9
Initial Margin Methodologies

9.1 ROLE OF INITIAL MARGIN

9.1.1 Purpose

The principal aim of derivatives margin is to reduce counterparty risk, either by a settlement or by a collateralisation process. Variation margin can reduce counterparty risk significantly, but in the event that a counterparty defaults, there will be a delay since the last variation margin was received. There will then be a further delay until the portfolio has been completely closed out. The total length of time for this to happen is typically known as the margin period of risk (MPoR), which is a term that originated in bilateral over-the-counter (OTC) markets for regulatory capital purposes. A counterparty, either central or bilateral, is exposed to market risk for the length of the MPoR. The aim of initial margin is to reduce the counterparty risk over the MPoR further, such that the residual risk is small or negligible and, therefore, the ‘defaulter-pays’ approach is likely to be upheld.

BCBS-IOSCO (2015) defines initial margin as covering ‘potential future exposure for the expected time between the last VM [variation margin] exchange and the liquidation of positions on the default of the counterparty’.

Regulatory guidance on initial margin amounts calculated by central counterparties (CCPs) is as follows:

A CCP should adopt initial margin models and parameters that are risk-based and generate margin requirements sufficient to cover its potential future exposure to participants in the interval between the last margin collection and the close-out of positions following a participant default. Initial margin should meet an established single-tailed confidence level of at least 99 percent with respect to the estimated distribution of future exposure.¹

Corresponding guidance for bilateral markets is as follows:

For the purpose of informing the initial margin baseline, the potential future exposure of a noncentrally cleared derivatives [sic] should reflect an extreme but plausible estimate of an increase in the value of the instrument that is consistent with a one-tailed 99 per cent confidence interval over a 10-day horizon.²

These statements suggest that there are two critical components that go into the determination of initial margin amounts:

• Confidence level. Both of the above suggest a confidence level of at least 99%, which would suggest – within the assumptions of the underlying methodology, at least – that initial margin would be sufficient in at least 99 out of 100 situations. Note that some regulation specifies a higher confidence level for OTC derivatives of at least 99.5%.³
• Time horizon. The time horizon for assessing the underlying market risk is also a key component. This is linked to the MPoR concept introduced earlier. Notice that for bilateral transactions this is clearly defined as 10 days, whereas there is no specific definition for centrally-cleared transactions.

The purpose of initial margin is to cover the market risk faced when a counterparty defaults. Of course, this cannot be done with certainty, but initial margins are intended to cover a very large proportion of potential price moves (99% or more when explicitly quantified) during the MPoR. There is a clear balance in setting initial margin levels: too low will imply that the CCP or bilateral party is facing material counterparty risks, whilst too high will mean trading costs may become excessive. A CCP must balance the need to be competitive by incentivising central clearing (low margins) with maximising their own creditworthiness (high margins). Not surprisingly, high margins have been shown empirically to have a detrimental impact on trading volumes (for example, see Hartzmark 1986 and Hardouvelis and Kim 1995).

Initial margin is perhaps the key aspect that defines the effectiveness of central clearing. It represents an additional margin required to cover the largest projected loss on a given transaction or portfolio. However, determining initial margin is a complex quantitative task and represents a difficult balance: undermargined trades impose excessive risk on a CCP, whereas excessive margins raise the costs of trading OTC derivatives. The methodology and assumptions used to compute initial margins will obviously have a significant impact on margin demands, as shown, for example, by Duffie et al. (2014).

Market participants will also need – or at least wish – to be comfortable with the initial margin calculation methodologies. Whereas variation margin relates to the current exposure, initial margin is providing coverage for future exposure. Initial margin is, by contrast to variation margin, much more complex and subjective.

Note that the regulatory guidance cited above implicitly suggests that initial margin methodologies will be dynamic, with initial margin amounts changing through time. This is explicitly stated in BCBS-IOSCO (2015), which states that initial margin should be

‘targeted’ and dynamic, with each portfolio having its own designated margin for absorbing the potential losses in relation to that particular portfolio, and with such margin being adjusted over time to reflect changes in that portfolio's risk.

Dynamic and risk-sensitive initial margin methodologies are clearly desirable in terms of reacting to the current risk on a given portfolio. However, this may lead to large changes in initial margin amounts during stressful market conditions (this is typically known as ‘procyclicality’). Dynamic approaches also make the prediction and quantification of the costs arising from future initial margin posting much more difficult.

Initial margin methodologies can be rule or risk based. Rule-based margin calculations make minimal reference to the underlying risk of the portfolio but are simple. Risk-based approaches are more complex to design and implement but have the benefit of recognising the offsetting nature of different trades in a portfolio.

Ideally, an initial margin model would take into account the following factors:

• Forecasting. The model can produce a reasonable forecast of potential exposures of the portfolio, accounting for all relevant risk factors and incorporating aspects such as non-Gaussian (fat-tailed) behaviour.
• Dependencies. Dependencies between different risk factors are modelled appropriately to capture (but not overstate) the diversification between different products. This is especially important for calculating the benefit achieved by cross-margining (Section 9.1.6).
• Procyclicality. The margin approach is designed to avoid procyclicality as much as possible. This may require incorporating different periods of market data, such as stressed periods.
• Margin period of risk. The MPoR is appropriate and based on the liquidity, market size, and specific characteristics of the product(s) in question.

9.1.2 Margin Period of Risk

Conceptually, initial margin is intended to cover potential losses during the so-called MPoR or ‘liquidation period’, as illustrated previously in Figure 7.6. The MPoR generally refers to the period from the point at which a defaulting party stops posting variation margin to the point at which the underlying market risk has been neutralised. It has been previously discussed for bilateral markets (Section 7.5.2) and cleared markets (Section 8.3.3).

Initial margin is generally quantified as a constant market risk for the MPoR in question and often does not make specific reference to components that may be relevant in the event of a counterparty defaulting. As such, as discussed in Section 7.5.2, it is probably not appropriate to consider the MPoR as an estimate of a literal time period, but rather as the correct value to use as an input into a quantitative model. The main problem here is one of ‘wrong-way risk’ (WWR). WWR refers to a linkage between default probability and exposure. This means that the MPoR should be assessed conditionally on the given counterparty being in default.

Such ‘default conditioning’ is not really practical for computing initial margin, as it would imply that it is not just specific to a given portfolio but also to the counterparty, and that every counterparty would have different initial margin requirements for the same underlying market risks. Such conditioning is therefore not a part of initial margin methodologies, and this is an important point to bear in mind. For example, Pykhtin and Sokol (2013) argue that the default of a more systemic party such as a bank will have a larger impact on the underlying market conditions, which would imply that more systemic counterparties should – ideally – post more initial margin.⁴ Interestingly, counterparties that actively use margining (e.g. banks) tend to be highly systemic and will be subject to these problems, whilst counterparties that are non-systemic (e.g. corporates) often do not post margin anyway.

Related to the above, there are a number of aspects that may be missed from the calculation of initial margin with a basic MPoR input:

• Volatility. The market volatility over the period is likely to be higher than normal market volatility, especially if the counterparty in default is large and/or systemically important. For example, Pykhtin and Sokol (2013) estimate that the volatility of credit default swap (CDS) index spreads in the aftermath of the Lehman bankruptcy was around four to five times greater than over the period just prior to their failure. Extending the MPoR to compensate for this increased volatility could be significant, as a doubling of volatility would approximately equate to an MPoR four times longer (see Section 7.5.2 for further discussion).
• Risk reduction. During the close-out process, the actual risk of the portfolio declines due to approaches such as macro-hedging (see Section 7.5.2), which would suggest a shortening of the MPoR. For example, being exposed to a portfolio with its risk reducing linearly for 10 days is approximately equivalent to being exposed to the full portfolio for about four days.⁵
• Downward pressure. In addition to the market volatility, there could also be downward pressure on prices, especially if the underlying portfolio is large.
• Costs. Any specific bid-offer or other costs experienced in rehedging positions or during CCP auctions will contribute further losses. For example, there have been claims of profiteering by clearing members in auction processes, which imposes losses on the defaulted member and potentially also the CCP (see Section 10.2.2).

The important point is that the above effects are not generally modelled in specific detail for initial margin calculations. There are exceptions to this: for example, the use of stressed historical data for initial margin calculations (discussed later) could be seen as capturing the impact of higher volatility in the close-out process. The MPoR is therefore defined by the literal time between the last margin payment and the time that the market risk has been completely hedged and adjustments for effects not captured explicitly.

Clearly, estimating the MPoR for initial margin methodologies is quite complex, product-/market-specific, and subjective. However, there are, broadly, only three different MPoR values that are used in practice:

• Exchange-traded markets (one or two business days). In exchange-traded futures markets, the MPoR used is generally one or two days, due to the underlying liquidity allowing for rapid close-out.
• Centrally-cleared OTC derivatives (five business days). In cleared OTC products, a longer MPoR typically of five days is used, although longer periods are sometimes used (e.g. SwapClear uses seven days for client portfolios).
• Bilateral OTC derivatives (10 business days). The MPoR in bilateral trades is explicitly defined as 10 days, as noted above. This is linked to the same parameter used for assessing risk in regulatory capital calculations for such transactions (Section 13.4.3).⁶ For example, the Commodity Futures Trading Commission (CFTC 2016) states that: ‘To the extent that related capital rules which also mitigate counterparty credit risk similarly require a 10-day close-out period assumption, the Commission's view is that a 10-day close-out period assumption for margin purposes is appropriate.’

Note that the choice of MPoR is partially at the discretion of the CCP in question (and will depend on the type of product being cleared), whereas initial margin requirements for uncleared bilateral trades must use a 10-day horizon. This 10-day requirement is not explicitly explained beyond the need for equivalence with the capital requirements, as mentioned above.

9.1.3 Coverage: Quantitative and Qualitative

In general, the following components are important considerations that can be seen to be assessed directly in quantitative initial margin models:

• Volatility. The most obvious aspect is the volatility of the portfolio in question. This is driven by the volatility of the underlying market variable(s) and the maturity. Long-dated products – such as many OTC derivatives – are likely to have significant initial margins. Likewise, more volatile asset classes should have higher associated initial margins.
• Dependency. A typical portfolio may consist of a variety of different trades with sensitivity to different market variables (‘risk factors’), potentially in different asset classes. It is therefore important to understand the offsetting nature of such trades. If dependency between the price moves of different trades is small (or even negative), then clearly the overall portfolio is less risky, and the benefit of this is that less margin needs to be posted. However, the dependencies within and between asset classes are notoriously difficult to quantify and can change significantly through time.
• Tail risk. Whilst volatility typically measures continuous price variability, some products (e.g. credit derivatives) can suffer from tail risk due to jumps or gaps in the underlying market variables. Likewise, it is possible for dependency between risk factors to be non-linear and, therefore, hard to predict. For example, risk factors may show particularly high dependence in a crisis period compared to their normal relationship.

