The volume of cleared FRAs has increased dramatically through 2012 as reflected in the increase in their share of cleared OTC interest rate contracts from 1 percent at end 2011 to 15 percent by the end of Q3-2012.

16

Our analysis indicates that the sensitivity of portfolio value changes to alternative distributions of the original TtM of outstanding contracts is low. Nonetheless, we use different fixed rates consistent with the approach described in table 2 to increase precision. In any event, the rate at origination, i.e. the fixed rate on a contract is not a key factor affecting our results since we are not interested in portfolio value per se, but rather, in the potential change in portfolio value.

17

The International Swaps and Derivatives Association, in a market overview, available at http://www.isdacdsmarketplace.com/market_overview/central_clearing, indicated that major swaps dealers are committed to clearing up to 90% of their clearing eligible interest rate derivatives and were doing so as of January 2012. Nonetheless, applying this ratio to a dealer’s reported swaps notional may overstate that dealer’s positions at SwapClear since some IRS products are not clearing eligible. Balancing this to a degree is the fact that the gross notional reported in the banking group’s financial statement may underestimate the total contracts outstanding across all group affiliates that are CMs at the CCP (see footnote 14). We have chosen a clearing ratio of 85 percent bearing in mind these considerations and also because it generates a reasonable set of remaining positions for the other 10 CMs who do not report the data.

18

This is also corroborated by the analysis of transaction-level data conducted by Fleming et. al. (2012).

19

They assume that the CMs’ overlapping ratios—called similarity metrics in their paper—lie within a range (0.95, 0.99) with the average value constrained to be no more than 0.001 away from 0.98.

20

For the three CMs that did not report gross protection bought and sold separately, we use the fact that, by definition, the total GN protection bought on ICE Clear has to be the same as the total GN protection sold. Therefore, once we have calculated the bought and sold gross positions for the 12 CMs that report both sides, we derive a net bought position that we allocated to these three remaining CMs in proportion to their gross notional outstanding.

21

Eight of the 15 CMs have an overlapping ratio of greater than 80 percent and only two have an overlapping ratio of less than 70 percent. Heller and Vause constrain this ratio to lie in a range [0.8, 0.94] with the average value being no more than 0.001 away from 0.89.

22

In this paper we consider traded CDS of 5 year maturity and therefore the default density is constant. For detailed discussions on the valuation of CDS contracts, see Duffie and Singleton (2003) and O’Kane and Turnbull (2003).

23

An introduction to historical simulation can be found in Hull and While (1998).

24

Except for the overnight rates of the US$ and the A$ for which daily returns are zero for a majority of the time.

25

LCH.Clearnet (2012b) provides further details.

26

The real FVA/FVL ratios for CMs’ swaps portfolios are those derived for the aggregate outstanding portfolio of cleared and uncleared trades rather than for cleared volumes alone. However, it is the latter that are relevant to assessing the validity of Positions 1, 2 and 3. If the FVA/FVL ratios for cleared portfolios deviate substantially from those for the aggregate portfolio, the case for using this validation metric is weaker.

27

This is akin to differences—under Basel 2.5—between an A-IRB bank’s market risk capital requirements derived under its internal model based approach and under the standardized approach.

28

See the Basel Committee on Banking Supervision (2011). Using stressed market condition calibrated model inputs assists us in incorporating potential violations of normal bases/correlations in cleared CDS market values. Using longer close-out periods assists in incorporation of heightened liquidity and concentration risk.

30

Yamai and Yoshiba (2002) demonstrate that the primary benefit of compelling banks to use ES instead of VaR is that the ES-optimal portfolio carries considerably lower tail risk relative to the VaR-optimal portfolio.

31

A discussion of modeling issues can be found in Marcucci (2005).

Capital Requirements for Over-the-Counter Derivatives Central Counterparties
Author: Ms. Li Lin and Jay Surti