20
MVA

20.1 OVERVIEW

This chapter follows on from the discussion of funding in Chapter 18 and discusses the specific funding cost of posting initial margin (IM). It also considers the potential benefit of receiving IM, in terms of reduction of credit value adjustment (CVA) and capital value adjustment (KVA).

As previously discussed, IM considerations are of growing importance due to two significant aspects of regulatory reform:

The clearing mandate. This requires that standardised over-the-counter (OTC) derivatives transactions are cleared through central counterparties (CCPs) (Section 4.4.1). CCPs impose various financial resources requirements and contractual commitments on their members for the benefit of their own risk management. The most significant of these is IM to cover a severe scenario at a high confidence level, which must be paid upfront and will vary during the life of a portfolio depending on the output of the CCP IM model. CCPs will only invest IM conservatively, if at all, and so the return paid on cash IM is typically low. A benefit of central clearing for banks is that the capital charges against CCPs are relatively favourable (Section 13.6). CCPs also require other financial commitments, notably via the default fund contributions and rights of assessment (future default fund contributions). Such requirements are definitely costly since, like IM, default funds are held by the CCP or third party and are not remunerated at anything more than an overnight rate (and typically less). It would seem logical to include the cost of default fund contribution alongside IM in margin value adjustment (MVA). Rights of assessment and other contingent loss-allocation methods are unfunded and potentially heavily capitalised (Section 13.6.3) and so would more likely appear via KVA.
Bilateral margin rules. From September 2016, non-centrally cleared transactions have become increasingly subject to bilateral margin requirements (Section 4.4.2). This means that both parties to a transaction must post IM, which partially mimics the CCP treatment. This IM must be segregated and cannot typically be rehypothecated (except potentially in one limited situation mentioned in Section 7.4.1) and so will be costly due to the need for segregation. The Standard Initial Margin Model (SIMM) is becoming market standard for the calculation of these amounts (Section 9.4.4). The IM must be held with an unaffiliated third-party custodian, and no return will be paid on cash.

The above rules apply, in general, to major players in the OTC derivatives market, and small end users are, broadly speaking, exempt (see Section 4.4.3).

Note that all of the above requirements are costly since they involve posting high-quality IM that is usually not rehypothecated, but is rather segregated and therefore remunerated at a low return. Furthermore, even if the IM was allowed to be rehypothecated, a higher return may be achievable, but it would then create additional counterparty risk via CVA.

Not all IM is regulatory driven, with a substantial amount of discretionary IM also being posted (see ISDA 2018). Note that – historically at least – such IM has often gone by the name of ‘independent amount’. Whilst there is, strictly speaking, no difference between IM and independent amount, the latter tends to be a non-regulatory, one-way payment without segregation and is often based on simple metrics such as percentage of notional (Table 20.1). The use of rating triggers is common with discretionary IM, but this is not allowed with regulatory IM, with the amounts being independent of credit rating.

An important feature is the increased complexity of risk-sensitive, model-based IM methodologies, such as the proprietary models used by CCPs and the International Swaps and Derivatives Association (ISDA) SIMM (Section 9.4.4). This dynamic feature is important because the computation of xVA in the presence of IM depends on the ability to simulate IM requirements in the future.

Some margin agreements require contingent posting in certain situations, most commonly upon a rating downgrade (see example in Table 7.4). Regulatory rules in the liquidity coverage ratio (LCR) require banks to hold a liquidity buffer to cover such outflows in the event of a three-notch ratings downgrade, and such an outflow, therefore, needs to be pre-funded (Section 4.3.3). Note that it may be beneficial for a bank to actually post a smaller IM¹ (than would be required in the event of the trigger) in order to have such rating-based triggers removed, since the IM needs to be held in high-quality liquidity assets (HQLAs) in the bank's liquidity buffer anyway. Sometimes there may be alternatives to contingent IM posting, such as transactions being terminated or novated; this is even more of a challenge to quantify since it would require the estimation of the price charged by a replacement counterparty. Note that a bank does not generally derive any benefit from contingent triggers in its favour because the prudent LCR rules would require the assumption that these triggers were not breached. As seen from Figure 20.1, market practice is divided on the treatment of such contingent liquidity requirements, but many banks do price them in, especially in relation to their own potential rating downgrade.

Table 20.1 Differences between discretionary and regulatory IM.

	Discretionary	Regulatory
Nature	Usually one-way and sometimes called ‘independent amount’	Two-way
Segregation	Uncommon	Required
Calculation	Often simple metrics or proprietary models	Standard schedule or ISDA SIMM
Determinants	Often linked to rating triggers	No linkage

Bar chart depicts the market practice around pricing contingent funding requirements. — **Figure 20.1** Market practice around pricing contingent funding requirements.

