21
Actively Managing xVA and the Role of an xVA Desk

21.1 THE ROLE OF AN XVA DESK

In this chapter, we look at the ways in which banks and other significant derivative users manage counterparty risk, funding, collateral (margin), and capital. Large banks have generally had ‘CVA desks’ for many years to facilitate the pricing and hedging of counterparty risk. These units have evolved into ‘xVA desks’, with a broader mandate including aspects such as funding, margin optimisation, and capital reduction. Smaller banks have, in recent years, embarked on the same process, driven by aspects such as IFRS 13 and Basel III. Even other financial institutions (e.g. supranationals) and non-financials (e.g. large corporates) have had the need to build some sort of xVA specialisation driven by accounting needs and pricing optimisation.

Most institutions have recognised the efficiencies of centralising xVA for both pricing and risk management. This allows risk to be managed across different business lines and also provides a centralised place for inception pricing. A key role of this centralised desk is to neutralise the overall xVA profit and loss (P&L) impact with respect to market movements. This has led to some xVA desks moving from a passive to a more active risk management role. This represents a significant challenge, as an xVA desk is essentially a cross-asset credit hybrid trading business with components that are difficult or impossible to hedge, such as illiquid credit risk and cross-gamma.

21.1.1 Motivation

Historically, derivatives pricing and valuation were thought to relate only to cash flows; aspects such as credit risk, funding, margin, and capital were ignored. In line with this, derivatives trading and risk management were siloed according to asset class (e.g. rates, foreign exchange (FX), commodities, equities, and credit) with the associated expertise. xVA is now a large part of derivatives pricing and valuation.

As xVA components have become more important, there has been a clear need to change approaches to pricing and valuation. However, xVA is not asset class specific and requires broad knowledge, not only of all asset classes, but also of underlying credit, margin, funding, and capital implications. It has been common to have an xVA desk (also known as a ‘central desk’ or ‘scarce resource desk’) to perform this function. This set-up is partly defined by a historical development: asset class-specific trading desks operate in much the same way, and the xVA desk picks up all of the complexities that have developed in recent times. However, this separation is also partly justified by the fact that xVA adjustments are often portfolio-level quantities and are not mutually exclusive, and their calculations are complex.

In general, the role of an xVA desk can be seen to address the following primary needs:

• Pricing. xVA arises heterogeneously, with long-dated trades, and lower quality and uncollateralised counterparties being the most significant contributors. It is important to charge the correct xVA to each transaction, taking into account the underlying incremental impact on counterparty risk, margin, funding, and capital. Failure to incorporate xVA correctly represents a failure to price properly. This, in turn, means that the correct compensation is not achieved for future costs. It is also important to consider aspects such as the restructuring of transactions and option exercising as part of the xVA pricing process. This creates the right incentives in terms of the utilisation of the balance sheet of a bank.
• Valuation. It follows that any xVA component in pricing should ideally be reflected in valuation so as to avoid spurious P&L being reported. It is also important to correctly capture and explain the volatility of xVA components. A general aim may be that the xVA priced at trade inception is ‘locked in’ over the lifetime without any additional costs (or benefits).
• Optimisation. Whilst some xVAs may represent hard costs, there are also situations where xVA can be optimised beneficially. Activities such as compression (Section 6.2.5), restructuring transactions, or margining terms can have a beneficial effect in terms of xVA reduction. The xVA desk is the best place to understand the benefits of such optimisation, especially where it may involve reducing one component (e.g. capital) at the increased cost of another (e.g. initial margin).
• xVA management. New transactions have impacts on credit limits, margin, funding, and capital requirements. These aspects are unpredictable and can also give rise to significant mark-to-market (MTM) volatility. It is, therefore, necessary for the xVA desk to own and – where desirable and possible – manage this underlying volatility.

An xVA desk is generally set up as a central unit within an institution. There is a benefit in centralising all the required expertise and systems in one place. It is also difficult to separate xVA components from pricing data (such as information on clearing prices, where a bank may have lost out on certain competitive transactions), but at least a centralised xVA desk should be able to aim to understand this. There are also cases where xVA components will be seen to interact and may not be additive, examples being:

• Credit risk warehousing. Due to the belief that warehousing credit risk will generate profits and, therefore, a lower credit value adjustment (CVA) can be charged (see also the comments in Section 19.4.1).
• Workout process. The assumption of a lower loss given default (LGD) from the view that the claim is more senior or will benefit from some form of structural support (Section 17.2.6).
• Capital relief. Reduction in capital value adjustment (KVA) due to the capital relief achieved from hedging – for example, with credit default swap (CDS) indices. See also the discussion in Section 13.3.6.

The above must be clearly rationalised and balanced against accounting policy, especially with respect to CVA, where accounting requirements are relatively prescriptive. For example, charging a lower CVA due to the view that LGD may be lower may lead to accounting losses due to the inability to include this assumption in the accounting CVA calculation.

21.1.2 Charging Structure and Coverage

It is informative to consider the historical development of CVA and how it has been managed in banks over the last three decades. In most major banks, there has been a historical development, which has involved the following activities in roughly the order presented below:

• Pricing. The need to correctly charge and not originate credit risk in derivatives too cheaply would tend to cause a bank to start to price CVA, potentially in line with the origination of credit risk in other areas, such as the corporate lending business. At this point, CVA would still be revenue but would provide a hurdle to entering a transaction.
• Passive reserving. Once CVA is clearly part of pricing, it makes sense to reserve these amounts so that they do not form part of revenue. Such a reserve can be used to absorb losses in the event of a counterparty default. However, in the absence of sufficient defaults, it will be released back to revenue. Whether this is done heterogeneously (CVA paid back at the transaction level) or more generally, the originating business will still see CVA as potentially being revenue.
• Accounting. The passive reserving eventually becomes a more rigorous accounting for CVA in financial reporting, potentially driven by accounting standards such as IFRS 13 and Financial Accounting Standards Board (FASB) 157 (Section 5.3.3).
• Hard transfer. There is a hard transfer of P&L from the originating business to the xVA desk in relation to underlying CVA. This is associated with the transfer of counterparty risk, which immunises the originating business against the risk of counterparty default. Typically, CVA would not ever be paid back unless the transaction was later unwound or restructured in some way.
• Active management. The final stage of the process is often the move towards active management of CVA, where xVA P&L is hedged so as to minimise accounting volatility. This has associated capital implications that must be considered (Section 13.3.6).

As previously mentioned, most major banks have already embraced all of the above in their approach to CVA – and, more broadly, xVA – pricing, valuation, and management. However, some smaller regional banks may still identify as being at an intermediate stage in the above developments.

An xVA desk is responsible for some or all of the below components, which collectively represent the cost of holding an over-the-counter (OTC) derivative to maturity:

• Counterparty risk. The most common and fundamental role of the xVA desk is to own the counterparty risk in the event of a counterparty default, but also to manage the MTM volatility of CVA.
• Margin optimisation. The xVA desk may be involved in margin optimisation by choosing the most efficient margin to post in line with pricing the ‘cheapest-to-deliver’ collateral (Section 16.2.3). Margin also mitigates various xVA components such as CVA, funding value adjustment (FVA), and KVA and, therefore, the negotiation and renegotiation of margin terms is a critical component of managing xVA.
• Funding and margin. The xVA desk may be responsible for managing funding and initial margin posting requirements and costs – for example, via hedging internally with a treasury department. The overlap between CVA, debt value adjustment (DVA), and FVA (Section 18.2.5) is also important in this respect.

  Table 21.1 Consideration of xVA terms in different types of transaction.

  	Uncollateralised	Collateralised	Overcollateralised
  CVA	Yes	Partly	Partly
  FVA	Yes	–	–
  ColVA	–	Yes	Maybe
  MVA	–	–	Yes
  KVA	Yes	Yes	Yes

• Capital. Capital requirements for counterparty risk can be large and there are associated aspects such as the leverage ratio (Section 13.4.6). There may be a responsibility to manage the potential increase in capital requirements and reduce capital usage, for example, by hedging CVA with CDSs.

Note that some of the above roles are complementary. For example, hedging counterparty risk with CDSs with respect to either default events (single-name CDSs), or generic credit spread movements (index CDS) would also be expected to provide capital relief. However, these aspects are not always complementary, as discussed later.

Since xVA arises in different combinations for different types of transactions, the consideration of different xVA terms requires evaluation of a different sub-portfolio of derivatives transactions (Table 21.1). CVA and FVA are mainly concerned with uncollateralised transactions, although there may be some need to quantify CVA on collateralised or even overcollateralised portfolios. Collateral valuation adjustment (ColVA) exists only on collateralised and overcollateralised portfolios, although in the latter case, simplifications of the margin agreement may mean that it is less relevant. Margin value adjustment (MVA) is relevant only for overcollateralised portfolios where initial margin is present. KVA is relevant for all cases, although in some situations (e.g. central clearing) it may be considered far less relevant due to favourable capital requirements.