Some of the above may not raise obvious concerns over initial margin quantification since, at a confidence level of 99%, there are clearly scenarios where the initial margin is – by design – insufficient. In these relatively extreme cases, market participants have loss absorbency in the form of some sort of capital that may be utilised. Hence, whilst initial margin is intended to cover a fairly bad scenario, it may not capture some of the more extreme behaviour, such as very heavy-tailed distributions or strong dependencies. Such effects, where relevant, may be better captured by default fund contributions at CCPs or capital requirements by banks. Correspondingly, such amounts are driven by more qualitative approaches, such as stress testing and standardised models.

Margin methodologies do make use of supplementary and more qualitative approaches that may increase initial margin in certain cases. For example, they may penalise large portfolios that would be more difficult to manage in a default scenario (see Section 9.3.6).

Regulation also puts restrictions on initial margin methodologies that can be seen to mitigate some of the inherent problems that the above considerations imply in terms of model risk. Two examples of this are the requirement to use ‘stressed data’ as inputs to the margin methodology and the inability to gain benefit from the offsets between different asset classes (cross-margining, Section 9.1.6).

The requirement to use stressed data for bilateral trades is stated clearly in BCBS-IOSCO (2015) as requiring initial margin to be based on ‘historical data that incorporates a period of significant financial stress’. Likewise, guidelines for CCPs also refer repeatedly to ‘stressed market conditions’ (CPSS-IOSCO 2012). By using an inherently stressed environment, initial margin will, to some extent, capture the impact discussed in Section 9.1.2 (e.g. a current definition of a stressful period may include the period immediately after the default of Lehman Brothers in 2008).

9.1.4 Haircuts

Whereas variation margins are generally cash only, both bilateral markets and CCPs allow initial margins to be posted in other securities. This raises the issue of whether the value of the initial margin assets held would decline during the close-out period. In general, this can be mitigated in two ways:

• Eligible securities. Securities eligible for initial margin will be restricted to those without any significant credit or liquidity risks that could cause extreme adverse price moves. Moreover, securities that might be adversely correlated to the credit quality of a clearing member would not be accepted.
• Haircuts. Given the above, a margin recipient should be concerned only with the market risk, which can be mitigated by the appropriate choice of haircut. Indeed, even assets such as gold and equity indices are potentially acceptable, as they have large market risks that can be mitigated by accordingly large haircuts and probably do not suffer from other sources of adverse price moves, such as liquidity.

Haircuts, as discussed previously, are generally defined to cover the majority of detrimental price moves over a representative liquidation period (e.g. a two-day price movement and a 99% confidence level). Note that the assumed period may be shorter than for initial margin calculations (MPoR) because selling margin securities is not dependent on the successful bilateral close-out or completion of a CCP auction or other default management functions. Haircuts will also be applied to cash margin with similar assumptions about the liquidation period and confidence level, and can be relatively significant.⁷

9.1.5 Linkage to Credit Quality

Initial margin is generally considered to be linked wholly to market risk and is therefore not dependent on the probability of default of the party in question. This is counterintuitive since parties with stronger credit quality often naturally expect to receive more favourable trading conditions. This also implies – to some extent – a homogeneity of parties in the market and otherwise implies that weaker ones will gain at the expense of stronger ones. Indeed, Pirrong (1998) argues that the delay in adopting central clearing on certain exchanges was related to stronger credit quality members not wishing to subsidise weaker ones.

Another reason to decouple initial margin from credit quality – in particular, credit ratings – is to avoid some of the ‘cliff-edge’ effects seen when a party becomes financially distressed. Such distress inevitably leads to credit rating downgrades, which in turn may trigger the requirement to post more margin at the worst possible time, and this was illustrated clearly in the global financial crisis (see Section 2.4.4). This was also relevant in the default of MF Global in 2011. MF Global was a member of several CCPs and faced increased margin requirements as its rating was downgraded. In line with these potential issues, banks now experience costs associated with credit rating triggers under the liquidity coverage ratio (LCR), as discussed in Section 4.3.3.

In the bilateral margin requirements (BCBS-IOSCO 2015), no mention is made of the credit quality of either party and, therefore, initial margin calculations are credit-quality independent. Of course, it could be argued that parties may choose not to trade with bilateral counterparties with low credit quality.

The regulatory requirements and treatment of credit quality by CCPs are more complicated. Generally, CCPs have moved away from linking initial margin to credit ratings issued by nationally-recognised statistical rating organisations (NRSROs).⁸ Previous to this, SwapClear had required that initial margin for clearing members rated A–, BBB+ and BBB be multiplied by 1.1, 2.0, and 2.5 respectively (and below BBB the clearing member was required to leave).⁹ Indeed, regulation explicitly forbids CCPs from linking margin to external credit ratings as required by the Dodd–Frank Wall Street Reform and Consumer Protection Act, and instead requires them to use ‘other appropriate standards of credit-worthiness’.¹⁰ CCPs do not, therefore, increase initial margin if a clearing member is downgraded.¹¹

CCPs do, however, use their own internal rating systems to determine credit quality based on a number of factors, including CDS spreads, asset quality, and capital adequacy. If a clearing member's credit quality is determined by the CCP to have deteriorated to a level that does not support the volume of risk it has cleared, then it may be subject to margin multipliers and/or limitations to new business. The CCP may also assign credit limits based on its internal ratings in order to prevent counterparts with lower credit quality from building up excessive exposure.¹² CCPs may also limit membership to supervised firms.

Another aspect related to this is the linkage of haircuts to credit quality. This was illustrated quite clearly by the MF Global default. MF Global held $6.4bn of European sovereign debt (which was financed through repo trades). When, due to the declining credit risk of the issuers, haircuts on these assets were increased, this created a negative asset shock that helped to catalyse the decline of MF Global. Whilst CCPs should ideally increase haircuts to mitigate declining credit risk in such situations,¹³ there is a clear danger that this increases systemic risk, especially when done suddenly. Even if the CCP is better off after such a move (which is debatable, since it may push the clearing member into default), it is unlikely that the market as a whole would benefit. Such effects are less likely in bilateral markets, as a receiver of margin would typically not be able to change contractual haircuts without agreement from a counterparty.

Finally, it is worth noting that the WWR ideas in Section 9.1.2 actually suggest a completely opposite idea, in that higher (not lower) credit quality parties should be charged more initial margin, since their default would be a more unexpected event and therefore may create more turbulent market conditions and be more difficult to manage. Mathematical models for WWR typically predict this behaviour (Section 17.6). This is also true since parties with strong credit ratings are also more likely to be large and systemically-important institutions.

9.1.6 Cross-margining

Cross-margining is a general term that refers to margin calculations made on a portfolio rather than on a product-by-product basis. The advantage of this is that margins will be more competitive as they will benefit from reductions due to offsetting positions. Gemmill (1994) illustrates the diversification offered to CCPs from clearing several markets that are not highly correlated. Cross-margining offers the following inter-related benefits:

• Lower margin costs. Lower initial margins due to the diversification benefit between positions.
• More efficient auctions. In the event of a default scenario, all cross-margined positions could be liquidated together as an offsetting or hedged portfolio. This may minimise CCP auction or bilateral close-out costs and reduce the systemic impact of the default.
• Reduced legal and operational risk. Since initial margin represents funds not actually owed to counterparties, this also provides a reduction of exposure to losing margins in the event of non-segregation, fraud, or operational problems.

Firms and their clients will be actively looking to receive the benefits of such favourable dependencies in the form of lower initial margins. In particular, some sophisticated financial institutions use a variety of different transactions and often execute combinations of positions that are partially hedged. In such situations, the cross-margining benefits would be expected to be particularly significant.

There are a number of different ways in which cross-margining could be applied – by a CCP or in bilateral markets – that increase in complexity:

• within a given product type (e.g. different currencies of interest rate swaps);
• between products within a given asset class (e.g. fixed to floating interest rate swaps and basis swaps, or index and single-name CDSs);
• between centrally-cleared exchange-traded and OTC products (e.g. interest rate futures and interest rate swaps);
• between products in different asset classes (e.g. interest rate swaps and CDSs); and
• between different CCPs.

Some of the above are more challenging – for example, due to the need to develop sophisticated models to represent the dependencies in a portfolio, for operational reasons (e.g. futures versus OTC products), or due to jurisdiction differences (between CCPs in different regions). However, particularly as OTC clearing and bilateral margining become more widespread, the possibility of achieving lower margins through cross-margining will become increasingly important for market participants.

There is also some evidence that clearing multiple asset classes may be useful in default management. For example, Lehman Brothers traded a combination of interest rate, equity, agriculture, energy, and foreign exchange (FX) positions on the Chicago Mercantile Exchange (CME), and whilst they suffered losses on two out of five of these asset classes, this was covered by excess margin from the other three (Pirrong 2013), meaning that the overall initial margin was sufficient. LCH.Clearnet's diversified spread of business was a help in the same default, with the CEO stating, ‘Without this degree of diversification it is doubtful whether we would have had the time to identify and transfer the client positions. Instead we would have had no option but to close-out all the positions in the house account, leaving many clients unhedged.’¹⁴

Historically, CCPs have tended to avoid extending cross-margining excessively. This is not surprising, as in the presence of cross-margining, initial margin methodologies will have to be more complex and represent dependencies and basis positions, which would not be important for silo-based portfolio calculations. However, as the use of initial margin increases (especially in the OTC derivatives space), it would be expected that cross-margining may increase as CCPs expand and cover more product types.

Probably the most difficult aspect in cross-margining is understanding and quantifying financial risk and the dependency between different financial variables. It is well known that historically-estimated correlations may not be a good representation of future behaviour, especially in a more volatile market environment. In a crisis, correlations have a tendency to become very large on an absolute basis. It is also important to represent that, unlike volatility, it is not immediately obvious how to stress a correlation value, as the underlying sensitivity of a portfolio may be positive or negative and may not even be monotonic. Therefore, whilst multidimensional modelling of risk factors can lead to increased benefits from margin offsets, it also increases the underlying model risk.

One example of the competitive benefit of cross-margining has been between exchange-traded (e.g. futures) and OTC products (e.g. swaps). For example, the CME has offered cross-margining benefits between Eurodollar and Treasury futures contracts and OTC interest rate products since 2012.¹⁵

However, such a coming together is not completely trivial.¹⁶ Firstly, initial margin methodologies have historically differed for futures and OTC products (see discussion in Sections 9.2 and 9.3). Secondly, the assumed MPoR for more liquid futures products is shorter (typically one or two days) than their OTC counterparts (typically five or more days). Thirdly, margin account structures for these products may differ. A final potential problem could be regulatory driven – for example, in the US, where futures products are regulated by the Securities and Exchange Commission (SEC) and OTC products by the CFTC.