Source: Solum CVA Survey (2015).

In terms of the incorporation of IM into xVA measures, there are two main considerations:

the extent of risk reduction due to receiving IM from bilateral counterparties; and
the cost of posting IM to bilateral counterparties and CCPs.

The latter component generally gives rise to MVA costs, whilst the former may lead to a reduction in counterparty risk, seen via lower CVA and KVA components. However, this also depends on whether or not the IM is segregated (Table 20.2). Non-segregated IM will create a cost for the poster due to an increase in counterparty risk, but an associated benefit for the receiver in the form of a funding benefit. Segregation will remove these cost and benefit components. The benefit of segregation, with the loss of funding benefit, is that IM can only reduce, and not increase, counterparty risk. Due to the bilateral margin requirements, segregation of IM is becoming increasingly common.

Table 20.2 IM impact on xVA. Note that regulatory IM must be segregated, but discretionary IM need not be.

	Posted IM		Received IM
	Non-segregated	Segregated	Non-segregated	Segregated
Counterparty risk (CVA and KVA)	Cost	–	Benefit
Funding (MVA)	Cost		Benefit	–

20.2 INITIAL MARGIN FUNDING COSTS

20.2.1 Introduction

MVA, like funding value adjustment (FVA), represents a funding cost, although there are fundamental differences between the two (Table 20.3) and it is therefore probably relevant mainly to consider them separately. In general, FVA is associated with being uncollateralised and therefore making and receiving cash flow payments and their impact on the underlying valuation without any associated and offsetting margin flows. As discussed in Section 18.2.2, FVA is not really driven by margin posting per se, although it is sometimes explained in this context. Nevertheless, FVA is largely a result of imperfect variation margin posting. MVA is the cost of posting IM, which is to a large extent not related to cash flows and valuation, but rather to the future risk of the position. MVA is also simpler than FVA in that it is only a cost and there is no question over symmetry (Section 18.3.2). There will, however, be the question of overlap between FVA and MVA, which will be considered in Section 21.3.1. Unlike FVA, which has cost and benefit components, MVA is a cost only, due to the fact that regulatory IM received must typically be segregated and so provides no funding benefit.

Since cash IM is remunerated at only a short-term rate (if at all), there is a significant funding or opportunity cost, similar to the situation for FVA. Indeed, the fact that IM is generally remunerated at a sub-overnight-indexed-spread rate means that it is unlikely to be optimal to post cash and that eligible securities (such as government bonds), effectively providing remuneration at the repo rate, are a more natural asset to use. The relative ease of segregating securities over cash also supports their use for IM posting. The cost of IM naturally leads to MVA representing the lifetime cost of posting IM against a transaction or portfolio.

20.2.2 MVA Formula

A formula for MVA (Kenyon and Green 2015) can be written as:

(20.1)

with images being the funding spread, and images being the discounted expected initial margin profile over time. The funding spread should reflect the type of margin being posted (currency, type) and any related remuneration (cash) or repo rate (securities). There will be cheapest-to-deliver optionality (Section 16.2.3) with respect to the posting of IM, since both bilateral and CCP requirements will typically permit IM to be posted in different currencies and types of securities (this is in contrast to variation margin, which is often in cash in the currency of the transaction). This optionality would be most obviously accounted for in the estimation of the funding cost term. Note that received IM may also constitute a cost since it will typically have to be segregated, and this segregation cost may be viewed as contributing to MVA. This would involve computation of expected initial margin (EIM) on the reverse portfolio.

Table 20.3 Differences between FVA and MVA.

	FVA	MVA
Nature	Funding assets, cash flows and variation margin	Funding IM posting
Symmetry	Potentially symmetric (asset and liability)	Asymmetric due to segregation (liability only)
Cost/benefit	Potentially a cost and benefit	Cost only
Reference	Remuneration rate (typically overnight indexed spread) or repo rate	Remuneration rate (typically sub-overnight indexed spread) or repo rate

The images term above represents the expected IM posted at a given future time images . This is complex to quantify since the underlying IM calculation methodology may be sensitivity or simulation based and subject to unpredictable changes in model assumptions and calibration choices. There are also components – as with KVA (Section 19.2.3) – which are impossible to quantify (except perhaps qualitatively) since they relate to changes in the underlying IM methodology. Examples of this are the decision of a CCP to change its IM calculation methodology or the recalibration of the SIMM (Section 9.4.4). Unlike FVA, MVA is therefore not trivially calculated alongside CVA and requires additional work and potential computation challenges.