It is also important to constantly challenge xVA assumptions with anecdotal feedback from the salesforce and pricing resources such as the Totem xVA service (Section 5.3.5). This may avoid assumptions that may materially over- or underestimate xVA charges compared to peers and market practice.

A challenge for an xVA desk, especially in the early stages of development, is the coverage of transactions. It is important to address the biggest xVA users, which tend to be uncollateralised, long-dated transactions. For CVA assessment, it is possible to ignore many transactions, such as those that are well collateralised or with high-quality counterparties. However, the biggest xVA-related losses for banks in the global financial crisis arose from transactions with monoline insurers (Section 2.4.4), which were generally ignored for these reasons. Furthermore, xVA generally applies to every transaction in some way, and it is important to assess all components correctly.

From a pricing perspective, broadly speaking, there are two roles that an xVA desk can perform:

• Transfer pricing. Here, xVA pricing is similar to buying insurance. The xVA desk requires a hard transfer of cash, at inception, from a trading or sales desk, with respect to a given new transaction. The trading or sales desk, in turn, will charge this to the client, and any margin it can make on top of this is generally realised. It is hard for the originator (e.g. the trading desk) to avoid passing on the charge in full, since this would likely lead to them generating a loss (in limited situations they may do this in order to build the client relationship). The xVA is only returned in the event that the transaction is restructured or unwound and is, therefore, a real cost (or benefit).
• Hurdles. In this case, the xVA desk only sets a hurdle for the trading or sales desk to achieve, and there is no actual transfer of profit or risk. The originating desk is guided but not forced to charge this full amount to the client. Any charge is likely still to appear as revenue, and there is a reduced incentive to restructure transactions unless this can generate direct profit (as opposed to profit from xVA reduction).

Historically, xVA has tended to migrate from the latter to the former category as xVA desks have been built out. Smaller banks tend to follow more of a hurdle approach, whilst larger and more sophisticated ones transfer price. The increasing impact of accounting standards (e.g. IFRS 13), regulatory rules (Basel III capital requirements, leverage ratio), and market practice (FVA, MVA) have increased the need for active management of xVA, which, in turn, has led to the need for transfer pricing. However, not all xVA components are routinely transfer priced: the obvious current exception is capital (KVA), where hurdles to achieve the correct return on capital (ROC) are defined, but most banks have not yet moved to upfront transfer pricing of KVA. In the current environment, transactions may be executed even though their KVA is not sufficient to meet the relevant ROC hurdle. This situation will not materialise immediate losses, but will lead to poor returns compared to the required regulatory capital actually deployed over the lifetime of the transaction. This will be discussed in more detail in Section 21.3.2.

In the transfer pricing regime, xVA charges are typically not returned to the point of origination, even in the event of favourable outcomes (e.g. counterparties not defaulting). Such xVA charges are instead used indirectly or to offset other costs. For example, an xVA desk may use CVA premiums to buy options: this is not offsetting CVA per se, but is one component in managing CVA volatility. However, any other economic decision in relation to the trade (e.g. unwind, restructuring, option exercise – including cancellation – termination, or change in risk mitigants) should trigger an xVA adjustment. Indeed, in recent years, optimisation via various restructurings (e.g. unwinds, change in margining terms) has been proactively used by banks to minimise costs and maximise returns. An xVA desk should price such restructurings and pay out any xVA reduction so as to give trading and sales desks the right incentive in such situations.

In a hurdle-based regime, it is harder to incentivise the correct behaviour, since an xVA cost increase is not explicitly charged when entering a transaction and, by construction, cannot be paid out when exiting. However, in such a regime, it is easier to apply qualitative adjustments to xVA charges, such as the belief that a client will restructure or early-terminate transactions.

Note also that, when pricing a new transaction, aspects such as hedging activities have become increasingly important. For example, suppose a client executes a swap, which in turn is hedged with the reverse swap. Since this hedge is likely with a financial counterparty, it will give rise to initial margin costs either bilaterally or due to the requirement for central clearing. The cost of this initial margin may be charged to the original client, even though they themselves may be exempt from posting initial margin. At the current time, banks may only consider this to be important for large transactions, but it may become more standard to capture these components more rigorously.

21.1.3 Time Decay

An important aspect to understand in the management of xVA, in general, is the time decay (‘theta’) that is experienced against a real cost or benefit experienced in the future. This occurs because – all things being equal – the movement of time will cause xVA to become slightly smaller as the portfolio reduces in maturity. In opposition to this theta gain will be a future cost that is experienced over time in an unpredictable way. xVA components that are benefits will have a theta loss offsetting a potential future gain. The unpredictable nature of the cost or benefit leads to xVA volatility, some of which can be hedged and some of which is unhedgeable (Table 21.2).

Regarding CVA, the accrual cost comes from defaults, which usually cannot be hedged directly (unless there is a single-name CDS or similar contract available). The market risk in relation to CVA volatility can be hedged, although the credit spread risk may only be partially hedgeable. For ColVA, the theta term arises from (positive or negative) carry from the margin securities, together with the return from any margin transformation trades (e.g. repos). The cash component of this can be partly hedged, but the part involving securities may be unhedgeable. For funding (FVA/MVA) and capital (KVA), there are borrowing costs which are largely unhedgeable, but market risk which, as for CVA, can be hedged.

The performance of an xVA desk will ultimately be a balance between the carry component versus hedging costs (Table 21.3), together with other uncertain and unhedgeable components such as methodology changes. It is very important that the xVA desk has a clear mandate that is implemented via relevant metrics such as risk limits. A more aggressive strategy will tend to lead to lower P&L volatility but higher losses, due to the theta benefit being offset by the cost of hedging. On the other hand, a passive strategy – whilst cheaper in the long term – will create more short-term P&L volatility, which may not be acceptable.

Changes in documentation terms – such as the introduction of break clauses, thresholds or margin eligibility/terms, segregation, and initial margin – can all have material impacts on the risk characteristics of the exposure and, therefore, xVA. It is important that the xVA desk is a stakeholder in any documentation changes. It is also often the case that the xVA desk incentivises the salesforce to introduce these risk-mitigating factors into documentation by paying out the resulting reduction in CVA (and FVA).

Table 21.2 Accrual costs in opposition to xVA time decay.

	Accrual cost	Hedgeable components	Unhedgeable component
CVA	Defaults	Market risk	Defaults (usually), credit spread risk (partly)
ColVA	Remuneration of margin and transformation trades (e.g. repos)	Cash remuneration rates	Remuneration of securities
FVA/MVA	Funding costs	Market risk	Cost of funding
KVA	Dividends to shareholders	Market risk	Cost of capital/ regulatory change

Table 21.3 Example performance breakdown of an xVA desk.

P&L component	Gain/Loss	Comment
Net theta	37.3	Time decay of portfolio
New trades charged	4.2	Difference between charged amount and incremental xVA due to new trades (e.g. due to extra charges for hedging costs)
Cost of hedging	(17.3)	CDS hedging, vega hedging, bid/offer spreads
Defaults	(12.3)	Loss following workout process
Changes in methodology, static data and illiquid parameters	(6.5)	Rating changes change in recovery marks
Net P&L	5.4

Wrong-way risk (WWR) is present in all asset classes and embedded in all xVA portfolios. It is easily observable in hindsight, but dependency between a client exposure and market risk factors can evolve over time and be poorly represented by standard measures such as correlation. An example of a macro or general WWR can be represented as increased defaults when interest rates are low, which can be the worst time for a bank in terms of increased exposure in a one-directional receive fixed interest rate position. Specific WWR or tail risk is normally a result of concentrated exposures across multiple counterparties or oversized structural positions. Specific WWR can lead to severe negative cross-gamma losses, even when the client does not default.

The main challenge of WWR or tail risk is to identify and define scenarios in order to better understand the impact on xVAs and hence the P&L. This type of analysis, also described as stress testing, presents choices to better risk-manage the portfolio, to diversify the business away from a particular WWR scenario, or incentivise risk-reducing trades.

21.1.4 Profit Centre or Utility?

Another question is whether or not an xVA desk is a ‘profit centre’ or a ‘utility’, although these terms are generally not that distinct. It is generally agreed¹ that an xVA desk should be a utility function with a zero (or even slightly negative)² P&L target. This partially mitigates challenges such as when an xVA desk may be perceived to charge excessive prices, leading to reduced client revenue and lost business opportunities. A zero P&L target should also incentivise good behaviour for an xVA desk compared to a traditional trading desk. There should be no incentive to overcharge (or undercharge) xVA, and active management via hedging and paying out for risk-reducing transactions is encouraged. In an ideal world, xVA would represent the total cost of a transaction, and there would be no chance of the institution in question experiencing future losses in excess of this amount. The utility approach also implies that the xVA desk is not undertaking proprietary trading activity and would, for example, support a ‘risk-mitigating hedging’ exemption under the Volker rule in the US.³

Obviously, the above ideal is impractical as hedging xVA is imperfect. It is, therefore, important for a given institution to define its risk appetite to xVA. In general, the more one seeks to reduce the volatility of xVA, the greater will be the long-term cost. This is particularly true for counterparty risk: warehousing credit risk will lead to large CVA volatility, but expected long-term gains as actual credit losses are smaller than those priced in via risk-neutral default probabilities (Section 12.1.1). Banks traditionally warehouse credit risk arising from lending activities and have often looked at counterparty risk from derivatives in a similar fashion. This is particularly true for smaller and regional banks, and is especially relevant since the relative illiquidity of the CDS market makes hedging of counterparty risk on a single-name basis impossible in most cases. The warehousing approach to CVA has become increasingly difficult over the years due to developments such as IFRS 13 and Basel III. An xVA desk will need to have a carefully defined limits structure so that it cannot run significant open risks. That said, it should also have leeway to make tactical decisions when hedges might be expensive and inefficient and, subject to its limits, it may prefer to warehouse the risk. Some components will be relatively easy to hedge, some less so and some will be unhedgeable, as discussed in Section 21.2.4. Future capital requirements may create even more incentive to hedge CVA, with the greater recognition of CVA hedges as being capital reducing (Section 13.3.5).