Regulation does restrict the extent of cross-margining that can be done, due to the view that modelling such dependencies is notoriously difficult. For bilateral transactions, BCBS-IOSCO (2015) states that:

At the same time, a distinction must be made between offsetting risks that can be reliably quantified and those that are more difficult to quantify. In particular, inter-relationships between derivatives in distinct asset classes, such as equities and commodities, are difficult to model and validate. Moreover, this type of relationship is prone to instability and may be more likely to break down in a period of financial stress.

Requirements for CCPs are not prescriptive but do state that initial margin offsets can only be recognised between products that are ‘significantly and reliably correlated’ (CPSS-IOSCO 2004) with each other.

The rules for bilaterally-cleared transactions are clearer by defining that initial margin must be additive across asset classes, which are defined as currency/rates, equity, credit, and commodities (BCBS-IOSCO 2015). There can, therefore, be no cross-margining benefit between these asset classes, but the benefit can be taken within each one. This is also the approach of CCPs generally, where cross-margining occurs within asset classes (e.g. interest rate swaps and swaptions),¹⁷ but not across different ones. This also explains why CCPs have tended to specialise and potentially dominate individual asset classes.

9.2 INITIAL MARGIN APPROACHES

9.2.1 Simple Approaches

In the early days of derivatives trading, initial margin was only used on exchanges, and the amounts were typically based on simple approaches. For example, consider a single equity position: the key inputs to determining initial margin could be considered to be the volatility , the time period in question (MPoR), and the confidence level required (). Under normal distribution assumptions, this would lead to the simple formula and example given below, where the initial margin is calculated to be 2.4% of the size of the position.

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Simple initial margin (IM) formula

For example, consider:

, MPoR = 1 business day, and (this represents the 99% confidence level for a normal distribution).

Assuming 252 business days in a year, this would give:

---

The first obvious criticism of the above approach is that it makes an assumption about the underlying risk factor distribution (e.g. normal) and therefore ignores aspects such as fat-tailed behaviour. The second problem is that it needs to be extended to other dimensions (so as to appreciate portfolio effects). This would be possible by introducing correlations between risk factors as well as their volatilities, although this would then have the problems associated with modelling dependencies. Such problems are particularly acute for balanced portfolios where the risk of positions cancels, as opposed to a directional portfolio where the risks are – more or less – additive.

Probably the biggest issue with approaches built on the above idea is that, for large portfolios, it is not clear whether the sensitivity to a given risk factor overall will be positive or negative, since there may be some positions that make money from an increase in the risk factor, whilst others lose money. Furthermore, such sensitivities can be non-linear, especially when more complex products – such as options – are included. Hence, whilst the example above essentially generates only a single scenario (since it is obvious that a long equity position is sensitive to a downward move in stock prices and vice versa), a portfolio initial margin calculation needs to consider multiple scenarios.

9.2.2 SPAN^®

For exchange-traded clearing, in 1988 the CME developed a method known as Standard Portfolio Analysis of Risk (SPAN) to assess risk effectively on an overall portfolio basis.¹⁸ SPAN was licenced by the CME, and by 2008 was being used by more than 50 exchanges and CCPs globally. Similar approaches such as the Theoretical Intermarket Margin System (TIMS) or the System for Theoretical Analysis and Numerical Simulations (STANS) have also been developed.¹⁹

The introduction of SPAN was revolutionary at the time, since it allowed margins for futures and options to be calculated based on the overall portfolio risk. A typical example would be the margining of a portfolio containing offsetting exposure to different equity indices (e.g. S&P 500 and Nasdaq), where the high correlation would create beneficial margin reduction.

SPAN groups together financial instruments with the same underlying for analysis (e.g. futures and options on an equity index). SPAN works by evolving individual risk factors (e.g. spot price, volatility) combinatorially based on movements in either direction. Products with the same underlying will share risk factors. A series of shifts are applied to each risk factor, which is intended to be representative of one- or two-day moves in the underlying variables. Some more extreme shifts may also be applied (which may be particularly relevant – for example, for an out-of-the-money position).²⁰ Most SPAN exchanges and clearing organisations use 16 scenarios (‘risk arrays’). The portfolio is then revalued under the different moves, and the worst scenario is normally used to define the initial margin.

The scenarios used by SPAN consider the following:

• variation of underlying price;
• variation of underlying volatility; and
• impact of time on the option price.

An example of SPAN shifts applied to an option position is shown in Figure 9.1.

An example of a SPAN calculation is shown in Table 9.1. This corresponds to a combined position in an S&P futures contract (long) and an S&P call option (short). The underlying movements are represented with respect to a ‘price scan range’ and ‘volatility scan range’, which are the maximum movements reasonably likely to occur over the time in question (one or two days). The change in value for the future, option, and combined (portfolio) positions are shown. Note that for the futures contract, the valuation is trivial and objective, whilst for the option position, a subjective valuation model is required.

Figure 9.1 Illustration of risk factor shifts applied for determining the initial margin of an option position using SPAN. The underlying index is shifted up and down by four different amounts and single up/down volatility shifts are applied to each (note the fourth index shift is an extreme scenario intended for deep out-of-the-money options).

Table 9.1 Example of a SPAN calculation. The price scan range is 22,500 and the volatility scan range is 7%.²¹

Scenario	S&P move	Volatility move	Future	Option	Portfolio
1	Unchanged	Up	0	1,807	1,807
2	Unchanged	Down	0	−1,838	−1,838
3	Up 33%	Up	−7,499	7,899	400
4	Up 33%	Down	−7,499	5,061	−2,438
5	Down 33%	Up	7,499	−3,836	3,663
6	Down 33%	Down	7,499	−8,260	−761
7	Up 67%	Up	−15,001	14,360	−641
8	Up 67%	Down	−15,001	12,253	−2,748
9	Down 67%	Up	15,001	−8,949	6,052
10	Down 67%	Down	15,001	−13,980	1,021
11	Up 100%	Up	−22,500	21,107	−1,393
12	Up 100%	Down	−22,500	19,604	−2,896
13	Down 100%	Up	22,500	−13,455	9,045
14	Down 100%	Down	22,500	−18,768	3,732
15	Up 300%	Unchanged	−22,275	21,288	−987
16	Down 300%	Unchanged	22,275	−9,160	13,115

By plotting the movements from the above table, it is possible to understand the risk of the combined position (Figure 9.2). The (long) call option makes losses when the underlying index goes down and also when volatility goes down.²² The (short) index position gains in value when the index falls, offsetting losses on the option position.

Future and option positions' gains or losses can be combined to give the total portfolio position, shown for down and up volatility scenarios in Figure 9.3. Note that the worst-case scenario for the CME (largest gain)²³ in both volatility scenarios is the maximum down move in the S&P index, where the gains on the index position are not fully offset by the losses on the option. The volatility up scenario is worse from the CME's point of view, since the option time value is lower.

In the above example, the initial margin would be 13,115 (Table 9.1), which is the gain in Scenario 16, which is the extreme down move of 300% of the price scan range (not shown in Figure 9.3). Note that SPAN only applies a 33% weight to this scenario.

SPAN can potentially identify the risk in more subtle scenarios. For example, suppose a client clears a position which is long an index but with downside risk hedged by buying an out-of-the-money put option. Figure 9.4 shows the position, from the CCP point of view. The worst scenario is not a maximum downwards move on the index, where the option is strongly mitigating client losses, but rather a more moderate move, where the option has a more limited effect. This shows that SPAN can potentially identify the worst scenario in a balanced position as not necessarily being the largest move in the underlying variable(s). However, note that because of the limited number of scenarios and the relatively large required scanning range, SPAN does not capture this point accurately.

Figure 9.2 Variation for S&P future and option contracts according to the data in Table 9.1 (ignoring the extreme shifts). Note that the futures contract has no sensitivity to volatility.

Figure 9.3 A combined move of total portfolio position in down and up volatility scenarios according to the data in Table 9.1 (ignoring the extreme shifts).

Figure 9.4 Gains and losses for a portfolio consisting of a short equity index position hedged by a long put option and SPAN points.

The strong standardisation of exchange-traded transactions (e.g. where the number of expiration dates or strikes for a given product is small) supports a relatively simple method such as SPAN. SPAN is quite well suited to risk assessment on simple portfolios such as futures and options, which are generally of low dimensionality (the above example needs only really to consider two dimensions: index level and implied volatility). Whilst SPAN-type methods work well and are tractable for simple portfolios, they have drawbacks. Most notably, they do not scale well to a large number of dimensions (as the number of combinations of moves grows exponentially).

OTC derivatives portfolios are typically of high dimensionality, with many more risk factors than for exchange-traded markets. For example, even a single interest rate swap is sensitive to the full term structure of interest rate moves, and cannot be represented as a single parallel shift in rates, since this implies unrealistically that rates for different tenors (maturity dates) are perfectly correlated. SPAN also makes relatively simplistic assumptions on implied volatility changes, normally expressed as a single volatility shift, which will not capture volatility risk in portfolios sensitive to more subtle changes in the volatility surface. SPAN approaches give results which are relatively static through time and also do not clearly attach an underlying probability to the scenario defining the initial margin, and are therefore not especially risk sensitive. Finally, the up and down moves that define the worst move of a given market variable are somewhat subjective.

For the above reasons, OTC derivatives CCPs have been moving towards more value-at-risk-like methods for initial margin calculation, as discussed below. Bilateral margining has adopted a similar, although simpler, method.

9.2.3 Value-at-risk and Expected Shortfall

As discussed in Section 2.6.1, value-at-risk (VAR) is a key approach for quantifying financial market risk that has been developed by large banks over the last two decades. A VAR number has a simple and intuitive explanation as to the worst loss over a target horizon (e.g. five days) to a certain specified confidence level (e.g. 99%). Given this definition, VAR has a natural application for defining initial margin requirements for given MPoRs and confidence levels.

One problem with VAR is that it is not a coherent risk measure (Artzner et al. 1999), which means that in certain (possibly rare) situations, it can exhibit non-intuitive properties. The most obvious of these is that VAR may not behave in a sub-additive fashion. Sub-additivity requires a combination of two portfolios to have no more risk than the sum of their individual risks (due to diversification). This could translate into the requirement that the initial margin when clearing a large portfolio through a single CCP would be no greater than the total initial margin when clearing the same portfolio as sub-portfolios through different CCPs.²⁴ Such properties cannot be guaranteed when using VAR as a risk measure.

Expected shortfall (ES) is the average loss equal to or above the level defined by VAR, and it does not suffer from the above problems. An example of the sub-additive behaviour of VAR and ES is shown in Table 9.2. Here, the 90% VAR²⁵ is defined by the ninth highest loss, which is higher in the combined portfolio (100) than in the sum of the two individual portfolios (80). ES is an average of the highest two values and does not exhibit this problem.