For centrally-cleared transactions, as noted above, it may be relevant to include any default fund contribution with the IM requirement in Equation 20.1. Furthermore, the relatively small capital charges arising from IM and default fund contributions may be incorporated qualitatively at this stage or assessed more accurately via KVA.

20.2.3 EIM Term

Future IM requirements can evolve in many different ways, depending on a number of factors:

Changes in the portfolio composition as transactions mature (excluding new transactions, which can be priced as they occur). Note that the profile may actually increase when transactions that are offsetting more longer-dated transactions in the portfolio mature.
Continuous changes in the look-back period for historical simulation (in particular when important days drop in and out of the data set) and the periodic recalibration of the parameters in the ISDA SIMM.
Alterations in methodology, such as changes in underlying assumptions and changes in the stress periods used. For example, several years ago, most CCPs switched from the assumption of ‘relative returns’ to ‘absolute returns’ (Section 9.3.3) for interest rate movements, which is usually more conservative in a falling interest rate environment.

The main challenge of MVA is calculating the EIM term in Equation 20.1. Ideally, doing this would capture:

the specific IM methodology being applied;
the ageing of the portfolio;
modelling the entire portfolio of transactions together;
the variability of future IM requirements; and
potential changes in the IM methodology.

Table 20.4 Balanced and directional portfolios of interest rate swaps for IM analysis.

	Balanced portfolio				Directional portfolio
	Maturity	Notional	Pay/Rec	Currency	Maturity	Notional	Pay/Rec	Currency
Trade 1	3 years	250m	Rec	USD	3 years	50m	Pay	USD
Trade 2	5 years	100m	Pay	GBP	5 years	30m	Pay	USD
Trade 3	7 years	50m	Pay	USD	7 years	30m	Pay	USD
Trade 4	10 years	30m	Rec	EUR	10 years	30m	Pay	USD

The importance of the above points will be highlighted using two portfolios (Table 20.4) of interest rate swaps, one of which is balanced across pay fixed and receive fixed positions, and the other which is (relatively) directional, being all pay fixed, although in different currencies. IM calculations will use the ISDA SIMM methodology as described in Section 9.4.4. Note that the same SIMM parameters are used for the entirety of the simulation. In reality, there is an annual recalibration of these parameters, but this is difficult to model.

The forward IM is first shown based on a single scenario based on ageing the portfolio through time and calculating the future IM using forward rates. For single trades and directional portfolios, the IM usually behaves in a predictable fashion, often simply decaying to zero, as can be seen for the directional portfolio in Figure 20.2. For balanced portfolios, this is often not the case as shorter-dated trades age and drop out of the portfolio, potentially changing its overall directionality. This is the case for the balanced portfolio in Figure 20.2. The portfolio initially has a negative sensitivity to interest rate movements (as interest rates increase, the portfolio loses value) and so it represents a receive fixed position overall. This means that the ageing impact of the large, short-dated (three-year) receive fixed swap is initially beneficial and reduces IM, since the portfolio becomes more balanced. However, at approximately the two-year point, the overall interest rate sensitivity of the portfolio – mainly due to the ageing of the large three-year swap – becomes positive. As a result, the further ageing of this swap starts to increases the future IM.

Graph depicts the forward IM for the balanced and directional interest rate swap portfolios under the SIMM methodology. — **Figure 20.2** Forward IM for the balanced and directional interest rate swap portfolios under the SIMM methodology.

Capturing the variability of future IM requirements is challenging due to the need to run the underlying methodology (ISDA SIMM, in this case) many times in different future scenarios. The scenarios are generated using the same simulation methodology, as described for the exposure simulations in Section 15.6. In certain situations, using simulation is not particularly important as the variability is small, as shown for the balanced portfolio in Figure 20.3. In this case, IM at the 5% and 95% confidence levels is only slightly higher and lower than the EIM value. In such cases, forward IM represents an accurate approximation to the EIM profile, and there is minimal variation around this.

There are two reasons for the above being a relatively simple case with only a small variation in future IM requirements. First, the underlying portfolio is simple and has approximately linear risk-factor sensitivity (delta and not gamma or vega). Second, the underlying calculation methodology (SIMM) is assumed to remain fixed (in reality, SIMM would update, but only annually when the parameters are recalibrated). These points together mean that the only variability in future IM arises from a change in the underlying sensitivities of the swap portfolio. The change in these sensitivities is relatively small and broadly symmetric (a certain increase in rates reduces the sensitivity, and a corresponding rates decrease leads to an increase in the sensitivity by about the same amount).