With respect to other components, such as FVA, the incentive to hedge may or may not be stronger. On the one hand, without any potential benefit, such as the credit risk premium, hedging would seem natural. On the other hand, potential additional capital requirements for the hedges (since only CVA is considered explicitly in regulatory capital requirements) can be problematic. This is discussed in more detail in Section 21.2.9.

Reducing P&L volatility is one of the primary purposes of an xVA desk's hedging activity, although capital considerations can also sometimes play a part in this process. Due to the relative illiquidity of many of the hedging instruments, it is important to have a practical balance between minimising volatility and trading costs. Hedging is, to a degree, discretionary in nature due to the complexity of the xVA risk and the significant transaction costs, especially with respect to credit risk.

The key to running a successful xVA desk is to find the right balance between inception pricing, risk taking, and active hedging. Although xVA may be hedged to avoid dramatic P&L swings, it is not possible to hedge perfectly, and the residual risks and resultant P&L need to be understood by stakeholders and senior management. As an xVA desk has a P&L component, it is normal to view the desk as a trading desk; however, unlike most trading desks, it is typically not expected to be a profit centre. The zero or negative P&L target implies requiring a balance between xVA prices charged at inception to cover the risk and the general interests of the firm in advancing its business.

Given that xVA hedging is sometimes not possible or desirable, whilst an xVA desk may have a zero P&L target, it is important to consider the allocation of potential excess gains or losses periodically in some way. Some of these losses or gains may be accounting driven (e.g. from a credit spread widening), whilst some will be actually realised (e.g. default losses). In the former case, a homogenous allocation back to the point of origination would be most obvious, potentially weighted by the xVA charge (i.e. those paying the most xVA will experience most of the excess gains or losses). In some scenarios, such as defaults, it may be appropriate to consider a more heterogeneous allocation to the point of origination. Otherwise, there is a potential adverse selection problem that the originating salesperson or trader may choose to transact with the wrong type of clients (e.g. lower credit quality), based on the fact that all risks are perceived to be passed fully to the xVA desk. In some client relationships, the originating trader or business may be best placed to understand the nature of the underlying risk, especially in relation to complex aspects such as WWR. Of course, this type of allocation may also be seen as unfair in some situations.

In the event of default, the workout process (the process of negotiating claims with a defaulted counterparty) is also important, and the xVA desk should be an active participant, managing its claims optimally.

21.1.5 Pricing

The xVA charge is often the key determinant in the price of a derivative, in particular for many end user transactions, and especially if they are long-dated and/or uncollateralised. A key aspect of the transfer pricing of xVA is, therefore, that there must be a robust and industrialised process in place for the calculation of xVA charges in real time. To do this properly is complex from both an operations and a systems point of view, and simple methods are sometimes used by necessity. The ways in which real-time pricing is implemented vary in sophistication, as below:

• Static definitions. A static definition, such as a lookup grid with dimensions of product type, maturity, and counterparty credit quality, will provide an easy estimate of an xVA charge. Such calculations cannot, of course, account for trade specifics or risk mitigants, but they do make for a very simple, rapid, and transparent approach. There may be little or no consideration of the nature of the counterparty. Such approaches are required in many markets where price quotation has to be either immediate (electronic trading) or rapid. Of course, in such markets, xVA will be low or immaterial due to the level of collateralisation and the short-dated maturity of the underlying transaction.
• Standalone calculations. Standalone xVA pricing for given products can be implemented relatively simply (e.g. in spreadsheets) and does capture more transaction-specific aspects, but ignores potential risk mitigants. For directional transactions, this is sometimes not as problematic, as components such as netting may be only weak.
• Full simulation-based pricing. Incorporation of all aspects (especially netting and margining) can only be done accurately with simulation-based approaches that can run the entire portfolio of transactions. This needs to consider counterparty-specific terms, but also aggregate at the appropriate portfolio level (which depends on the xVA term in question). Practically, this requires a simulation engine that can generate all relevant market variables and compute values of the current portfolio and the new transaction in all required scenarios through time. This requires very rapid processing power and/or the use of significant data storage.

Full simulation-based pricing is a requirement for accurate incremental pricing at the counterparty or portfolio level. As discussed previously (see Figure 15.15), the aggregation level is important here. In particular:

• CVA and DVA. CVA and DVA are typically required at the netting set level. This will usually be the same as the counterparty level, but could, in theory, be different if there is more than one netting agreement for the counterparty.
• FVA. Depending on the nature of the margin agreement and the underlying assumptions, FVA may need to be calculated at the standalone (transaction) level or potentially the entire portfolio level (Section 18.3.2).
• MVA. The computation of initial margin for bilateral transactions will be at the portfolio level (unless a simple methodology, such as the standardised schedule shown in Table 7.11, is used). For centrally-cleared transactions, the initial margin will be calculated depending on the extent of the cross-margining at the central counterparty (CCP). Typically, this means that all transactions within an asset class at the same CCP will constitute the portfolio for the calculation.
• KVA. The counterparty credit risk (CCR) capital charge (Section 13.2) is linear across netting sets and, therefore, follows a similar calculation to CVA. The leverage ratio depends on a similar methodology. However, due to the portfolio-level assumptions for CVA capital, this element of KVA would, in theory, constitute a calculation for the whole portfolio.

The requirement for near real-time calculations with a flexible level of aggregation requires relatively sophisticated systems implementations, which will be discussed below. In most banks, the volume of pricing requests is too large for them all to be funnelled through the xVA desk (although the particularly large ones may well be),⁴ which means that the implementation also needs to be robust enough to be useable by non-xVA specialists.

Note that it is not only new transactions that need to be priced. Anything that represents a choice and has an economic implication for xVA needs to be considered, such as:

• restructuring (of transactions or portfolios);
• novations (the replacement of a party in a transaction or portfolio, which may involve reducing or taking on new exposure);
• changing margining terms or credit support annexe (CSA) renegotiation; or
• moving bilateral transactions to a CCP (‘backloading’).

All of these factors will have an impact on one or more xVA terms and may need to be quantified on a dynamic basis. From a bank's perspective, the above situations are usually proactively used to reduce xVA. The xVA desk will be able to incentivise them by at least partially paying out any accounting xVA gains (see Figure 5.3). Two further related situations are:

• option exercise (including cancellation); and
• exercise of a break clause.

A break clause such as an additional termination event (ATE) or ‘mutual put’ (Section 7.1.1) may be easier to deal with quantitatively since it will typically cause xVA to be cancelled, and it is, therefore, always optimal to break where possible (unless the overall xVA is seen as a benefit). Indeed, banks are much more likely nowadays to terminate such transactions or charge clients for not doing so (and communicate upfront to clients that they will do this). However, if break clauses are linked to a trigger event, such as a rating downgrade, then they are much more difficult to quantify and impossible to hedge.

Option exercises are complex because they involve the overall value of the underlying, not merely xVA, and essentially xVA changes the exercise boundary. For example, the exercise of a physically-settled swaption should be done optimally with respect to the xVA components of the underlying swap. Failure to do so may lead to sub-optimal exercising, where the base value of the swap is positive, but the xVA-adjusted value is not. Ideally, an xVA desk would impose a cost or refund on any economic decision to avoid this. This may translate into a conditional xVA charge for exercising an option, or a rebate for cancelling a transaction, so as to achieve the correct exercise boundary.

Banks will also sometimes incorporate behaviour-driven adjustments in xVA, such as charging less for a transaction in anticipation of future, more profitable transactions, or the assumption that it will be unwound or restructured later and lifetime xVA costs will not, therefore, be realised. Note that, when the xVA term is considered as a transfer price rather than a hurdle (Section 21.1.2), this is more difficult to achieve, as the xVA desk will be unable to accept a loss in the hope or expectation of a later xVA benefit. Indeed, this is why, currently, banks may be willing to apply behavioural assumptions to ROC (KVA) but not CVA or FVA costs.