Note that VAR and ES allow the precise scenario(s) upon which the initial margin is based to be identified and that these are different for each portfolio. This is rather like the SPAN approach described in Section 9.2.2. However, unlike SPAN, VAR and ES are defined to a known statistical confidence level, as opposed to simply being the worst of a small number of scenarios. Since VAR and ES are general definitions, they can be used to define the initial margin for any portfolio.

Table 9.2 Example showing the sub-additivity properties of VAR and ES metrics. The scenarios corresponding to the VAR and ES are shown in bold. Note that all values represent losses.

	Portfolio 1	Portfolio 2	Total
Scenario 1	10	30	40
Scenario 2	30	40	70
Scenario 3	40	30	70
Scenario 4	10	90	100
Scenario 5	80	30	110
Scenario 6	35	5	40
Scenario 7	20	25	45
Scenario 8	15	35	50
Scenario 9	20	25	45
Scenario 10	10	30	40
VAR (90%)	40	40	100
ES (90%)	60	65	105

VAR models can be ‘backtested’ as a means to check their predictive performance empirically. Backtesting involves performing an ex post comparison of actual outcomes with those predicted by the model. VAR lends itself well to backtesting since, for example, a 99% number should be exceeded once every 100 observations.

Given the drawbacks of SPAN for more complex and potentially multidimensional derivatives portfolios and the general usage of VAR models for market risk applications, it is not surprising that CCPs have moved towards more risk-sensitive VAR-type approaches for initial margin calculations for OTC products. Such approaches are suited to, for example, high-dimensionality multicurrency swap portfolios.

However, VAR and ES are merely statistical measures. There is still the much bigger question of how to define them for a given portfolio. Following an approach used by banks for many years for the quantification of market risk, CCPs have generally used ‘historical simulation’ approaches for this. As described in Section 2.6.1, historical simulation essentially simulates how a given portfolio would have performed over a given period in history and uses the worst losses to define the VAR or ES. This has the advantage of being able to use many scenarios without the need to decide specifically on the underlying modelling of each risk factor. Historical simulation has now become a fairly standard approach for the initial margin methodologies for centrally-cleared OTC derivatives.

In the bilateral markets, historical simulation has been considered too complex an approach, since both parties need to agree on the initial margin amounts. Hence, bilateral markets are adopting the International Swaps and Derivatives Association (ISDA) Standard Initial Margin Model (SIMM^TM), which can be seen as a more simple and tractable version of historical simulation. Both the historical simulation and SIMM approaches will be discussed below.

9.3 HISTORICAL SIMULATION

9.3.1 Overview

The most common implementation of VAR and ES approaches is using historical simulation. This approach takes a period (usually several years) of historical data containing risk-factor behaviour across the entire portfolio in question. It then resimulates over many periods how the current portfolio would behave when subjected to the same historical evolution. For example, if four years of data were used, then it would be possible to compute around 1,000 different scenarios of daily movements for the portfolio. The 99% VAR would then be estimated as the 990th worst loss (so that 10 – or 1% – of the losses are higher).

Historical simulation can simulate, self-consistently, potential moves in all relevant risk factors by following a simple rule:

Following any simulation of risk factors, the portfolio can be valued using these new risk factor values, and the resulting change in portfolio value forms a distribution. From this distribution, a metric such as VAR or ES can be calculated. A historical simulation approach can, therefore, be summarised as follows:

1. select a set of risk-factor changes that collectively drives the value of the underlying portfolio (e.g. equity, commodity prices, interest rates, FX rates, bond yields, and implied volatilities) observed over a given historical period(s);
2. revalue the portfolio multiple times, assuming that each of the risk-factor changes happened again; and
3. calculate the statistical quantity required from the distribution of changes in portfolio value.

Inevitably, historical simulation relies on a fundamental assumption that the past is a good guide to the future. Whilst this might be criticised, it is an almost inevitable requirement for any model for assessing financial risk. There are also a number of other choices and problems when implementing historical simulation:

• Look-back period. The choice of how long to make the data window is subjective. A long window or ‘look-back period’ (e.g. 10 years) will provide more data points but might contain old and irrelevant data. A short window may contain more recent, relevant data but will contain fewer points overall and be subject to noise, and may cause procyclicality (Section 9.3.5). It is not necessary to use a single continuous period, which is often the case when stressed periods are included.
• Scaling. Since risk factors will be at a different level to where they were in the past, there is a choice to be made about how to scale past change to produce potential future changes. This inevitably requires an implicit assumption about how the underlying risk factor behaves.
• Autocorrelation. This refers to the fact that data over sequential time horizons may be quite dependent (such as during quiet or volatile periods). For estimating the initial margin over a period such as five days, there may not be enough data to use non-overlapping returns. Using overlapping returns presents further complications. Alternatively, the initial margin over one day could be scaled using the ‘square root of time’ rule or more sophisticated approaches (Danielsson and Zigrand 2003).

The above points will be analysed in more detail in the next sections.

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Spreadsheet 9.1 Initial margin calculation of an interest rate swap using historical simulation.

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9.3.2 Look-back Period

The look-back period refers to the historical range of data used. Choosing the look-back period is quite subtle: a very long period may use old and meaningless data, whereas a short period may lead to unstable results. Banks have typically used between one and three years for the purposes of VAR models for capital calculations, and not usually more than five years. Typically, shorter look-back periods are more problematic as very volatile periods (such as the period in the aftermath of the Lehman default) drop out of the data set.

Figure 9.5 Evolution of initial margin for an interest rate swap calculated with different look-back periods.

Figure 9.5 shows the calculation of the initial margin for a single five-year interest rate swap and its evolution through time (that is to say, the initial margin is calculated repeatedly each day, as would be the case in practice) for 3- and 10-year look-back periods. Whilst the average initial margin is the same in both cases, the shorter look-back period leads to much more instability. This instability is caused because, when large moves in the risk factor drop out of the back of the look-back window (‘ghost effects’), the initial margin falls. Correspondingly, as recent large risk-factor moves enter into the look-back period, the initial margin can increase rapidly. With the long look-back period, the impact of observations moving in and out of the data is damped by the much larger amount of data present (approximately 2,500 days compared to 750).

Clearly there are advantages and disadvantages to the choice of longer or shorter look-back periods: shorter may be overreactive, whereas longer may not be reactive enough. Rather than choosing a fixed look-back period where all events have recent weights, Boudoukh et al. (1998) proposed to assign more probability to recent events than those in the more distant past. This is related to volatility scaling methods and also the discussion on procyclicality in Section 9.3.5.

9.3.3 Relative and Absolute Returns

Being more explicit about the implementation of historical simulation, the simulation of risk factors can be written as:

where is the current value of the risk factor, is its simulated value in scenario s, and and are the value of this risk factor at the start and end of the same time period in the past. Implicit in the above equation is the assumption that it is the relative (percentage) changes in the risk factor that are important. This is consistent with a distribution assumption such as lognormal, where the risk factor cannot change sign, and up moves (in absolute terms) can be larger than down moves. This approach is generally referred to as ‘relative returns’.

Alternatively, one could consider ‘absolute returns’ which would correspond to the following equation:

Absolute returns are consistent with a symmetric distribution (such as a normal distribution) and do allow the risk factor to change sign.

Some risk factors are more suited to relative returns since they are naturally bounded between zero and infinity (e.g. an FX rate or a credit spread). Others may be more suited to absolute returns (e.g. interest rates, which have been seen to be negative in some cases in recent years). Other assumptions could also be used.

Relative returns have traditionally been used in historical VAR approaches. This means that a move in interest rates from 3.0% to 3.6% is interpreted as a 20.0% increase. In a low interest rate environment, where rates are 1.0%, this would translate into quite a small upwards move to only 1.2%. If instead the absolute rate change were used, then the equivalent move would be to 1.6%. This is illustrated in Table 9.3, showing two different scenarios. It is also worth emphasising that absolute returns may produce negative interest rates (which may be unrealistically large), whilst relative returns cannot (unless interest rates themselves become negative).

Whether absolute or relative scenarios are most appropriate depends on the current rates regime. Absolute moves are more conservative in a falling interest rate environment, as illustrated in Figure 9.6. On the other hand, the reverse will be true during a period of rising rates. This is a well-known problem in the area of interest rate models, where behaviour can move between normal (absolute shifts) and lognormal (relative shifts).

Figure 9.7 shows a calculation of the initial margin for a single five-year interest rate swap and its evolution through time when using relative and absolute returns. In this case, absolute returns lead to higher initial margin since the period in question is one where interest rates are generally falling. This can be seen to reverse slightly towards the end of the calculation range. Note also that absolute returns are inherently more stable since they apply the same risk factor change regardless of the current level of the risk factor. This can also be seen from Figure 9.7, where the increase in the initial margin after day 2,000 for relative returns occurs mainly due to an increase in the level of interest rates (as opposed to a change in the data being used).

Table 9.3 Comparison of historical simulation using absolute and relative returns.

	Historical data			Historical simulation
	Initial rate	Final rate	Change	Initial	Simulated
Absolute	3.0%	3.6%	0.6%	1.0%	1.6%
Relative	3.0%	3.6%	20.0%	1.0%	1.2%
Absolute	4.0%	3.2%	−0.8%	1.0%	0.2%
Relative	4.0%	3.2%	−20.0%	1.0%	0.8%

Figure 9.6 Illustration of historical simulation for an interest rate process using absolute and relative scenarios. The simulation begins at the 250-day point.

Figure 9.7 Evolution of initial margin (99% VAR) for an interest rate swap calculated with relative and absolute returns.

9.3.4 Volatility Scaling

It is well known that financial processes are not well described by a process with constant volatility. A standard historical simulation model associated with equal weights over a look-back period implicitly assumes constant volatility of the underlying risk factors. It will also be unable to produce an initial margin that is higher than that which corresponds to the worst historical move it has ever ‘seen’.

Different approaches to the treatment of volatility emerged in the early days of VAR models, with the exponentially-weighted moving average (EWMA) estimation proposed in RiskMetrics (Zangari 1994; J.P. Morgan 1996). This applies a non-uniform weighting to time-series data so that a lot of data can be used, but recent data is weighted more heavily. As the name suggests, weights are based upon an exponential function, which means that large risk-factor returns will drop out of a data set gradually. It is necessary to choose the value for the ‘decay factor’ (RiskMetrics set it to 0.94), which defines how quickly the weight of past data decreases.

More generally, ‘volatility scaling’ is an approach that seeks to use an estimate of the current level of volatility to scale returns with respect to the current volatility estimate at the time they occurred. In other words, it scales the generation of possible future returns (Section 9.3.3) by a ratio of , where is the current estimate of volatility and is the past estimate. This approach implies that current market conditions have some information: for example, if current volatility is higher than usual, then this may be indicative of market moves being larger than usual.