One case where the above is not true is for a non-linear transaction such as an option. Figure 20.4 shows future IM for a long position in a physically-settled, five-year, European-style swaption on a five-year payer swap using SIMM methodology. In this case, future IM before the five-year point is very variable due to the potential for the swaption to be very in-the-money (high delta contribution in SIMM) or out-of-the-money (low delta contribution in SIMM). The contribution from the vega component in SIMM is smaller and more linear. After the five-year point, the profile is also variable due to possibility of the swaption being exercised (in which case there will be an IM requirement on the underlying swap) or not exercised (in which case there will be zero IM). EIM during the last five years, therefore, represents an average over paths, some with and some without IM requirements. For the same reason, the forward IM is not accurate in such a case and will be zero after the exercise date if the swaption is OTM.

Graph depicts the distribution of future IM quantified by EIM and high and low quantiles for the balanced swap portfolio under the SIMM methodology. — **Figure 20.3** Distribution of future IM quantified by EIM and high and low quantiles for the balanced swap portfolio under the SIMM methodology.

Graph depicts the distribution of future IM quantified by EIM and high and low quantiles for a physically-settled payer swaption under SIMM methodology. — **Figure 20.4** Distribution of future IM quantified by EIM and high and low quantiles for a physically-settled payer swaption under SIMM methodology.

This swaption example with SIMM methodology is more relevant than the swap example above because many swaps are now centrally cleared, leaving a significant number of bilaterally-cleared swaption transactions with associated IM tied to the SIMM methodology.

Whilst future IM for cleared trades should be simpler to calculate for the reasons shown above (e.g. linearity), CCP IM methodologies are more difficult to capture. These methodologies are typically more complex and use approaches such as historical simulation with ‘look-back’ periods that continuously update as new data becomes available. They may also include data from stressed periods which may sometimes be changed. Whilst other changes in CCP methodologies are impossible to predict, the continual updating with new data can be modelled by including the simulated scenario data within the future CCP IM calculation.

To illustrate the above effect (Figure 20.5), an IM methodology based on 99% value-at-risk (VAR) and a 10-year look-back period are assumed. When simulating future IM, the look-back period will incorporate the simulated data. For example, IM in two years will be based on the last eight years of known data, plus the two that have been generated in the scenario in question. This is essentially a historical simulation within a Monte Carlo simulation. Using this approach, Figure 20.5 shows future IM distribution for a centrally-cleared interest rate swap assuming a CCP-like methodology. There is material variation in the future initial paths, mainly caused by sharp increases driven by relatively volatile scenarios which increase IM via their future inclusion in the historical look-back period. Note that IM cannot reduce substantially due to the use of a high quantile, and reductions only occur due to data dropping out of the look-back period.

Note that the above effect makes future IM, like capital (Section 19.2.4), more likely to increase than reduce. It may be important to quantify such ‘convexity’ of IM for pricing and management purposes. It may also need to be calculated for the LCR (Section 4.3.3).

Graph depicts the distribution of future IM quantified by EIM and high and low quantiles for an interest swap using a typical CCP methodology based on VAR and historical simulation. — **Figure 20.5** Distribution of future IM quantified by EIM and high and low quantiles for an interest swap using a typical CCP methodology based on VAR and historical simulation.

Recall that MVA computation also raises the question of whether or not to use the P- or Q-measure for the underlying simulation (Section 15.3.3). In the above example, the historical-simulation IM calculation represents a physical (P-measure) calculation. Choosing to use the risk-neutral (Q-measure) for the simulation would be consistent with the calculation of other metrics such as CVA and FVA. However, it would be inconsistent with the fact that future IM requirement is largely unhedgeable. It also means that future IM is driven partially by historical data and partly by risk-neutral data (from the prior simulation path). A simulation using the physical measure would be more natural, but would then require different scenarios compared to those used for CVA and FVA.

20.2.4 Computation Challenges

IM requirements for derivatives are increasingly being calculated using measures such as VAR or expected shortfall (ES): this is the case for both CCP and bilateral transactions. A typical methodology uses historical simulation and a VAR or ES metric at the 99% confidence level or more over a time horizon of five (CCP) or 10 (bilateral) business days. It is now common for a stressed period of data to be included in the calculation to dilute any procyclical problems where consistent periods of low volatility may lead to excessively low IMs. Examples of centrally-cleared and bilateral markets in this regard are:

Bilateral. BCBS-IOSCO² (2015) recommends IM to be based on a 99% confidence level with a 10-day time horizon and calibrated to a period including financial stress.
CCP. SwapClear³ uses historical simulation with a five-day time horizon calibrated to a long-time period, with the IM defined by the average of the worst six moves in this period. This equates to an ES at a high (more than 99.5%) confidence level.