21.2 HEDGING

21.2.1 Overview

The increasing volatility of xVA has led more banks to consider some sort of hedging strategy. A key aspect of xVA, as mentioned first in Section 5.2.1, is the ability to separate the basic valuation of a derivative from xVA adjustments. The same applies to hedging (Figure 21.1): whilst the market risks on a derivative may be hedged by a trading desk in isolation, the xVA desk will seek to hedge its own market risk. This separation of xVA is relevant due to the asset-specific nature of different classes of derivatives, combined with the fact that xVA generally depends on counterparty risk, margin, funding, and capital. Additionally, whilst the basic valuation of any derivative portfolio is additive, xVAs generally are not. This requires special treatment of xVA hedging at the portfolio level. Furthermore, xVA tends to be more complex than basic valuation, often involving components such as volatility and cross-gamma, which may be dramatically more complex, especially for simple products.

An xVA portfolio will experience sensitivity to every single market parameter for the underlying transactions in every currency, asset class, and product type. Furthermore, there will be sensitivities specific to xVA, such as where volatility risk arises from non-volatility-sensitive products. It is possible to compare xVA management to managing a book of options. For example, the Sorensen–Bollier analogy that represents swap exposure as a series of European swaptions (Section 15.1.3) implies that the problem of hedging should be approached in a similar way to that of hedging options. Furthermore, this ‘option book’ is fairly complex, with aspects such as cross-asset exposure and moneyness being important considerations.

Figure 21.1 Illustration of xVA hedging.

It is important to be pragmatic and bear in mind that some components can be hedged, some can be hedged with difficulty, leading to residual basis risks, and some cannot be hedged at all. In order to understand this, take a simple example of hedging xVA on an interest rate swap. xVA is sensitive to interest rates, interest rate volatility, and credit spreads, and so to hedge could require an interest rate swap, single-name CDS, and interest rate swaption. In theory, these hedges would not be single transactions (e.g. one would hedge with a series of swaptions to match the vega profile). The single-name CDS that would ideally be used is likely to be illiquid, and so some index or another proxy must be utilised. The hedges will also require frequent rebalancing as market movements occur. Finally, even if xVA is hedged on rates and credit, a simultaneous move where interest rates go down and credit spreads widen can cause significant P&L movements (cross-gamma).

It is also important to emphasise that xVA hedging for reducing P&L volatility alone may not be the only consideration. There are at least three different aspects here:

• Actual economic risk. The actual underlying financial risk (e.g. defaults).
• Accounting xVA. The changes in xVA driven by the accounting practices (e.g. credit spread widening).
• Regulatory capital. The regulatory capital requirements.

In an ideal world, the above would be perfectly aligned but, in reality, the misalignment can be significant. For example, DVA is a component of accounting xVA that is not generally recognised as being economically realistic (Section 17.3.5). Banks generally view FVA as being an important consideration (Section 18.2.1), but it is not yet mentioned in accounting standards or regulatory capital rules. Different banks will have a different focus on the above: a bank that is capital constrained may primarily aim to reduce capital, whereas another may focus on reducing accounting volatility. There are also potential issues with some xVA hedges increasing regulatory capital requirements, as discussed in Section 21.3.2.

Finally, any change in funding and capital costs will potentially impact the P&L of the xVA desk. However, this generally reflects internal parameters, such as a return on equity (ROE) target or a funds transfer pricing (FTP) curve. These parameters are likely to be semistationary, although indirectly driven by continuously evolving market rates. Any changes here will cause a P&L move that is very difficult to hedge, and it is probably not relevant to continuously remark such parameters, since this will merely cause spurious P&L volatility for the xVA desk. However, when such rates are changed, there will be a P&L change that may have to be absorbed by the xVA desk.

21.2.2 Sensitivities

In general, xVA can be represented as a combination of market risk and some underlying credit, margin, funding, or capital cost. It is possible to discuss the hedging of xVA in general without specific reference to the terms under consideration.

The market risk sensitivity of xVA can be broadly broken down into:

• Spot/forward rates. The sensitivity to spot and forward rates, such as interest rates and FX. This is generally hedgeable, with the underlying hedging instruments being liquid, potentially exchange-traded or centrally cleared.
• Volatility. The sensitivity to implied volatility, such as FX options or interest rate swaptions. This is also hedgeable, although the underlying instruments will generally be bilateral OTC products and may be illiquid and unavailable in some cases. For example, hedging long-dated volatility may not be possible.
• Correlation. The sensitivity to the correlation between different exposure variables (such as two different interest rates). This is generally unhedgeable, except via exotic products such as quantos, basket options, and spread options, which are not usually liquid.

Note that market risk will be hedged on aggregate and not at the counterparty level, and it is also helpful to combine market risk hedges across some or all xVA terms. For example, an interest rate hedge may exist because an increase in rates could cause both CVA and FVA to increase. If an xVA desk does not have the mandate to hedge the change in a particular component (e.g. capital costs via KVA), then this would obviously not be included in its P&L.

The number of sensitivities that the above categories can constitute is large, even in some rather simple cases, let alone for large portfolios of trades. Due to the cross-asset nature of xVA, the number of sensitivities (or Greeks) can become very large, even for vanilla trades. For example, a single vanilla cross-currency swap will give rise to the following CVA risks:

• interest rate risk (for the two currencies);
• interest rate basis risk;
• interest rate volatility (for the two currencies);
• FX spot risk;
• FX vega risk;
• cross-currency basis risk;
• credit delta;
• gamma/jump to default (JTD) risk (the impact of a large credit spread movement or default); and
• cross-gamma (correlation) between market risk factors themselves (interest rates and FX), and between credit risk and market risk factors (interest rates and FX to credit risk).

All hedges should also ideally be considered across the term structure, which is often impractical as it leads to increasing numbers of hedging transactions. Other xVA terms will introduce more sensitivities, such as the relationship to the cost of funding in the case of FVA. There is also the need to consider the sensitivity to credit spreads and other components such as funding costs.

A general representation of xVA Greeks is set out below:

(21.1)

In general, sensitivities can be seen to be broken down into exposure (E) components (such as interest rate and FX deltas) and vegas, spread (S) components (such as credit deltas), and cross-gamma components. Not shown in the above are cross-gammas between exposure terms (e.g. interest rate and FX) and second-order (gamma) terms in general.

From a hedging point of view, it is possible to consider – broadly speaking – four categories:

• Liquid hedges. Where the underlying risk is reasonably straightforward to hedge and where the underlying costs of doing this are only small or moderate due to liquid hedging instruments. An example of this is interest rate and FX delta hedges.
• Illiquid hedges. Where the underlying risk can be hedged but the associated hedging costs are relatively high, such as when hedging vega, which would involve, for example, buying swaptions and FX options.
• Proxy hedges. Where the underlying risk can only be hedged using instruments that are correlated to the underlying sensitivity, such as when using CDS indices to hedge credit delta or buying out-of-the-money (OTM) options so as to hedge ‘tail risk’.
• No hedge. Where the underlying risk cannot be practically hedged, such as with respect to correlations or cross-gamma, except on a completely bespoke basis.

It is also important to note that there may be exposure to multiple currencies, FX pairs, etc. In such cases, it may be relevant to actively hedge certain components that are linked to large exposures, but treat other, less significant components less dynamically or not hedge them at all. There may also be proxies used for calibration, such as using swaptions in one currency to calibrate interest rate volatility for another currency where there is no volatility market. In these cases, it may be possible to reduce accounting volatility by hedging, although this may not provide regulatory capital relief.

Whilst market risk hedging is reasonably practical, the hedging of credit and funding aspects is less straightforward. Credit hedging is clearly more difficult due to the illiquidity of the underlying CDS market. Potential hedging instruments are:

• Single-name CDS. If liquid, then this is the ideal hedge against counterparty credit quality. However, there is a difference between hedging the credit spread and the JTD risk. In the former case, the focus is on a small credit spread change, and the latter on an actual default event (Section 17.2.5). Ideally, one should buy protection from a high-quality counterparty with minimal correlation to the original counterparty (if the CDS is centrally cleared, then this may be viewed as resolving this problem).
• Single-name proxy CDS. Hedging using a similar credit may be viewed as efficient, although this obviously depends on the underlying credit spread correlation. Also important is whether the proxy credit would default in the same situations. In some situations, this may be the case (e.g. the proxy is a sovereign that would always support the counterparty in question) and in some cases not (e.g. a name in a similar region and sector).
• Index CDS. Credit indices are more liquid and can be used to provide a macro-hedge of a general credit spread widening, but do not provide any protection against actual counterparty default.⁵ The benefit of index hedging (and associated capital relief) also depends heavily on there being a significant correlation between the index and single-name CDS, which may not always be observed in practice.⁶

Due to the above, most institutions would consider some credit hedging to be relevant in order to avoid excessive fluctuation in their accounting CVA. They may also use, where possible, credit options to manage convexity and single-name CDSs to hedge large exposures.

Hedging of funding costs is generally not possible, but in case the xVA desk is responsible for these costs, credit indices would be one potential proxy. This depends on the policy for setting the funding cost for FVA purposes. Capital costs are also largely unhedgeable.