In general, volatility-scaled historical simulation has better backtesting properties due to it anticipating a potential increase in volatility. Accordingly, it can also produce low estimates for initial margin where there has been a period of low volatility. The result is that there is increased variability of the initial margin estimator or procyclicality (discussed in Section 9.3.5).

9.3.5 Procyclicality

Whilst initial margin models that are ‘targeted’ (towards a given portfolio) and dynamic (in terms of reacting to market conditions) are clearly desirable, this also raises the issue of procyclicality. CPSS-IOSCO (2014) recommends that financial market infrastructures (FMIs) such as CCPs adopt stable and conservative margin requirements to prevent procyclicality.

In times of higher market volatility, price changes are larger, so the minimum level of initial margin required to cover potential price changes must also be higher. Risk-sensitive initial margins will tend to be lower in quiet times and higher in turbulent markets. This dynamic can have a destabilising effect since it encourages high leverage in bullish market environments, leading to sudden shocks where a sharp increase in volatility can lead to additional initial margin being required from market participants. However, at this point, firms may be under stress in general and will, therefore, be required to post additional margin precisely when it becomes most difficult to raise cash or other liquid assets. Risk-sensitive margin requirements are therefore procyclical as they may amplify shocks. Whilst initial margin reduces counterparty credit risk, the procyclicality of initial margin provides a channel for the spread of contagion.

Heller and Vause (2012) estimate that without any adjustment for procyclicality, initial margins for interest rate swaps could increase by around a factor of two between a low- and high-volatility regime, and CDSs could show an impact of approximately an order of magnitude.

An alternative to the above is to try and set initial margin at higher ‘through-the-cycle’ levels, which are therefore less sensitive to current conditions. However, it is clearly not desirable for these levels to be excessively high or to have initial margin levels that are completely unreactive to market conditions.

This difficult balance is well articulated in the following text (ESMA 2018), which suggests the need for a balance between promoting risk sensitivity and preventing excessive procyclicality:

It is important to recognise that it is not the intention of the regulation to prevent CCPs from revising their margins to address changes in volatility. Instead, the regulation propagates the notion that CCPs should prevent big-stepped, unanticipated calls on clearing members during periods of extreme stress. The following guidelines should therefore be read in this context.

There are a number of choices that can influence initial margin procyclicality:

• Historical time series. The choice of the look-back period is a key input. If the period is short, then it may arguably contain the most relevant recent data, but it will also lead to margins moving rapidly through time, as turbulent days move in and out of the data set (ghost observations) and cause rapid oscillations (see procyclical example in Figure 9.9). Using a long history will tend to smooth out such effects, as given periods will have less overall impact on the measure calculated (similar to the normal result in Figure 9.9).
• Volatility scaling. Certain VAR methods use various ways to capture volatility clustering in financial data. A simple example is to use EWMA historical data,²⁶ which means that the data points have less impact the further away they occur. Another common approach is known as filtered historical simulation (FHS). Whilst these approaches arguably all get closer to the realities of financial markets (e.g. that there are long periods of small market moves followed by short periods of strong moves), they potentially lead to greater procyclicality and would cause initial margins to increase quickly at the start of a crisis but then drop quickly as the crisis is averted.
• Autocorrelation. VAR approaches sometimes use overlapping returns to maximise the number of individual data points. This creates problems since overlapping data will, by definition, show dependencies, and a single extreme event will show up in several overlapping periods and have a large impact. The only simple methods to prevent autocorrelation are to use either the single worst-case loss or non-overlapping returns.
• Risk measure. The choice of risk measure has some impact on procyclicality. For example, suppose the worst-case scenario in a five-year window is used to calculate VAR. When this day drops out of the data window, then the initial margin will fall. If, on the other hand, the initial margin is the average of the worst few days, then one day dropping out will have a smaller impact. Figure 9.8 shows initial margin computed at the 95% and 99.5% confidence levels, with the latter being higher and more rapidly varying. Note that scaling up the 95% initial margin (assuming normal distribution quantile levels) is more stable than the 99.5% result.

Figure 9.8 Evolution of initial margin for an interest rate swap calculated with VAR at the 95% and 99.5% confidence levels. Also shown is the 95% confidence level scaled by 1.56, which is the ratio between these confidence levels implied by a normal distribution.²⁷

The impact of procyclicality on VAR is illustrated in Figure 9.9. A procyclical initial margin will change sharply with underlying market conditions. In order to avoid this procyclicality, it is necessary to have a higher initial margin most of the time. For example, Glasserman and Wu (2017) show that a non-procyclical initial margin is higher than the average procyclical initial margin and that this effect increases for higher confidence levels. Avoiding procyclicality is, therefore, costly.

An obvious way to prevent (or reduce) procyclicality is to use stressed data within the historical look-back period. For example, under the so-called Basel 2.5 changes (BCBS 2009), banks were required to include a one-year period of ‘significant financial stress relevant to the bank's portfolio’ in their VAR calculations. In addition, the Fundamental Review of the Trading Book (BCBS 2012a) has recommended a move from VAR to ES for bank market risk capital requirements as a more coherent risk measure (see Section 9.2.3). Both the use of stressed data and ES-type approaches have recently made their way into initial margin methodologies, as discussed in Section 9.3.6. Practically, such measures ensured that data around the global financial crisis – in particular, the Lehman bankruptcy – have remained in VAR data sets. A stressed data period could be combined discontinuously with a more recent data history.

Likewise, CCP regulations have sought to prevent procyclical initial margins. For example, in the European Union, one of the following options must be implemented (ESMA 2018):

Figure 9.9 Illustration of procyclical and non-procyclical initial margin calculations through time.

• apply a margin buffer at least equal to 25% of the calculated margins which is allowed to be temporarily exhausted in periods where calculated margin requirements are rising significantly;
• assign at least 25% weight to stressed observations in the look-back period; or
• ensure that initial margin requirements are not lower than those that would be calculated using volatility estimated over a 10-year historical look-back period.

The above aspects were partly implemented on the basis that – at the time in question – the period of Lehman bankruptcy was close to dropping out of a then commonly used five-year data window.

Choosing the second of the above options as an example, Figure 9.10 shows the difference between the initial margin calculated with a three-year period, with and without an additional one-year stress period. The estimator including the stress period gives a generally more conservative estimate, but one that is more stable across time. Note also that the initial margin in this case can be seen to be (not surprisingly) driven mainly by the stress period, since it is close to the value calculated using this data alone (with a lower confidence level).

Glasserman and Wu (2017) show that the use of a stressed period is a potentially reasonable way to combat procyclicality, but they also argue that there is significant heterogeneity across asset classes, which suggests that stressed periods should be asset-class specific.

Of course, it is not possible – nor even desirable – to avoid procyclicality in initial margin entirely. Indeed, it is potentially useful that CCPs can adjust margins in response to changes in market conditions, as this limits their vulnerability (Pirrong 2011). Highly-sensitive approaches, prone to procyclicality, will also probably lead to lower average margin requirements (although these will rise significantly in a crisis). However, market conditions can change quickly, and large margin changes can influence prices through effects such as causing forced liquidations of assets. Of course, the safest approach is for initial margins to be conservative, but, as illustrated above, this is also the most expensive solution. Whilst regulation and pressure from members will prevent margin methods from becoming excessively aggressive,²⁸ competition between CCPs will encourage this to some degree.

Figure 9.10 Evolution of initial margin (99% VAR) for an interest rate swap calculated with a three-year look-back period, with and without a period of stress. The 96% confidence level initial margin from the stressed period only is also shown.

Even if procyclicality is minimised, it is still important to emphasise that dynamic and risk-sensitive initial margins will change almost continuously and may exhibit significant changes over time due to:

• Look-back period. Old data will drop out of data windows, and new market events will be included.
• Volatility scaling. Changes in the current estimate of volatility.
• CCP methodology decision. CCPs will change their margin methodologies (e.g. changing the data window or moving from relative to absolute returns).

Given that it is important to be able to assess the cost of posting initial margin (margin value adjustment, discussed in Chapter 20), it is important to consider the potential impact of these types of effects.

As an example of the potential issues caused by the above, Table 9.4 shows estimates of the change in the initial margin for a GBP interest rate swap as a result of market moves following the 2016 United Kingdom European Union membership referendum (‘Brexit vote’). The calculation assumes that the initial margin is defined by the worst six scenarios from a 10-year data history, which is the methodology that was being used by SwapClear at the time (this is the ES at the 99.76% confidence level; see Section 9.3.6).

Table 9.4 Estimation of the initial margin of a GBP pay-fixed interest rate swap before and after the Brexit vote in the United Kingdom on the 23 June 2016.

Source: Clarus Financial Technology.²⁹

23 June 2016		4 July 2016
Scenario	P&L	Scenario	P&L
26 November 2008	−3.49	23 June 2016	−4.74
25 November 2008	−3.40	22 June 2016	−3.97
31 October 2008	−3.39	26 November 2008	−3.94
27 November 2008	−3.09	31 October 2008	−3.86
3 November 2008	−2.92	25 November 2008	−3.84
8 October 2014	−2.78	21 June 2016	−3.69
Average	−3.18		−4.01

The large change in initial margin is due to:

• additional scenarios (21–23 June) with large negative swap rate moves being included in the look-back period;
• the use of volatility scaling (so that even the P&L change for the same historical date, such as 26 November 2008, increases due to a higher volatility estimate); and
• the lower interest rate environment (which means that the swap is slightly more sensitive to a move in interest rates, given the assumption of absolute returns).

Note that due to the second and third effects above, the initial margin of the opposite position would also increase, despite there not being any new scenarios of positive interest rate moves.

9.3.6 Current CCP Methodologies

Whilst the more straightforward exchange-traded products have maintained simpler approaches, such as SPAN for margining, historical simulation has emerged as a fairly standard approach for OTC derivatives. In general, OTC CCPs have evolved their methodologies in line with regulatory guidance and pressure from their clearing members (who themselves have experience from their own application of similar models for their market risk capital requirements). Ideally, margins should be stable through time, but they should also respond to new data and methodological advances. Certain changes may only be regarded as short-term fixes. For example, the move from relative to absolute returns becomes inappropriate when rates begin to rise.

One particularly difficult aspect of initial margin methodologies is whether to continue to extend the look-back period to the global financial crisis.³⁰ Whilst this was originally seen, for example, in CCPs moving from five- to 10-year data windows, it now seems to have been sufficiently long ago that the events around the bankruptcy of Lehman Brothers can be ignored, despite this being the last time a major clearing member defaulted.³¹

CCPs may include additional qualitative components in the determination of initial margin. One example is the use of ‘margin multipliers’, which will lead to increased margins for excessive amounts of liquidity, credit, concentration, and sovereign risks. These may account for the fact that the liquidation of a reasonably large and/or complex portfolio would be subject to substantial bid-offer costs, and could move the market. Multipliers may apply based on clearing volumes exceeding certain thresholds based on the whole portfolio and sub-portfolios (e.g. currencies). Client trades may also attract a larger margin requirement. It is also important to account for FX risks for positions denominated in different currencies.