The form of MVA as an integral over the EIM profile leads to computation problems, since a traditional approach would require a Monte Carlo simulation similar to the exposure methodology but with IM calculations at each point. Noting that an IM calculation itself may require another simulation, this leads to a classic computational bottleneck. There are a number of methods that can be used to solve this, including:

Simple amortisation assumptions. The simplest approach is to approximate by making amortisation assumptions based on current IM. However, this may not be a good approximation, as shown in Figure 20.2.
Approximation with forward IM. This approach involves calculating only forward IM (i.e. a single path), which may be a good approximation for some portfolios (e.g. Figure 20.3) and not others (e.g. Figure 20.4).
Using a quantile of the exposure distribution. Since IM is generally a certain quantile, a reasonably simple and cheap approach is to use a quantile of the exposure distribution to approximate this quantile, essentially reusing the simulation data.
Regression methods. A more sophisticated approach is to estimate IM via regression (also known as American Monte Carlo; see Section 15.3.2). This is discussed by, for example, Green and Kenyon (2015) and Caspers et al. (2017). Such approaches generally require scaling so as to reproduce the current IM. A fixed scaling is often not accurate, and Anfuso et al. (2017) suggest a scaling function with a parametric form.
Adjoint algorithmic differentiation (AAD). In the case of SIMM, IM is driven mainly by sensitivities and aggregation rules, with the former representing the bottleneck of the calculation. Hence, a method such as AAD – which calculates sensitivities (partial derivatives) directly – is useful.

20.2.5 Pricing and MVA Example

Note that the IM term (EIM) in Equation 20.1 will also be typically defined for a portfolio of transactions with a bilateral counterparty or CCP. In particular:

Bilateral. The bilateral margin rules require IM to be calculated across four asset classes (currency/rates, equity, credit, commodities). If a model-based approach is being used, then there will be a portfolio IM for all transactions within a given asset class. Due to the nature of SIMM, this can be further broken down into risk contributions (e.g. delta risk, vega risk).
Centrally cleared. CCPs generally net (‘cross-margin’) IM across transactions in the same asset class (e.g. rates in different currencies), although they may not net across asset classes. This means that there will be a total IM requirement for all CCP-netted transactions.

The portfolio shown in Table 20.4 – being all interest rate products – would, therefore, be cross-margined with respect to a given bilateral counterparty or CCP. The above means that there will be a need for an ‘incremental MVA’, similar to the incremental CVA defined in Section 17.4.1. This increases the computational requirements further, since it will be necessary to calculate a portfolio MVA with and without the impact of a new transaction.

Graph depicts the incremental EIM profiles for the five-year swap in the portfolios shown in Table 20.4. — **Figure 20.6** Incremental EIM profiles for the five-year swap in the portfolios shown in Table 20.4. Note that all cases are scaled to a notional of 100 million for illustration.

As with other xVAs, the magnitude of incremental MVA that would be required for pre-deal pricing depends on the size and directionality of the underlying portfolio. To illustrate this, consider adding the five-year swap in Table 20.4 to the remainder of the portfolio. Figure 20.6 shows EIM for adding this transaction to the other three swaps in the (relatively) directional and balanced portfolios, and compared to the standalone profile. For the directional portfolio, there is a relatively predictable reduction in EIM due to the fact that the currency of the swap is different. For the balanced portfolio, EIM has a more complex shape and is mainly negative, which is indicative of the overall portfolio IM being reduced by the addition of this swap.

The corresponding MVA values for the EIM profiles in Figure 20.6 are shown in Table 20.5, assuming a funding spread of 100 bps per annum. For the directional portfolio, MVA is substantially reduced. This can be seen as the portfolio being dominated by USD swaps, making the cost of transacting a GBP swap cheaper due to a portfolio effect. For the balanced portfolio, incremental MVA is positive, representing a benefit. Such benefits, if material, may be important to capture in order to make pricing more competitive.

Table 20.5 Incremental MVA for the five-year swap in the balanced and directional portfolios shown in Table 20.4, compared to the standalone calculation. A funding spread of 100 bp pa is assumed.

	MVA (bps upfront)
Standalone	−6.7
Incremental (directional portfolio)	−2.6
Incremental (balanced portfolio)	2.5

20.3 MVA

20.3.1 A Need to Charge MVA?

Banks internally calculate the cost of funding IM posting and are clearly paying more attention to pricing MVA. It would seem likely that the costs of funding IM, via MVA, will become more standard adjustments to the accounting of fair value of derivatives, in a similar way to the current use of FVA for funding costs of uncollateralised derivatives. Banks are generally directing the responsibility for pricing IM costs towards the xVA desk. However, there are a number of reasons why MVA may not be as necessary and viable as other traditional valuation adjustments, such as CVA and FVA. Note that MVA primarily arises on interbank trades and trades with financial institutions above the regulatory threshold (Section 9.4.1). It represents the cost of overcollateralisation, as opposed to more traditional terms such as CVA and FVA, which are the result of undercollateralisation.