In an xVA context where multiple terms may be hedged in aggregate (e.g. CVA and DVA or CVA and FVA), different sensitivities may either be additive or will offset one another. In general, exposure deltas (e.g. interest rate and FX delta hedges) will tend to be in the same direction for all xVA terms, leading to a larger overall sensitivity. On the other hand, credit deltas and vegas will tend to offset, since CVA/FCA (funding cost adjustment) hedges would tend to involve buying vega and credit protection, whilst DVA/FBA (funding benefit adjustment) hedges would sell vega and credit protection.

As an example, Table 21.4 shows the Greeks for a receiver interest rate swap. An increase in interest rates will cause the swap to be more OTM, which will reduce expected positive exposure (EPE) and increase expected negative exposure (ENE). This will, in turn, make CVA less negative and DVA more positive, both of which are positive effects. In the case of a vega, both the EPE and the ENE will increase, and the effect will be offsetting (CVA impact negative, DVA positive). The credit spread sensitivity causes a similar effect to that of the vega. The impact on FCA and FBA follows that of CVA and DVA, respectively.

Table 21.4 xVA Greeks for a 100 million notional receive fixed 10-year interest rate swap. The deltas are with respect to a parallel shift of the curve (of 1 bp), whilst the vega is calculated based on a 1% increase in the implied volatility.

	Interest rate delta (DV01)	Interest rate vega	Credit spread delta (CS01)
CVA	1,083	−3,848	−1,487
DVA	1,271	1,640	2,252
FCA	540	−2,022	−1,507
FBA	1,400	1,750	2,328

As discussed in Section 15.3, the calculation of xVA is computationally demanding due (usually) to the use of Monte Carlo simulation and the need to evolve the portfolio across the entire lifetime of trades (which in turn require full revaluation). If sensitivities are calculated using a finite-difference ‘bump-and-run’ approach, then there is potentially adverse linear scaling with respect to computation time and the total number of sensitivities required. Whilst optimisations are possible,⁷ this does require a significant degree of computational power, unless a method such as adjoint algorithmic differentiation (AAD) is used.⁸ It is often important to limit the sensitivities that will be calculated to ones that are required for hedging purposes, or in order to be able to explain materially-important P&L movements. Furthermore, in the case of curves, it is important to choose a relatively compact representation of the risk to minimise the number of sensitivity calculations required. Note that simplifying assumptions such as constant basis (Section 15.4.2) keep the required number of sensitivities low, as they essentially mean that the sensitivity to multiple curves is calculated altogether.

Banks may also choose to calculate a number of important sensitivities on a daily basis, and some less important ones less frequently (e.g. weekly basis). This may also apply to running stress scenarios, which may represent large and/or simultaneous moves in various risk factors. Since such scenarios define the general directionality and risk of an xVA portfolio, they do not typically need to be recalculated on a very frequent basis.

In the event that the xVA calculation assumes independence between the exposure and spread components (no WWR), credit-related sensitivity calculations are greatly simplified. This is because defaults are not simulated and the calculation is based only on an analytical calculation of default probabilities (e.g. Equation 12.1). This also applies to cross-gamma components, including credit risk elements. An example of this would be that – in a no-WWR setting – a credit delta calculation should be very fast, as it would not require the Monte Carlo simulation to be rerun. Credit rates cross-gammas would also be easy to calculate, as long as they were evaluated alongside the relevant interest rate bump scenario.

Technical problems with xVA models can also cause hedging problems. For example, potential instability of calibrated parameters can cause day-to-day swings in xVA and the associated sensitivities. Clearly, it is desirable to reduce such effects, which is why simple and more parsimonious xVA models are often preferred. Another example is that the time discretisation of the xVA integral can be problematic moving from one day to another, as cash flows move between discretisation dates. This is less easy to control and is often simply accepted as creating background noise.

Most banks compute xVA for collateralised counterparties based on assumptions around the close-out process and the value of the margin period of risk (MPoR). However, this is an inherently quite subjective and noisy calculation due to the precise assumptions regarding the margin exchange and cash flows within the MPoR, and can be particularly problematic where cash flow payments fall inside the MPoR. As a consequence, many banks are less concerned with hedging and with P&L explain of such counterparties, which may also make up only a relatively small fraction of the total xVA.

21.2.3 Gamma, Cross-gamma, Tail Risk, and Rebalancing

Gamma refers to the change in the delta, and a large gamma will, therefore, make a required delta hedge change significantly with market conditions. Where there is significant gamma or convexity with respect to a delta-hedged parameter, it may be helpful to construct a profile that better matches this gamma (e.g. buying swaptions against interest rate sensitivity). This would be more expensive upfront, but would reduce the need to balance the delta position frequently.

Whilst gamma generally refers to a large move in an underlying variable, cross-gamma refers to the joint move of two variables. Even if the two variables are hedged or explained independently, their joint move may have a material impact. Cross-gamma components are typically unhedgeable, but can be sizeable for xVA portfolios, especially the credit-related cross-gamma terms. As an illustration of cross-gamma, Figure 21.2 shows the credit spread sensitivity (CS01) for a receive fixed interest rate swap for different levels of interest rates. As interest rates increase, the swap moves OTM and the credit delta reduces, and vice versa. In practical terms, cross-gamma might be experienced as a result of a major market movement, such as interest rates falling, together with a credit spread widening. In such a situation, the larger uncollateralised exposures on receiver swap positions will then require more credit hedges, but the cost of these hedges will not be funded by gains on existing interest rate hedges, unless these accounted for the underlying cross-gamma effect.

Figure 21.2 CVA credit spread sensitivity (parallel CS01) as a function of different parallel interest rate moves for an interest rate swap. Note that the CS01 is defined by a negative shift of one basis point and is, therefore, a positive number.

Cross-gamma is often realised when there is a significant move in two underlying variables that effectively amounts to a delivered correlation of close to +/-100%, associated with large volatility. This often occurs in the aftermath of a significant event: for example, the vote in the European Union referendum on 23 June 2016. This event led to GBP swap rates tightening and credit spreads widening. For interest rate swaps receiving the fixed rate, this would have led the swap to have a larger exposure, coupled with a deterioration in the underlying credit quality, leading to losses even if interest rates and credit spreads were delta hedged on an individual basis.⁹

Cross-gamma is generally unhedgeable, but can be partially neutralised in various ways:

• Finding a direct hedge. For example, it is possible to trade CDS protection in two currencies (Section 17.6.4) against a reference entity which allows a hedge against a potential credit/FX WWR and, therefore, cross-gamma.
• Overhedging or underhedging the relevant deltas based on the known directionality of the position, together with a market view. Due to the over- or underhedging, this leads to more P&L volatility in normal scenarios, but a lower change in a more extreme scenario.
• Buying options referencing one or both underlying risk factors. Hedging of these types of risk typically involves buying OTM options which have a low delta but more significant gamma.

Individually and jointly stress testing each of the market input variables used in calculating xVA allows the xVA desk to gain an understanding of the portfolio behaviour in various environments. When an adverse scenario is identified (e.g. internet rate tightening and credit spread widening), consideration should be given to how to best manage the scenario by either adopting a hedging strategy or incentivising risk reduction and diversification by the business.

Due to the relative illiquidity of xVA hedges, rebalancing must be done pragmatically, with the underlying bid-offer costs taken into account. Being able to hedge some convexity components may be an efficient way to reduce rebalancing costs if the convexity hedges are not prohibitively expensive. For example, some banks will use swaptions together with a normal delta hedge to manage their interest rate sensitivity, the advantage being that the hedges remain relatively stable for moderate moves in the underlying.

As noted above, banks often charge xVA to mid. Due to hedging costs, this will be likely to lead to P&L losses, which should at the least be understood. Sometimes – and where systems are sophisticated enough – there will be additional charges for approximate rehedging costs. This requires an incremental calculation of the hedging costs, as illustrated for credit delta (which is likely to be the most significant) in Table 21.5. Here, a bank may charge for a certain bid-offer for the rehedging. For example, if the bid-offer were 10 basis points (bps) and the duration of the portfolio was four years, then a charge of half the bid-offer times the net CS01 sensitivity times the duration would be , which may be added to the other incremental xVA components. This envisages a hedge of only the overall sensitivity. If all tenors were to be rehedged, then the gross CS01 change would be more relevant (although, given the liquidity of the CDS market, this is unlikely).

Table 21.5 Illustration of the calculation of rehedging costs.

Tenor	CS01 (before)	CS01 (after)	CS01 change
6 months	−11,380	−7,988	−3,390
1 year	13,845	8,458	5,387
2 years	4,000	631	3,371
3 years	2,732	2,341	391
4 years	5,959	7,278	−1,319
5 years	11,427	11,472	−44
7 years	9,824	9,676	148
10 years	5,501	5,384	117
Total	41,912	37,249	4,661

21.2.4 Market Practice

Many large banks now have a fairly long history of hedging CVA. Hedging is generally, to a degree, discretionary in nature (Figure 21.3), due to the complexity of CVA risk and the underlying illiquidity or lack of availability of hedges. Market risk hedges are most common, which is not surprising due to the underlying instruments being the most liquid and not being subject to significant additional counterparty risks. Credit spread risk is the next most commonly hedged, but it is less liquid and, as noted above, banks would prefer in general to warehouse some counterparty risk. Not surprisingly, vegas, gammas, and other terms are less commonly hedged.