Table 9.5 contrasts the initial margin assumptions used for interest rate products at three significant OTC CCPs. It can be seen that there is a reasonable convergence on aspects such as historical simulation methods, liquidation periods, volatility scaling, and liquidity charges. Differences still exist, in terms of methods to avoid aspects such as procyclicality and autocorrelations, which are seen by the use of different data windows and measures used. Given the small differences, the methods would be expected to give reasonably material differences (e.g. 10–20%) on a standalone basis. However, this may be blurred by portfolio effects in the actual initial margin calculation.

Table 9.5 Comparison of initial margin methodologies for interest rate products. Note that details of methodologies can sometimes be hard to ascertain and can change over time.

	LCH.Clearnet (SwapClear)	CME	Eurex
Name	Portfolio Approach to Interest Rate Scenarios (PAIRS)a	Historical value-at-risk (HVaR)b	Portfolio-Based Risk Management Methodology (PRISMA)c
Look-back period	10 years	To 1 January 2008 (fixed)	3 years + 1 year stress period and ‘event scenarios’
Measure	99.7% expected shortfall (average of six worst scenarios out of 2,500)	99.7% VAR	99.5% VAR (using sub-samples to avoid overlapping effects)
Returns	Absolute	Absolute	Absolute
Volatility scaling	Yes	Yes (with volatility floors)	Yes (for non-stress scenarios)
Liquidity period	5 days (7 days for clients)	5 days	5 days
Addition charges	Credit risk and liquidity risk	Liquidity charge multipliers	Historical correlation breaks, liquidity costs, and compression adjustments

a www.lch.com.

b www.cmegroup.com.

c www.eurexclearing.com.

The above analysis focused largely on interest rate products, which represent a large amount of OTC derivatives clearing. Another asset class worthy of special mention is credit derivatives. Calculating initial margin requirements for CDSs represents greater challenges. This is due to the sparseness of data and the fact that credit spread distributional changes can be highly complex and especially prone to aspects such as fat-tail effects. CDS clearing also has to take into account the fact that clearing members can be reference entities in CDS indices and single-name transactions.

For the above reasons, CDS initial margin methodologies tend to differ from historical simulation approaches. ICE Clear uses a proprietary Monte Carlo simulation to evaluate a large five-day decline in portfolio value based on 20,000 simulations and incorporating asymmetric distributional assumption and co-movements in relation to credit spreads.³² Both LCH and ICE include additional components to capture effects such as bid-offer costs and concentration risks of large portfolios. CDSs with significant WWR – such as a bank selling protection on its sovereign – may be disallowed completely.

9.3.7 Computational Considerations

It is not surprising that initial margin methodologies for OTC derivatives have become broadly based on simulation methods. These methods are the most accurate as they are the only way to incorporate important effects such as irregular probability distributions, time changing volatility, and multidimensionality. They are also the only generic approaches, which makes product development and cross-margining more practical.

However, these relatively sophisticated approaches are also costly. Margin calculations are portfolio based and therefore, to calculate the initial margin on a new trade, the incremental effect vis-à-vis the entire portfolio must be calculated. Such incremental effects will be important when deciding where to clear trades and whether to backload trades to CCPs. Even with pre-computation and parallel processing, such a calculation is often not achievable in real time and therefore cannot be part of the execution process for a new trade (as discussed in Section 20.2.4, regulation may require trades to be accepted for clearing in narrow time windows such as 60 seconds). Furthermore, clearing members and clients will want to be comfortable with approaches and understand the magnitude of initial margins for various trade and portfolio combinations. One obvious way to optimise computation times is to use sensitivities (‘Greeks’) to approximate the change in the value of each trade, rather than resorting to a ‘full revaluation’. Given the number of scenarios generated, full revaluation generally tends to be time consuming, especially for complex derivatives, which require relatively sophisticated pricing models.

Given the above, CCPs have developed tools for calculating approximate initial margins without the need for full resimulation. An example is the SwapClear Margin Approximation Risk Tool (SMART), which is also available on Bloomberg.³³ Regarding the treatment of initial margins for new trades, CCPs will either calculate these approximately in real time, or rely on initial margin buffers intended to cover the risk until the true margin impact can be calculated (probably overnight). This incremental risk may also be covered by an additional component of the default fund, which could be based on the relative utilisation by a clearing member over the most recent period. This means that a member clearing large volumes of trades may have to make a relatively large additional contribution to the default fund to cover the intraday risk such trades are generating.

9.4 BILATERAL MARGIN AND SIMM

9.4.1 Overview

As discussed in Section 7.4, regulation is requiring that parties post initial margin on bilateral OTC derivatives that cannot be centrally cleared (BCBS-IOSCO 2015). Unlike initial margin at a CCP, bilateral initial margin is posted by both parties (Figure 9.11), although they will not always be symmetric (same amounts), in particular for more complex portfolios with embedded optionality.

Regulation specifies that the initial margin amounts can be either based on a ‘quantitative portfolio margin model’ or a ‘standardised margin schedule’. In both cases, margins must be calculated separately for the following ‘asset classes’:

• currency/rates;
• equity;
• credit; and
• commodities.

This choice between model- and schedule-based initial margins must be made consistently by asset class, and firms cannot switch in order to cherry-pick the most favourable initial margins. However, it is possible to use model- and schedule-based approaches for different asset classes (e.g. to reflect the fact that a firm has only a small position in some derivatives).

In the case of schedule-based margins, the simple methodology is defined explicitly by BCBS-IOSCO (2015). This has the advantage of being easy to implement and unlikely to lead to disputes. However, like any simple methodology, this approach is not especially risk sensitive and will usually lead to quite conservative initial margin amounts. On the other hand, a model-based approach will produce lower and more risk-sensitive margins, but will require more effort in implementation and agreement with counterparties. The design of internal models is also open to substantial interpretation and would inevitably lead to disputes between counterparties and a large effort for regulatory approvals of different models.

Figure 9.11 Illustration of the impact of bilateral initial margin. The party concerned holds initial margin to cover its close-out costs to a 99% confidence level over 10 days. It also posts an amount to cover the associated costs of its counterparty. These amounts will not necessarily be equal.

In terms of model-based margins, there is no specific model determined by regulation, but a number of general requirements are described (BCBS-IOSCO 2015):

• the initial margin must be posted by both parties and must be based on a 99% confidence level and a 10-day MPoR;
• the model should be calibrated to a data period of no more than five years, which includes a period of financial stress (the requirement to use the stress period is aimed at avoiding procyclicality);
• the period of financial stress used for calibration should be identified and applied separately for each asset class;
• the data within the identified period should be equally weighted for calibration purposes; and
• large, discrete calls for initial margin (as could presumably arise due to procyclicality of the margin model or use of volatility scaling) should be avoided.

Together with the major banks, ISDA has developed the SIMM in order to have a single, model-based margin approach and avoid a proliferation of margin models where parties would inevitably dispute initial margin requirements.³⁴

Eligible collateral assets for fulfilling initial margin requirements is relatively flexible (e.g. to include liquid equities and corporate bonds), which aligns with central clearing where CCPs accept a reasonable range of collateral assets. However, appropriate haircuts must be applied, and ‘wrong-way collateral’ (e.g. securities issues by the party or related entities) is not allowed. Margin assets should – after accounting for an appropriate haircut – be able to hold their value in a time of financial stress. Margin can be denominated in a currency in which payment obligations may be made or in liquid foreign currencies (again subject to appropriate haircuts to reflect the inherent FX risk involved). Collateral assets should also be reasonably diversified.

Haircut requirements should be transparent and easy to calculate, so as to avoid disputes. As in the case of initial margin models, either an approved quantitative model or a defined standardised schedule can be used to define haircuts. In the latter case, BCBS-IOSCO defines that haircut levels should be risk sensitive and reflect the underlying market, liquidity, and credit risks that affect the value of eligible margin in both normal and stressed market conditions. As with initial margins, haircuts should be set conservatively so as to mitigate procyclicality and avoid sharp and sudden increases in times of stress.

The time horizon and confidence level for computing haircuts are not defined explicitly but would likely follow those for clearing. The time horizon for computing a haircut could be argued to be less (say two to three days) than the horizon for initial margin, since the margin may be liquidated independently and more quickly than the portfolio would be closed out.

Table 9.6 Comparison of initial margin methodologies in centrally-cleared and bilateral markets.

	Centrally cleared	Bilateral
Methodology	CCP model (typically historical simulation)	Quantitative model (SIMM) or schedule
MPoR	5 days	10 days
Threshold	Zero	Up to €50m35
Calculation and reconciliation	Calculated and called by CCP	Reconciliation and dispute-resolution process
Haircuts	CCP-defined	Quantitative model or schedule

Table 9.6 contrasts initial margin methodologies in centrally-cleared and bilateral markets.

9.4.2 Standard Schedules

The standard schedule, previously shown in Table 7.11, defines initial margin as being based on notional with pre-calibrated weights which represent a conservative estimate of the 10-day 99% move in the relevant instrument of the asset class in question. To account for portfolio effects, the well-known net gross ratio (NGR) formula is used, which is defined as the net replacement divided by the gross replacement of transactions.³⁶ The NGR is used to calculate the net standardised initial margin requirement via:

The NGR gives a simple representation of the future offset between positions, the logic being that 60% of the current offset can be assumed for future exposures.

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Example of margin schedule calculation

Consider two four-year interest rate products with notional values of 100 and 50 and respective mark-to-market (replacement cost) valuations of 10 and -3.

Trade 1: Gross initial margin = 2

Trade 2: Gross initial margin = 1

Total gross initial margin = 3

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Such an approach is not risk sensitive and does not properly account for netting effects and is especially punitive for hedged (balanced) portfolios. In general, this leads to an overestimate in initial margin requirements and does not give the right incentives to market participants. However, it is a simple fallback method which clearly cannot be expected to be a risk-sensitive and accurate approach.

The standardised haircuts (assuming a bank is not using a quantitative model) were previously defined in Table 7.12.

9.4.3 Variance-covariance Approaches

The standard margin schedule also likely leads to particularly large requirements (ISDA 2012 estimates over $8trn for schedule-based margins), which suggests that applying a more sophisticated methodology for initial margin calculations could be quite important to prevent requirements being overly conservative. The SIMM has been implemented to provide a market-standard quantitative initial margin model that can potentially be used by all bilateral market participants.