In general, where other xVA terms have become standard adjustments both in pricing and valuation, the following points generally apply:

End user clients. The standard xVAs apply mainly to relatively unsophisticated, non-margin posting, end user clients. Such clients – depending on jurisdiction and the precise level of their derivatives usage – are often exempt from the mandates that give rise to IM and therefore MVA.
Directionality. Related to the above, the underlying portfolio is likely to be directional, driven by the hedging requirements of the client. This will limit netting benefits and make xVA prices close to their standalone values.
Lack of optimisation opportunities. The client will be unlikely to want to restructure transactions or margin terms. Nor will there be portfolio compression (Section 6.2.4) opportunities due to directionality and the client's standalone need for transactions (e.g. for cash flow accounting purposes).

MVA tends to arise with more sophisticated clients that may not have directional portfolios and may want, or be willing, to restructure transactions at some point in the future. Such optimisations will recover previous incremental MVA, which may suggest that it does not need to be charged, or accounted for, in the first place. Hence, MVA charges are only really necessary where there is clear directionality with respect to a new trade such that the cost cannot be offset in the future. Regional banks tend to experience such directionality, whilst many global banks do not as they are able to balance their portfolios. It is important to note that bilateral IM requirements will create more need to attempt to balance bilateral portfolios with counterparties and consider opportunities for optimising IM and utilising central clearing (discussed later in Section 21.3.4).

When MVA is important, it might not be directly chargeable. The hedges of a trade may have associated MVA components that often cannot be charged directly (since the counterparty will likely be another bank). Hence, in certain circumstances, an end user may be charged MVA, in addition to CVA and KVA components, representing a cost associated with the hedging of their trade.

There is also the question of the pricing of MVA where the €50m threshold has been utilised in the contractual terms. The threshold rules imply that a firm must have in place a system to identify the exposure to a counterparty across an entire group. It would then be necessary to decide how to identify the benefit created by the threshold. It could be allocated across entities a priori or used on a first-come-first-served basis. In such a case, MVA would not – in theory – be necessary until IM breaches the threshold, whereupon the pricing with respect to a given counterparty may change materially. It is probably best not to treat such a situation in a completely binary fashion.

At the current time, banks often do not have the capability to rigorously and industrially calculate MVA for all situations, and may only consider it material for large client trades (either directly or with respect to the hedges of uncollateralised trades). On the one hand, this could be seen as being due to a lack of development of procedure and analytics to handle this (similar to CVA, which many years ago was only considered on significant trades). On the other hand, the fact that IM is harder to charge and may not always be directional (leading to potential optimisation opportunities) may not require an advanced treatment of MVA. Time will tell whether or not MVA becomes more rigorously treated or whether this is seen as overkill.

20.3.2 Accounting MVA

When it comes to including MVA in valuation, there are similarities with the FVA debate (Section 18.2.6). For example, Andersen et al. (2016) illustrate the same wealth transfer from shareholders to creditors, illustrating that the total value of a bank is invariant to IM payments. This has accounting implications, and these authors suggest that – like FVA – MVA should not be a component of financial reporting. Nevertheless, shareholders need to be compensated for the wealth transfer, and so MVA can be charged.

IM actually represents another form of wealth transfer between creditors, as described by Gregory (2016). Derivatives creditors (CCPs and bilateral counterparties) become more senior by virtue of holding IM that can be used in default scenarios. By symmetry, other creditors, such as unsecured senior bondholders, become less senior and should expect to experience larger default losses (lower recovery rates). Hence, the funding costs associated with IM may increase due to the worse payoff afforded to non-derivatives creditors. Andersen et al. (2016) argue that the total value of a firm has no net MVA component. This requires a net consideration of shareholders, other creditors, and derivatives creditors, with only the last category seeing any benefit.

Leaving aside some of the above differences, it would seem that if the cost of funding is included in financial reporting for FVA, then the cost of IM, via MVA, should also be accounted for. There is already some evidence for this,⁴ although the adoption of MVA is proceeding more slowly than the equivalent adoption of FVA from around 2012 onwards. The likely reason for the slower adoption of MVA accounting is the inability to charge it in most situations.