Figure 21.3 Market practice on hedging of CVA Greeks.

Source: Deloitte/Solum CVA Survey (2013).

Table 21.6 Summary of market practice with respect to xVA hedging.

Risk factor	Practicality of hedging	Market practice
DV01s (interest rate, FX, inflation, etc.)	Liquid	Usually hedged
Volatility (swaptions, FX options, etc.)	Less liquid Long-dated and OTM volatility harder to access	May be hedged (e.g. major currencies and FX pairs)
Credit CS01	Relatively liquid (indices) Illiquid (single-name CDS)	May be hedged or partially hedged with credit indices
Correlation and cross-gamma (e.g. rates–rates, rates–FX)	Not liquid	Only hedged in special and bespoke circumstances

Most banks hedge the market risk of CVA in aggregate with FVA, although a small number still hedge CVA and DVA. An xVA desk will pay the mid-to-bid or mid-to-offer when hedging its positions, as illustrated in Table 21.5. This is a real cost, since standard xVA pricing will usually be calculated at mid. Whilst bid/offer of standard rates and FX hedging instruments may be quite small, CDS bid-offer spreads are quite significant, even for index hedges.

A summary of the market practice on hedging is given in Table 21.6. Exposure delta (DV01) risk is hedged by most banks (in full or in part) and on the most frequent basis. This is due to underlying hedges being the most liquid. Interest rate hedges are generally liquid, with futures being the cheapest hedges for directional risk. Swaps for hedging curve risk are quite liquid in major currencies for all tenors of the swap curve up to 10 years. Long-dated swaps can sometimes be less liquid. Due to the number of different interest rate curves (London Interbank Offered Rate, overnight indexed spread, short-term interest rates – STIRs), basis risk can be material, giving rise to some P&L volatility. Spot FX markets for most currency pairs are also quite liquid.

An xVA book is almost always short volatility risk (vega). Vega is more difficult to hedge and is, therefore, not hedged as frequently, except in situations where the underlying sensitivity is very large. In some specific cases, buying vega can be a macro-hedge for managing WWR in situations where the currency is correlated to the creditworthiness of large companies in those countries. It can also allow a closer match to the profile and, therefore, requires a less frequent rebalancing of DV01 hedges.

Correlation and cross-gamma hedges are completely illiquid and are only done in special circumstances.

Credit risk delta (CS01) is sometimes hedged, but it can generally only be done on a macro basis, given the illiquidity of the single-name CDS market (especially for typical uncollateralised counterparties such as non-financial corporations). Proxy single-name hedges (e.g. a parent company or sovereign) may be available and used for some counterparties, but single-name CDSs are generally illiquid, except for large counterparties, and even then they are generally available only for financial institutions and sovereigns (see discussion in Section 12.2.2). Due to the relative illiquidity of most CDS tenors, there is also a balance between hedging curve risk and minimising bid-offer costs. Due to the better liquidity in five-year CDS maturities, xVA desks tend to build up a ‘steepener’ position over time, which must be managed by, for example, rolling index hedging into the on-the-run index after each index roll and rehedging single-name CDS positions periodically.

Table 21.7 Summary of market practice with respect to hedging CVA (and potentially DVA, if relevant) credit risk.

Hedging instrument	Practicality	Market practice
Index CDS	Reasonable liquidity Spread hedging Benefit linked to mapping methodology	Hedged for P&L volatility reduction and capital relief
Proxy single-name CDS	Limited liquidity Spread hedge Possible partial JTD hedge	Sometimes used for P&L volatility reduction
Single-name CDS	Very limited liquidity Spread hedge JTD hedge	Hedged where liquid for P&L volatility reduction, capital relief, and JTD hedging

In addition, most banks ideally do not want to hedge credit risk, since this is often seen as being profitable (due to the inherent risk premiums). Hence, the hedging of credit is generally driven by the need to reduce P&L volatility (and possibly capital), rather than to reduce actual economic risk. The key considerations relating to credit risk hedging for CVA are set out in Table 21.7 below.

21.2.5 Jump to Default Risk

Whilst credit hedging is primarily done to minimise P&L volatility, xVA desks also need to analyse potential default scenarios, especially for distressed counterparties. As discussed in Section 17.2.5, the impact of a sudden default for a delta-hedged counterparty can be either positive or negative, depending on the current exposure.

A calculation of JTD P&L can be represented as follows:

(21.2)

When the above term is negative, it provides an estimate of the potential loss in the event of default, considering exposure, recovery rates, CDS notional, and xVA release.

Figure 21.4 JTD P&L as a function of the positive shift in the credit curve for a 10-year ITM interest rate swap, assuming a hedge of the credit spread sensitivity with a single-name CDS hedge of either five- or 10-year maturity.

For in-the-money (ITM) portfolios that do not have single-name CDS hedges, JTD risk is always negative and driven by the size of the current exposure less the xVA contribution (which is generally small in comparison). When there is a single-name CDS hedge, JTD risk is more complex and depends on the level of the current exposure and the maturity of the portfolio and CDS hedge. As an example, Figure 21.4 shows JTD P&L for an ITM receive fixed interest rate swap, which is assumed to be delta hedged with a single-name CDS. For the 10-year CDS, there is JTD risk, which reduces as the credit spread widens. With the five-year CDS, a larger notional is required to neutralise the credit spread volatility, which makes JTD P&L positive. As the credit spread widens and the counterparty moves towards default, JTD tends to zero, but not necessarily in a monotonic fashion.

JTD risk can only realistically be hedged by adjusting the credit spread delta by tenor (e.g. buying short-term protection). Whilst this is often not possible, it is good practice to report and monitor JTD values for each counterparty and consider acting if these become relatively large and/or the credit quality deteriorates.

21.2.6 Beta Hedging

The potential for hedging with indices or proxy single-name CDS raises the question of the efficiency of such a hedge. The hedging of one underlying with another different but correlated asset is often known as beta hedging.

A simple analysis (see Appendix 21A) shows that the optimal amount to hedge within this situation is driven by the level of the correlation between the counterparty exposure and the hedging instrument. With this optimal hedge, the residual variability (standard deviation) is . This means that, for a correlation of , the residual variability would be 87%.¹¹ Such a hedge appears fairly inefficient unless the correlation is very high. However, for a portfolio, there is a greater benefit since the idiosyncratic risk is diversified away, making the resulting hedging of systematic risk more efficient. This makes the residual variability lower, as illustrated in Figure 21.5 (see Appendix 21A for a more detailed description). This means that hedging a portfolio of 50 equal counterparties with an index that is 50% correlated to all of them leaves a residual variability of only 23%. This suggests material reduction of accounting volatility and capital relief from index CDS hedges, as will be discussed below.

Figure 21.5 Potential hedging benefit with a credit proxy, depending on correlation and (equal) portfolio size.

When the credit spread sensitivity of xVA (mainly CVA)¹² is hedged, it is necessary to estimate the ‘beta’ to the index (or indices) that is used for hedging. Such betas will be partly driven by the mapping methodology used to define illiquid credit curves (Section 12.3) and partly by actual empirical data. They can be estimated by examining the historical relationship between xVA volatility and that of the associated index. This is a subjective process, with the length of the time series and the frequency of updating being important considerations. If the beta is too high (low), then the credit spread volatility will be overhedged (underhedged), leading to xVA gains (losses) when credit spreads widen. The correct beta will be a function of the correlation between index and counterparty credit spreads and their associated volatilities. This can clearly change quite dynamically and is a challenge to predict accurately, especially as past behaviour may not be a good guide as to future relationships.

21.2.7 Risk Limits and P&L Explain

It is important to have limits in place to define the appetite for P&L volatility for the various different Greeks (Figure 21.6). Delta limits for market risk should generally be reasonably small so as to incentivise the hedging of these relatively liquid risk factors. Vega limits may be higher given the more limited liquidity and potential costs of buying options. Credit spread delta limits are probably the most important to define, since, whilst it may be profitable to warehouse credit risk, this is usually the biggest driver of accounting volatility. Credit spread hedging is, therefore, a balance between reducing the volatility of xVA and not ‘paying away’ the full credit risk premium. It is also important to have JTD limits (to avoid a single counterparty exposure being too high) and concentration limits (e.g. with respect to a given region).

Figure 21.6 Market practice on CVA limits.

Source: Deloitte/Solum CVA Survey (2013).

It is important to be able to predict and explain P&L changes in relation to xVA. This is a common requirement for trading desks to understand the performance of their hedging and the source of any material unhedged moves. P&L explain or predict is generally performed at the end of each trading day. It aims to predict the actual P&L based on changes in risk factors and then explain the actual observed change in xVA (which should be available the next day).