An obvious starting point for a bilateral initial margin model would clearly be the models adopted by CCPs (Section 9.3). However, an important difference in bilateral markets is that parties need to agree on quantities such as initial margins (compared to centrally-cleared markets, where the CCP has the right to enforce its own calculation). More complex margin calculations methodologies, such as VAR-based methods, should be expected to lead to significant disputes. Indeed, in bilateral markets, even variation margin calculations (based on current exposure) have often led to significant valuation disputes. It is therefore inconceivable that initial margin calculations (based on future exposure estimates) would not lead to more disputes over what is, by its nature, a highly-subjective and complex estimation. It seems impractical that an institution would replicate the margin model and data set used by all of its bilateral counterparties. On the other hand, it would probably be unwilling to agree blindly to initial margin requirements generated by such a model.

The complexities of historical simulation approaches used by CCPs are related to several aspects:

• Historical data. The historical data for all risk factors over the entire look-back period and also including any stress periods. Issues such as market close times can cause discrepancies here.
• Methodology. The precise methodology used to generate the scenarios, such as the choice of absolute or relative returns and volatility scaling.
• Revaluation. Generally, OTC derivatives are valued using models – the same models need to be used for revaluing the underlying portfolio in all of the generated scenarios. Differences in valuation models can cause discrepancies here.

Given the complexities of the above, agreeing bilaterally on initial margins across multiple portfolios with different counterparties on a daily basis would at best represent a large operational workload. There is, therefore, a need to consider a simplified approach.

A well-known, simpler VAR-type method is a parametric approach often known as ‘variance-covariance’ (Jorion 2007). This involves making some assumptions about the form of the distribution of the underlying profit and loss distribution of the portfolio in question (Figure 9.12). This allows a quantity such as the initial margin to be written in terms of the moments of the underlying distribution.

Figure 9.12 Illustration of a variance-covariance approach to approximate the portfolio profit and loss distribution.

A common assumption is to assume that the portfolio returns are normally distributed. This distribution has two moments, the mean and standard deviation, but commonly it is assumed that the mean of the distribution is negligibly small (which for a short time horizon is reasonable). As a result, only the standard deviation is required, and this normal distribution assumption, together with the square root of time rule (Section 7.5.2), allows initial margin to be written as:

where represents the inverse of a standard normal distribution function. In the above representation, there are three components:

• Scaling factor. The scaling factor depends on the metric, confidence level, and distribution assumptions. For VAR at a confidence level of 99%, this scaling is . Note that it is also possible to use different distribution assumptions and metrics.³⁷
• Time horizon. The square root of time scaling, with representing the MPoR (e.g. 10 days). Since the volatility is typically an annual quantity, this should also be an annual quantity (e.g. , assuming 252 business days in a year).
• Portfolio standard deviation. The standard deviation of the portfolio returns, estimated with some time horizon (e.g. one year).

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Variance-covariance initial margin calculations

Consider that the annual standard derivation of a portfolio is $100.

1. The 99% VAR for a 10-day time horizon is:
   
2. The 99% VAR for a 5-day time horizon is:
   
3. The 95% VAR for a 10-day time horizon is:
   
4. The 99% ES for a 10-day time horizon is:
   

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The main effort in a variance-covariance is the estimation of the standard deviation of the portfolio returns. This requires estimating the standard deviation of each underlying risk factor and the correlations between them (or equivalently the ‘covariance matrix’). Variance-covariance approaches typically use delta approximations (as opposed to full revaluation) in order to approximate the relationship between the value of the portfolio and the change in risk factors. For portfolios with non-linear risks, it is also important to consider additional sensitivities or Greeks to capture the portfolio risk more accurately. For example, Figure 9.13 shows the profit and loss distribution of a position with optionality (a short call option with a long position in the underlying). Since this position is close to being ‘delta neutral’, most of the risk is second order. This means that a delta approximation is poor, but a delta-gamma approximation gives results close to full revaluation.

Variance-covariance and delta or delta-gamma approximations simplify the calculation of initial margin compared to full historical simulation (see bulleted list at the start of this section). Firstly, it is not necessary to agree on the full historical data but only on the standard deviations and correlations between the risk factors. Secondly, it is not necessary to agree on the revaluation models but only on the representation of sensitivities such as delta and gamma. This does not mean that the variance-covariance method is simple; just that it is simpler than historical simulation.

There are some drawbacks of variance-covariance. Most obviously, it potentially misses effects such as fat tails (Section 2.6.2) and complex dependencies (Section 2.6.3) and will, therefore, be expected to underestimate initial margins, especially when high confidence levels, such as 99% or 99.5%, are used. One simple way to correct for such drawbacks is to be naturally more conservative when estimating the standard deviation of the portfolio returns.

Figure 9.13 Illustration of delta and delta-gamma approximations compared to full revaluation for a portfolio with embedded optionality. The change in implied volatility is not considered.

Another drawback of variance-covariance is data. The correlation matrix that is required for a typical portfolio can be extremely large. For example, suppose each interest rate curve is modelled via 12 tenor points,³⁸ and that there are two different interest rate curves in each currency and 10 currencies overall. The resulting dimension of the correlation matrix would then be 240 × 240, requiring the estimation of a total of 28,680 correlation parameters.³⁹ A portfolio with sensitivity to other risk factors will clearly have an even larger underlying correlation matrix. Furthermore, in asset classes such as equities and credit, there are potentially many curves representing individual companies that increase the dimensionality further.

The potentially large correlation matrix is not only a data problem but a technical one. An estimated correlation matrix must be valid (more technically described as being ‘positive semidefinite’). The larger the correlation matrix, the more likely that this will not be the case. Although there are methods to find the closest valid correlation matrix, this adds complexity to the approach.

Given the above, a simple and industrial variance-covariance approach may naturally require some sort of dimensionality reduction to create a simpler overall problem with fewer parameters and no technical problems, such as ensuring the positive semidefinitiveness of the correlation matrix.

9.4.4 The ISDA SIMM

Given that standardised margin schedules are too conservative, and proprietary models will lead to major dispute problems, there is an obvious need for a standard model that is risk sensitive but can be agreed by all parties across bilateral OTC markets. ISDA has pursued this idea in conjunction with the banks that were first impacted by the bilateral margin requirements (Phase 1 banks). It is worth noting that some of the inspiration for the SIMM has come from the so-called standardised approach under the Fundamental Review of the Trading Book (FRTB-SA), which defines market risk capital requirements for banks (BCBS 2019a).

The SIMM represents an initiative to develop a uniform methodology for calculating bilateral initial margins.⁴⁰ ISDA (2013e) broadly described a proposal for the structure of such a model based on the following important characteristics:⁴¹

• Non-procyclicality. Margins should not be subject to continuous changes linked to market volatility, which could exacerbate stress in volatile market conditions. It is proposed that margins are not explicitly linked to market levels or volatility and that scenarios should be updated periodically and not continuously.
• Ease of replication. To mitigate potential problems arising from disputes, a transparent methodology and data set must be used.
• Transparency. It must be possible to understand the drivers of the methodology and therefore drill down to understand discrepancies and avoid disputes.
• Quick to calculate. The calculation must be quick (e.g. seconds) to facilitate fast pricing checks.
• Extensible. It should be easy to extend to cover additional risk factors in order to facilitate the addition of new products.
• Predictability. Initial margin results must be predictable in order for institutions to price correctly and allocate capital.
• Costs. The cost to buy or build the model must not be prohibitive, so it does not restrict access.
• Governance. Regulators should approve the model and calibration, and review this on a periodic basis.
• Margin appropriateness. Margin should be risk sensitive and give an appropriate reduction for offsetting positions.

The ISDA SIMM is a variance-covariance-type approach which is simplified by:

• separation across asset classes (note that this is a regulatory requirement, as discussed in Section 7.4.3); and
• reduction of dimensionality by defining a generic set of underlying risk factors.

It can, therefore, be considered to be a sequence of small, ‘nested’ variance-covariance formulas, rather than a single, larger, and more complex variance-covariance formula covering all risk factors.

It is also a sensitivity-based approach, with the sensitivities being delta, ‘curvature’ (gamma), and ‘vega’, which are defined across risk factors by asset class, tenor, and maturity. There are also base correlation requirements that apply only to certain credit positions. Note that since the bilateral margin rules apply to transactions that cannot be centrally cleared, then by definition this will need to capture the more non-standard, complex, and illiquid OTC derivatives. Hence, the curvature and vega (and base correlation) components are important. The initial margin requirements are additive across these sensitivities. Within each asset class, the initial margin requirements are then driven by:

• sensitivities to various risk factors (e.g. interest rate delta in a particular currency);
• risk weights (essentially defining the variability of a risk factor, assuming the regulatory required horizon of 10 days and confidence level of 99%);
• concentration thresholds (that penalise large positions based on the size of the position compared to the traded market volume for the relevant risk factor); and
• correlations and aggregation (defining the extent of offset between positions in the same asset class).

Additionally, to account for the fact that a given transaction may have a sensitivity to different asset classes (for example, many non-rates products have interest rate sensitivity), a total of six risk classes are defined:

• interest rate;
• credit (qualifying);
• credit (non-qualifying);
• equity;
• commodity; and
• FX.

A product can, therefore, have initial margin contributions arising from its sensitivity to more than one risk class, with aggregation rules determining how such contributions should be combined. This can be problematic in certain situations. Consider various equity transactions in different currencies hedged with FX transactions. These will be in the equity and FX asset classes, respectively, with both asset classes having FX risk. However, the FX risk will not offset as it will appear in two different asset classes that must be treated additively.

The SIMM parameters are calibrated using a three-year look-back period together with a one-year stress period.⁴² The risk weights are calculated from the maximum of the 99% and 1% quantiles of this distribution (i.e. they are the worst up or down move seen at the relevant confidence level).

It is proposed that the parameters in the SIMM be recalibrated annually,⁴³ together with a review of the underlying methodology. As such, the methodology should have low procyclicality, at least between calibrations. Furthermore, any increases in initial margin should be predictable and will not occur suddenly as the new methodology and calibration will be known several months ahead.⁴⁴ The calibration and methodology are defined centrally, and participants do not need access to the underlying historical data being used.

Table 9.7 Calculation of weighted sensitivities for two interest rate positions.

	2 wa	1 m	3 m	6 m	1 yr	2 yr	3 yr	5 yr	10 yr
Trade 1	0	0	0	0	1	3	291	0	0
Trade 2	1	−1	2	−4	3	−18	20	−63	−852
Net sensitivity (s)	1	−2	2	−4	5	−15	311	−63	−852
Risk weight (RW)	113	113	98	69	56	52	51	51	51
Weighted sensitivity (WS)	−75	146	−182	264	−132	1,072	13,797	3,191	43,427

a w, week; m, month; yr, year

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Spreadsheet 9.2 Example ISDA SIMM™ calculations.