20.3.3 Contingent MVA

Due to the LCR (Section 4.3.3), there may also be the need to consider contingent IM posting alongside actual (non-contingent) requirements (Figure 20.7). This can arise due to the need to hold HQLAs against additional IM requirements in the liquidity stress period envisaged by the LCR, and is analogous to the case already discussed for FVA (Section 18.3.6). Most obviously, such requirements arise in relation to the three-notch downgrade, where contractual terms require additional IM (or ‘independent amount’) in the event of such credit rating changes. These contractual clauses are not market standard but do exist in certain relationships. Additionally, there is a need to consider the contingent IM that would arise from the potential ‘recalibration’ of the underlying methodology in such a stress period. This is difficult to quantify but is most significant for CCP methodologies, which are very dynamic and potentially volatile (for example, see Figure 20.5) compared to SIMM, which is more static and subject only to an annual recalibration. Note, therefore, that whilst non-contingent CCP IM may be generally lower than the equivalent SIMM values, contingent CCP IM may be more expensive.

Graph depicts the MVA with both contingent and non-contingent components. — **Figure 20.7** Illustration of MVA with both contingent and non-contingent components.

20.3.4 CCP Basis

The CCP basis is a price differential that exists due to IM costs for dealers clearing a swap at one CCP versus another. For a given trade that could clear at more than one CCP, a dealer will have a preferred choice. This choice may well be related to the fact that the dealer already clears most of its business with this CCP.

Consider the case where a party wishes to trade with a dealer and clear at CCP1, but where the dealer's optimal clearing venue is CCP2 (Figure 20.8). From the dealer's perspective, there is a potential cost of IM at CCP1 due to the original trade, and another potential cost due to the hedge at CCP2. One or both of these incremental IM costs is likely to be material.

Taking the situation where the party is happy to clear at the favoured CCP (Figure 20.9), the dealer can clear both the original trade and the hedge at this CCP and would expect no additional IM requirement (unless the portfolio was subject to a concentration or liquidity multiplier; see Section 9.1.5). The ability to perform compression at the CCP may also cancel the two cleared transactions, from the dealer's perspective, at a later point in time.

The above shows that the dealer would prefer to clear the underlying trade at CCP2 (Figure 20.9), compared to CCP1 (Figure 20.8). Despite the underlying contracts being equivalent, they may, therefore, quote a different price for clearing at different CCPs. This price would be driven by MVA and be specific to the dealer in question, depending on the nature of the business cleared at the CCPs in question. Note that MVA is not directly visible via the CCP basis.

Schematic illustration of the origin of the CCP basis where a party trades with a dealer and wants to clear at CCP1, but where the dealer clears most of its business (including the hedge) with CCP2. The grey lines indicate the original executed bilateral trades and the black lines the cleared trades. — **Figure 20.8** Illustration of the origin of the CCP basis where a party trades with a dealer and wants to clear at CCP1, but where the dealer clears most of its business (including the hedge) with CCP2. The grey lines indicate the original executed bilateral trades and the black lines the cleared trades.

Schematic illustration of the origin of the CCP basis where a party trades with a dealer and clears at the dealer’s favored CCP. — **Figure 20.9** Illustration of the origin of the CCP basis where a party trades with a dealer and clears at the dealer's favoured CCP. The grey lines indicate the original executed bilateral trades and the black lines the cleared trades.

In some situations, the CCP basis might not represent a particular problem. A party may want to clear a trade at CCP1 and may – through choosing the best price available – naturally select the dealer that prefers this CCP.⁵ When executing a different trade, a different dealer may prove to provide the optimal price. In such situations, whilst a CCP basis would exist for some dealers, it would not be a systematic charge across all participants, and would not need to be experienced by a party able to execute with the dealer giving the best price.

However, due to the hedging needs of similar clients and inherent directionalities and concentrations in the market, the CCP basis may persist across all dealers. For example, consider that a group of clients all want to do the same type of trade (e.g. pay the fixed rate). Furthermore, assume that all of these clients prefer a certain ‘local’ CCP, either due to regulatory (they are required to clear at this venue) or economic (this CCP allows a broad range of eligible margin) reasons. Suppose that all major dealers tend to use another ‘global’ CCP and have cleared the majority of their portfolios at this CCP. In such a case, there will be a persistent CCP basis in pricing seen across all participants. This has been seen to be the case in practice.⁶

Note that a given transaction cleared at two different venues is economically the same instrument but with a potentially different price. Since International Financial Reporting Standards (IFRS) 13 requires banks to measure derivatives fair values based on exit prices for accounting purposes, it is relevant to report the fair value of cleared trades by using rates specific to the respective CCPs. This results in a volatile profit and loss (P&L) of accounting fair values of the CCP basis position due to changes of the CCP basis in the market.