The illustration in Table 21.8 shows total xVA P&L calculated as the difference between xVA on day T-2 and xVA on day T-1 that needs to be explained. The attribution to credit, rates, and FX P&L is based on xVA sensitivities to the respective market factors (i.e. ). Unexplained P&L (UX) is the residual P&L that is not explained by changes to market risk factors. In the absence of any other changes to the portfolio (e.g. new trades or rating changes), this represents gamma and cross-gamma (and in the case shown, vega also, since it is not included).

The P&L explain may be aggregated in different ways. For example, from a credit point of view, it is useful to view by counterparty, but for most factors (e.g. interest rate risk), the entire portfolio view is relevant. It is also important to be able to decompose by xVA term (e.g. CVA and FVA). Whilst a small UX number is acceptable, if this number consistently exceeds a fraction of the overall daily P&L, it shows that material risks are not being captured. In such situations, the P&L explain may be expanded, even if the risk being explained cannot be hedged (e.g. cross-gamma). This will require more sensitivity calculations.

Table 21.8 Example P&L explain.

xVA T-2	xVA T-1	Total P&L	Theta	Credit delta	Rates delta	FX delta	UX
−58,381,190	−61,607,070	−3,225,880	120,960	−1,800,820	−1,610,770	279,335	−214,585

An alternative way to perform a P&L explain process is to shift risk factors sequentially, which, by construction, will explain total P&L. This approach may be favoured by finance departments, but it is not in line with the way in which an xVA desk sees and hedges its sensitivities.

Additionally, portfolio changes (new trades, novations, restructurings, etc.) should also ideally be incorporated in the P&L explain process, together with methodology changes (e.g. internal rating changes). Sometimes this is a manual process, with these components initially appearing to be unexplained and the formal P&L report being manually adjusted.

In summary, the following components may be part of a P&L explain process:

• changes in risk factors:
  • theta (time decay);
  • deltas (rates, FX, etc.);
  • implied volatility;
  • credit spread delta;
  • gamma;
  • cross-gamma;
  • defaults; and
  • funding and capital costs.
• portfolio changes:
  • new trades;
  • novations;
  • unwinds/terminations; and
  • exercise decisions.
• counterparty changes:
  • consolidation of netting terms;
  • changes to the margin agreement;
  • rating changes (leading to a change in spread mapping, for example);
  • credit events; and
  • model changes.

21.2.8 Examples

In order to give an insight into hedging xVA, Figure 21.7 shows the change in xVA driven by both interest rates (in the main currency driving the exposure) and credit spreads. In this case, the combination of CVA and FVA is being hedged. The performance of the hedges in each case and the overall effect is also shown. The interest rate hedges work well, with the total P&L variability being quite low. There is a small amount of noise due to curve movements and hedging frequency (the hedges are generally updated only periodically and/or when there is a material change in the sensitivity). For the credit spread hedges, the performance is worse, which should be expected due to the nature of ‘beta hedging’ (Section 21.2.6). There is a fairly systematic negative bias with respect to the credit hedges, which is partly due to bid-offer costs and partly due to the beta being slightly overstated. With respect to the latter, the general credit spread tightening regime leads to overall losses due to buying too much index protection (the xVA desk is, therefore, seen in hindsight to be short credit risk).

Figure 21.7 Hedging performance for xVA desk (CVA and FVA), showing behaviour with respect to interest rates (left) and credit spreads (right).

21.2.9 Impact on Capital

For some banks, alongside reducing P&L volatility, there is the question of the impact of xVA hedges on regulatory capital. In some cases, banks have even favoured regulatory capital reduction over P&L volatility control. Depending upon the regulatory approach and the type of hedging instruments used, there are different treatments with respect to regulatory capital relief.

Since capital relief can be gained with index CDSs, from a pure ROC – as opposed to an accounting volatility – point of view, there is an optimal point. This point occurs when the cost of buying index CDS protection is less than the capital benefit achieved. If the index CDS spreads are low enough, then hedging CVA capital will be optimal. This is illustrated in Figure 21.8, which shows the ROC as a function of CDS index hedge size for different spread regimes. If index spreads are too high, then it will not be optimal to hedge, but as for lower levels, an improvement in ROC can be achieved.

Figure 21.8 Overall ROC when using index CDS to hedge CVA capital.

Note that only single-name CDS hedges can provide capital relief against the CCR capital charge. However, this must reference the correct legal entity and have a cross-default provision so that bond default would be triggered in the event of derivative default. The main discussion over hedging relates to the CVA capital charge, where market risk hedges are potentially capital reducing.

The first point to make is that, under both current and future regulatory environments, the market risk of the actual value is not capitalised, but instead treated as the two components that have been previously referred to as base value and xVA (Equation 5.1).

Firstly, there are traditional trading book (TB) market risk capital requirements that generally can be seen to apply to the ‘base value’. Relatively sophisticated banks have used value-at-risk (VAR) methodology to quantify such requirements under an internal model approach, and there are more basic approaches for other banks. These requirements are in the process of being overhauled as a result of the Fundamental Review of the Trading Book (FRTB) regulation (BCBS 2019a).

Secondly, there are independent CVA-related capital charges. These are also subject to regulatory change with regards to, for example, the future FRTB-CVA rules, as has been discussed in detail in Section 13.3.

The market risk and CVA capital charges are independent, despite both being subject to incoming FRTB requirements. One reason for this is that CVA is seen as inherently more complex and, therefore, requiring more simplistic methodologies. Indeed, the most sophisticated methodology under the market risk FRTB rules is the internal model approach (IMA), with a standardised approach (SA) being a simpler methodology. However, for CVA, there is no IMA, and the standardised approach (SA-CVA) is the most sophisticated choice, with a less complex basic approach (BA-CVA) being the alternative.

The first obvious problem with the separate treatment of market risk and CVA-related capital requirements is that they cannot offset one another. It is not uncommon that a CVA desk may naturally have CVA-related market risk that offsets market risk in the TB of the bank (e.g. the TB has a negative sensitivity to interest rates, and the CVA desk has a positive sensitivity). However, the regulatory capital requirements of such a bank would not recognise this offset and would double-count the capital requirement. Since banks hedge their market risk actively and their residual risk is second order, whereas CVA desks often have first-order outright risk due to the hedging challenges, this point may not be seen to be particularly problematic by most banks.

A second more difficult point regarding the separate treatment revolves around eligible hedges (Figure 21.9). The CVA capital framework incentivises active management of CVA by giving capital relief for CVA hedges that are captured by the methodology and are, therefore, eligible. Such hedges do not need to be captured within the market risk framework, and in the event that they are risk increasing – and not risk reducing – this may lead to a larger CVA capital charge. Suppose, as shown in Figure 21.9, that an uncollateralised transaction is hedged back to back with a collateralised transaction. Note that the market risk capital framework may see no net market risk (if the same discount rates are used). There is, of course, xVA associated with this situation. However, any xVA market risk hedges are not recognised in the CVA capital charge and must, therefore, be recognised under the standard market risk rules, where they will increase capital. Non-eligible hedges must be treated as TB instruments and captured within the market risk capital rules.

Figure 21.9 Illustration of the impact of eligible and non-eligible xVA hedges.

Table 21.9 gives an overview of the eligibility of xVA hedges under the current and future regulatory regimes and for the different capital methodologies (discussed previously in Section 13.3). The first point to note is that all non-CVA hedges are ineligible, since they have no associated regulatory capital requirements. In the event that xVAs are captured naturally within the base value via a discounting approach (e.g. ColVA, discussed in Section 16.2.1, or symmetric FVA, as discussed in Section 18.2.4), then this will not raise any issue since the value and hedges will all be reflected within the TB. However, hedges for specific components such as FVA will be ineligible.

Secondly, not all CVA hedges are eligible for capital relief. Under the current rules and future BA-CVA methodology, the capital charge for CVA volatility is driven solely by credit spread movements and, consequently, only credit hedges can achieve capital relief; only single-name and index CDS hedges are eligible, with all other hedges ( including proxy single-name CDSs) being ineligible.¹³ Single-name CDS hedges are obviously most effective, as they can reduce both CCR capital and CVA capital (Section 13.3.6). Under the future SA-CVA methodology, most hedges will be eligible, except those not included in the IMA for market risk under the FRTB (e.g. tranched credit derivatives).

Table 21.9 Eligibility of xVA hedges under current and future CVA regulatory capital rules.

	Current regulation			Future regulation (FRTB-CVA)
	Standardised	Advanced	Ineligible	BA-CVA	SA-CVA	Ineligible
CVA	Single-name CDS		Proxy single-name CDS	Single-name CDS (including proxies)	Most CVA hedges	Non-IMA hedges
	Index CDS		All other market risk hedges	Index CDS
Other xVA	N/A		All	N/A		All

The non-capitalisation on other (non-CVA) xVA hedges has the problem that, since there is no xVA-specific capital requirement, the overall capital requirements of a bank may be over- or understated depending on whether the xVA hedges reduce or increase the TB market risk of the bank. There is, therefore, a strong argument for allowing banks to more properly reflect the risk in this situation by, for example, capturing xVA sensitivities alongside hedges in their market risk capital. Whilst there is no general Basel guidance on this point, local regulators are starting to address this.¹⁴ This also means that the xVA desk may need to separate some hedges (e.g. interest rate) into CVA and FVA components so as to properly recognise capital relief. The hedging of accounting xVA (e.g. CVA and FVA) may appear to over- or underhedge accounting CVA depending on the behaviour of non-CVA. For example, FBA or DVA will reduce the size of vega hedges but increase delta hedges for accounting xVA terms (see Table 21.4 and related discussion).