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Taking a worked example of an interest rate delta margin calculation and assuming two transactions of three-year and ten-year maturity with notional of one million each and denominated in the same currency. The first step is to calculate the underlying sensitivities, which are shown together with the relevant risk weights (which are the same for most currencies)⁴⁵ in Table 9.7.⁴⁶ The sensitivities can be netted across the products. The net sensitivities (s) and risk weights (RW) are now multipliers to generate the ‘weighted sensitivities’ (WS) for each tenor according to:

where is the concentration risk factor, which will be one unless the position is large and above a defined concentration threshold, which is defined by currency according to market liquidity. Assuming that , the weighted sensitivities are shown in Table 9.7.

The final step is to aggregate the sensitivities across tenor and sub-curve (for different reference rates).⁴⁷ Whilst the former calculation is a matrix multiplication, the majority of the contribution comes from the three- and 10-year tenors, where most of the risk exists. Hence, the simplified calculation is:

Table 9.8 SIMM delta margin for a different combination of interest rate swap trades with respect to currency and directionality.

	Directional	Anti-directional
Same currency	59,540	34,293
Different currencies	52,306	44,555

where 84% represents the correlation between the 3- and 10-year tenors. The actual calculation (including risk from all tenors) is slightly higher at 59,540.

The initial margin in the above example is relatively large because the positions are directional (same currency and positive sensitivity to the risk factor). In Table 9.8, we show the initial margins if the swaps are in different currencies and are anti-directional (sensitivities to the risk factors are of opposite signs).⁴⁸ The initial margin for different currencies is smaller due to the decorrelation that arises, which is effectively modelled by a currency correlation parameter of 23%. The anti-directional portfolio has a much lower initial margin due to the hedging effect of trades in opposite directions, which is strongest when the transaction is in the same currency. These results are risk sensitive, as would be expected.

Note that the gross initial margin under the standard schedule assuming par swaps is 60,000, which is reasonable for directional and same-currency positions, but too high for cases where the portfolio is more balanced, unless the NGR factor reduces this substantially.

For more detail on the implementation of the SIMM, the reader is referred to ISDA (2013e, 2016, 2017a, 2017b).

9.4.5 Implementation of Bilateral Margin Requirements

At the time of writing, the initial requirements are still being phased in, with only the major banks being required to post bilateral initial margin (Table 9.9). However, whilst the early phases only capture a small fraction of market participants, since these market participants are large banks, they do capture a significant amount of the total market (Condat et al. 2018).

In order to comply with the bilateral margin requirements, there is significant work on aspects such as:

• renegotiating credit support annexes;
• developing custodian relationships;
• being able to generate sensitivities for each transaction and map these onto the SIMM risk factors;
• handling any disputes over the quantity of initial margin (in either direction);
• identifying any margin shortfalls through backtesting of historical performance for each portfolio; and
• building connectivity with all counterparties in-scope for bilateral margin.

Table 9.9 Market participants subject to bilateral initial margin requirements. Note that due to initiatives such as compression and new trading activity, these numbers can change.

	Start date	Non-cleared notional threshold	Number of market participants (cumulative)
Phase 1	1 September 2016	€3trn	20
Phase 2	1 September 2017	€2.25trn	26
Phase 3	1 September 2018	€1.5trn	36
Phase 4	1 September 2019	€0.75trn	86
Phase 5	1 September 2020	€50bn	Hundreds
Phase 6	1 September 2021	€8bn	Thousands

The SIMM is becoming relatively standard for calculating initial margin in such situations. ISDA has defined standardised formats for the exchange of model inputs (sensitivities) and trade details via a Common Risk Interchange Format (CRIF).

In order to facilitate the required calculations, a utility called Exposure Manager, provided by AcadiaSoft in collaboration with TriOptima, is being utilised.⁴⁹ Exposure Manager is an end-to-end initial margin reconciliation, calculation, and dispute-resolution service which provides the following services:

• reconciliation of exposures, trades, and sensitivities;
• standard calculations (SIMM and schedule);
• initial margin call generation; and
• audit trail and reporting/analysis.

This can make it easier and cheaper for market participants to implement initial margin calculations with the SIMM, although there is still a concern in the industry about the many small institutions that will be captured in 2021 when the notional threshold drops to only €8bn. The standardisation of the margining process is fairly critical to allow for efficient initial margin exchange across a large number of counterparties.

There is not much evidence of the use of margin schedules or other approaches for calculating initial margin, although some banks have implemented an internal model for interaffiliate relationships where initial margin must be posted. It remains to be seen whether this will change as many more market participants become involved.

Note that, whilst all firms captured by the notional threshold must calculate initial margin between one another, this may not lead to actual posting due to the €50m threshold (Section 7.4.2) and the fact that initial margin only need be exchanged against new transactions. However, over time, the impact will clearly increase.

Regulatory initial margin is reported by ISDA as being largely made up of government securities (86.3%), which is not surprising as segregation is easier with securities. Only 13.7% of regulatory initial margin is in cash. This contrasts to variation margin, where 79.2% is reported as being in cash. Discretionary initial margin has a larger component of cash and other securities.

As with the requirements for clearing, there are objections to initial margin requirements. These are mainly based on the fact that posting initial margin, which has to be segregated, is extremely costly and margin rules may not reduce systemic risk due to the likelihood that they may increase sharply in crisis periods (procyclicality). Additionally, Cont (2018) has argued that the liquidity horizon (MPoR) should not be fixed at 10 days but should be related to the liquidity of the instruments in question, and should take more consideration of the size of the position relative to the daily trading volume. He also argues that the ability to hedge market risk in the aftermath of a default may mean that the 10-day MPoR is too large.

Note also that, whilst the threshold of €50m would relieve the liquidity strain created via the margin requirements, it would increase the procyclicality problem as margin amounts will be even more sensitive to market conditions near this threshold.

NOTES

1. 1 CPSS-IOSCO (2012).
2. 2 BCBS-IOSCO (2015).
3. 3 EMIR (2015).
4. 4 This might be considered to be intuitively similar to the G-SIB (globally-systemically-important bank) surcharge discussed in Section 4.2.2.
5. 5 See Section 7.5.2.
6. 6 Note that the MPoR for regulatory capital can sometimes be increased beyond 10 days, as discussed in Section 13.4.5, but this does not lead to any change in the MPoR for initial margin purposes.
7. 7 For example, with the two-day time horizon and 99% confidence level and assuming a foreign exchange volatility of 15%, a haircut would be: (assuming 252 business days in a year).
8. 8 There are currently 10 NRSROs, with the most significant (the ‘big three’) being Standard & Poor's, Moody's and Fitch Group.
9. 9 Cameron, M. (2012). SwapClear changes expulsion rules. Risk (4 May). www.risk.net.
10. 10 Commodity Futures Trading Commission Office of Public Affairs. Credit Ratings Q & A. www.cftc.gov. Note that this regulation applies to both clearing members or futures commission merchants (FCMs) and designated clearing organisations (CCPs).
11. 11 ICE Clear Europe (2018). Risk Management: Frequently Asked Questions v.6.0 (24 April).
12. 12 Eurex (2016). Spotlight on: CCP Risk Management (18 July). www.eurexclearing.com.
13. 13 Meakin, L. (2012). LCH Raises Margin Costs for Trading Spanish Government Bonds. Bloomberg (20 June). www.bloomberg.com
14. 14 De Teran, N. (2008). How LCH.Clearnet got clear of Lehman. Wall Street Journal (14 October). www.wsj.com.
15. 15 CME Group (2016). Invoice Swap Spreads and Portfolio Margining Benefits. www.cmegroup.com.
16. 16 Osborn, T. (2013). Cross-margining at CME slowed by practical challenges. Risk (1 August). www.risk.net.
17. 17 See Footnote 15.
18. 18 CME Group (2010). SPAN - Standard Portfolio Analysis of Risk. www.cmegroup.com.
19. 19 For more information, see www.theocc.com.
20. 20 Short option positions that are highly out-of-the-money near expiration represent a problem in the event that the underlying moves sharply, whereupon these positions could then be in-the-money. SPAN includes a large upwards and downwards move to consider this risk, but only a fraction of the total loss calculated is considered.
21. 21 See Footnote 18.
22. 22 Note that this is from CME's point of view, so it is the reverse of the position from the clearer's point of view.
23. 23 This could require the clearer to post more variation margin, which they would be expected to fail to do in the event of default.
24. 24 Assuming no concentration multipliers and that the CCPs use the same initial margin approach.
25. 25 A low confidence level is required due to the small number of scenarios shown.
26. 26 J.P. Morgan (1996).
27. 27 .
28. 28 Cameron, M. (2012). Member revolt forces SwapClear to revamp margin model. Risk (5 December). www.risk.net.
29. 29 Khwaja, A. (2016). Higher Swap Margins After Brexit. Clarus Financial Technology blog (5 July). www.clarusft.com.
30. 30 Osborn, T. (2018). Lehman's ghost: how three CCPs anchor models to crash. Risk (17 September). www.risk.net.
31. 31 Mourselas, C. (2019). CME no longer looking back to Lehman. Risk (28 August). www.risk.net.
32. 32 www.theice.com.
33. 33 Bloomberg (2013). Bloomberg Integrates Margin Calculator for Swap Participants. Press release (6 August). www.bloomberg.com.
34. 34 www.isda.org.
35. 35 See Section 7.4.2.
36. 36 NGR is used in bank capital requirements and the definition can be found in BCBS (2006). It is also discussed in more detail in Section 13.4.2.
37. 37 For example, under normal distribution assumptions, the expected shortfall is defined by where represents a standard normal distribution function.
38. 38 We will see in Section 9.4.4 that this is exactly what is done in SIMM.
39. 39 .
40. 40 Noting that this therefore does not give any opinion on initial margins calculated by CCPs.
41. 41 Note that this is the author's own description of the characteristics given by ISDA (2013).
42. 42 The stress period is chosen as the one-year interval from January 2008, with the maximum volatility of 10-day overlapping returns.
43. 43 For example, version 1.0 was effective 1 January 2017 and version 2.0 was effective 4 December 2017.
44. 44 Version 2.1 methodology was first published in July 2018, ahead of the implementation on 1 December 2018.
45. 45 These are the version 2.0 risk weights for regular volatility currencies, which are most major currencies. Low- and high-volatility current risk weights also exist.
46. 46 The sensitivities are defined as a prescribed set of tenors, as shown. The longer tenors (15 years, 20 years, and 30 years) are not shown.
47. 47 This uses a single correlation parameter of 98% to represent the relationship between different reference rates (e.g. three-month and six-month London Interbank Offered Rate or overnight indexed spread) in a given currency.
48. 48 For example, as arising from a pay-fixed and receive-fixed interest rate swap.
49. 49 www.acadiasoft.com.