20.4 LINK TO KVA

20.4.1 Overview

KVA and MVA are not mutually exclusive (Table 20.6). In a bilateral margin regime, posting IM will lead to MVA, but received IM may lead to capital relief and a lower KVA, although there may be a significant modelling challenge to being able to quantify this.⁷ In this respect, a part of the IM received can be seen as fulfilling the loss-absorbency role of capital. In a centrally-cleared regime, IM is not received, but there are potentially lower capital charges due to the perceived safety of the CCP.

The above implies that it is important to be able to capture KVA reduction in a bilateral margin or clearing regime, and to consider the offset of this component with the MVA cost. This also implies that KVA should be treated equivalently to MVA in terms of pricing and valuation. If this is not the case, then a bank may incorrectly incentivise opportunities such as ‘backloading’ portfolios to a CCP or posting ‘discretionary’ IM, which increase MVA but provide a more than offsetting KVA benefit, or vice versa. For example, suppose there is an opportunity to restructure a portfolio by posting and receiving more IM. This will create the following effects:

reduced cost of equity (lower regulatory capital); and
increased cost of debt (funding the required IM).

Both of the above need to be reflected in the valuation of KVA and MVA and the way in which this is transfer priced to the business. Without this, businesses will make decisions that do not reflect the actual cost of funding by the treasury, which will reflect sub-optimal choices for the bank as a whole.

Table 20.6 Impact of IM regimes on MVA and KVA.

	MVA	KVA
Bilateral	Cost of posting IM	Benefit of receiving IM, potentially leading to lower capital costs
Central clearing	Cost of posting IM	Benefit of lower capital costs for cleared trades

20.4.2 Example

To illustrate the above overlap between MVA and KVA, consider a 10-year interest rate swap in a bilateral margin regime. Regulatory capital is calculated using the standardised approach for counterparty credit risk (SA-CCR) methodology, which is equivalent to the results in Section 13.5.1. The regulatory IM is calculated under SIMM and considers IM requirements in a range around this value. The cost of capital is assumed to be 12%, and the funding cost of IM is 80 bp pa (0.8%). The MVA and KVA results as a function of bilateral IM are shown in Figure 20.10.

Obviously, the cost of posting IM will increase linearly with the amount, but the received IM will correspondingly produce a reduction in KVA. The gain in KVA is limited in the SA-CCR case due to the relative conservatism of this approach (e.g. the size of the add-ons and the 5% floor discussed in Section 13.4.3) There is a law of diminishing returns with KVA: every unit of initial margin received has a smaller relative impact.

The above example shows the reduction of KVA (under SA-CCR methodology) that occurs in combination with an increase in MVA with the bilateral IM amount. In this example, it is actually optimal to post a small, bilateral IM since the KVA reduction is slightly larger than the MVA increase. However, posting the regulatory IM amount (100% multiplier) is not optimal.

The above results depend on the bank's assessment of the cost of capital and funding IM. Figure 20.11 shows a similar example, but where the bank's cost of capital is perceived to be higher and its cost of funding lower. In this case, a larger bilateral IM posting is optimal, and the regulatory requirement is not far away from this optimum.

It may be expected that IM posting would be more favoured under internal model method (IMM) approaches, since the capital relief achievable may be better (although the capital requirements without IM will also be lower).

Note that the above result is not spurious – for example, due to the Modigliani–Miller theorem (Section 14.1) – and is largely driven by the nature of regulatory capital rules. However, clearly, the cost of funding debt and equity should be carefully chosen to represent correctly the impact of funding the balance sheet of the bank in question.

Graph depicts the KVA and MVA in bps upfront for a ten-year interest rate swap which is used as a function of the bilateral IM posted with a hundred percent multiplier corresponding to the SIMM result. — **Figure 20.10** KVA and MVA in bps upfront for a 10-year interest rate swap, as a function of the bilateral IM posted with a 100% multiplier corresponding to the SIMM result. A cost of capital of 12% is assumed, with a funding cost of IM of 80 bp pa.

Graph depicts a cost of capital of fifteen percent and a funding cost of IM of fifty bp pa. — **Figure 20.11** As in Figure 20.10, but with a cost of capital of 15% and a funding cost of IM of 50 bp pa.

In general, regulatory bilateral IM requirements (which require a conservatively high amount to be exchanged) are not favoured purely via a reduction in KVA. This is not surprising, as this would imply a form of regulatory arbitrage where it is cheaper for banks to give each other capital than to hold it themselves.