For ineligible CVA hedges, and given that there is a specific capital charge, the problem is mainly related to over- and not undercapitalisation, where ineligible CVA hedges consume TB capital rather than reducing CVA capital. The European Banking Authority (EBA 2015b) reports that banks are sensitive to these capital-consuming hedges, with interest rate swaps, FX forwards, interest rate options, and cross-currency swaps being mentioned in particular. This conservative treatment may not be as concerning for regulators, but has been criticised by banks for creating the incentive not to hedge CVA risks. In response to this, US and Canadian regulators have moved to exempt CVA-related market risk hedges and thus prevent them from at least adding to capital (although they would still provide no capital relief). Such a route requires a qualitative demonstration that these hedges are risk reducing and not risk increasing. A more robust approach is to allow CVA sensitivities to be included in the market risk capital calculation, which some local regulators have allowed banks to do.

A better solution to the above problem would be to integrate the CVA capital charge methodology – together with other xVA terms as appropriate – into the market risk methodology, but this is currently viewed by regulators as being too complicated, and this is not a provision of even future regulatory rules.

Finally, recall that even eligible hedges may not provide optimal capital relief, as discussed in Section 13.5.3. The relative conservatism of methodologies such as SA-CCR means that a CVA hedge for accounting volatility would typically be seen as being an underhedge from a regulatory capital perspective. In contrast, choosing the optimum hedge for regulatory capital minimisation would overhedge the accounting volatility. Whilst the future SA-CVA should align regulatory and accounting CVA (if not xVA), it still poses problems with index hedges, as previously shown in Figure 13.20.

21.2.10 Pushing xVA into Base Value

Given the problems with xVA adjustments such as those related to the capital (Figure 21.9), there may be an incentive to try and characterise xVA as much as possible as being within the base value (Equation 5.1), where it may be more straightforward to deal with from a quantification and management point of view. As noted previously (Section 5.4.7), this can only be easily done for situations where xVA is a simple, transaction-level quantity, just requiring, for example, a change in discounting. Whilst xVA cannot usually be generally represented like this, except in special cases, there is a potential hybrid approach which involves capturing most of the xVA within the base value with a small, more complex adjustment.

For example, with respect to asymmetric FVA, which is a portfolio-level quantity (Section 18.3.2), it could be broken down into the sum of:

• a symmetric FVA calculated using cost of funds discounting (Section 18.2.4); and
• an adjustment reflecting the difference between the real FVA and the above.

The symmetric FVA component would be captured within the base value and would naturally net with FVA hedges from a market risk capital perspective (Figure 21.9). The adjustment would reflect aspects such as asymmetries and thresholds. This approach would create additional operational costs in capturing FVA via two different calculations, ensuring consistency (e.g. in terms of trade population) and aggregation (e.g. consolidation of risk numbers). However, it would offer strong numerical efficiency, as only the adjustment component would need to be captured via simulation, and this may also largely retain the benefit of the market risk treatment of hedges. This approach may be advantageous for a bank that wants to use asymmetric FVA but believes that the adjustment term would generally be small. This would be the case for an ‘asset-heavy’ portfolio (Figure 18.11).

21.3 OPERATION OF AN XVA DESK

21.3.1 Interaction with a Treasury

From a CVA-ownership perspective, an xVA desk can potentially work in isolation and manage risk by executing internal or external market and credit risk hedges. However, the same is not true of margin, funding, and capital components. The management and transfer pricing of these components in a bank is usually managed by a central ‘treasury’ unit, and so the way in which this unit passes on costs is clearly key to defining the underlying adjustments.

It is sub-optimal for an individual desk to manage its funding, and it is better to manage this centrally on the xVA desk, which may have access to treasury funding on a portfolio basis (see Figure 18.1). The xVA desk then becomes responsible for charging components such as inception FVA in line with the FTP costs defined by the treasury. The time decay (Section 21.1.3) that the xVA desk accrues should then act as a profit, offsetting the charges from the treasury. The associated xVA volatility has two main components:

• Market risk. This can be hedged alongside the analogous CVA market risk volatility, although there will be capital implications, as discussed in Section 21.2.9.
• Funding risk. This probably cannot be hedged. If the treasury increases (reduces) the cost of funding via the FTP curve, then this may create losses (profits) for the xVA desk.

From the point of view of managing funding risk, there are different ways in which the xVA desk can interact with the treasury:

• Accrual based. In this scenario, funding would be charged on the current borrowing on a periodic basis. Whilst the xVA desk is able to hedge the market risk, it carries the risk of changes in the funding cost, and it is not possible to hedge the treasury-determined FTP or term liquidity premium (TLP) curve. An implication of this is that a given point on the curve used to calculate FVA should represent the expected cost of funding that would be charged at that point in the future. The treasury would know the current funding requirement, but may not have visibility over future needs.
• Term based. In this scenario, funding would be charged across the whole term structure of the funding profile. This creates an alignment between the curve used to calculate FVA and the FTP curve of the treasury. It also means that the derivatives funding could be a more integrated part of the asset-liability management (ALM) process. However, it does mean that the treasury is providing funding on the basis of expected cash and margin flows, and there could be large changes in the funding profile which may have led to only small changes in the accrual-based approach (however, from an ALM point of view, it may be important to capture this).

As discussed in Section 18.3.5, there is also the important question of the symmetry of funding. Whilst funding will always be done at a certain level, with costs and benefits naturally netting and offsetting one other, there is the question of symmetry at the portfolio level, with the choices being:

• Symmetric. Here, the treasury would consider funding costs and benefits to be equal and opposite (on a net basis), and so there would be a return when the xVA desk lends cash (overall), which would also be remunerated at the same rate as when the xVA desk is borrowing to the same term. The advantage of this approach is that it is very simple, and every trade can be considered in isolation (symmetric FVA is discussed in Section 18.2). The disadvantage of this approach is that the treasury may struggle to monetise funding benefits unless they are offsetting funding costs. When borrowing against net derivatives assets, the treasury may naturally see this – prudently – as a term funding cost. However, net derivative liabilities may be seen as an unstable source of funding and, therefore, difficult to monetise at a similar rate. Furthermore, charging symmetrically is antithetical to the net stable funding ratio (NSFR) (Section 4.3.4), which charges 100% required stable funding for net derivatives assets but gives 0% available stable funding for net liabilities (and, indeed, charges for a percentage of such liabilities). Depending on how granular a bank decides to be over NSFR costs and to what extent its business and funding strategy is naturally NSFR compliant, this may be an important consideration.
• Asymmetric. In this setting, the treasury would remunerate derivatives assets and liabilities differently, paying a lower return on the latter. This makes the calculation of funding costs by the xVA desk much harder, as an accurate consideration can only be made at the portfolio level. However, it more closely aligns with a conservative funding strategy, which would term fund derivatives assets but not term lend against derivatives liabilities. Such a strategy is also more consistent with the NSFR rules. In an asymmetric funding regime, there is also a question of defining the underlying portfolio to be funded and whether, within this portfolio, there are offsets from different requirements, such as variation margin received and initial margin posted. It is also important not to create the wrong incentives – for example, to novate into ITM portfolios as a way to lend to derivatives counterparties rather than the internal treasury of the bank.

There is also a need for margin optimisation in terms of aspects such as the ‘cheapest-to-deliver’ option (Section 16.2.3) and the pool of high-quality liquid assets (HQLAs) (Section 4.3.2). This optimisation can be owned by either the xVA desk or the treasury. It is clearly important to align this with pricing so that the remuneration of the margin posted/received is in line with the remuneration rate used in discounting. If this is not the case, then there will be accrual losses faced by the bank. This suggests that both pricing and ownership of margin optimisation should be done by the xVA desk. However, it is important to bear in mind that the treasury will also have its own derivatives transactions (for hedging the interest rate and FX risk in its borrowing and lending arrangements) that will have margining implications.

21.3.2 Capital

Whilst capital is a form of funding, it is not managed in most banks in a similar way to funding from FVA, as discussed in 19.3.1. This is probably in large part due to the fact that derivatives are marked-to-market and any profits are recognised on day one, which is beneficial to shareholders and employees, who benefit from such profits in the form of dividends and bonuses. Although deferring such profits may provide long-term benefits and incentives, it is not of interest to investors, such as shareholders, with relatively short-term views.

Whilst xVA desks have started to assume responsibility for charging KVA, this may be seen as a formalisation of setting ROC hurdles, which has long been a practice within banks. In order to understand whether practices might change in this respect, we consider three possible scenarios with respect to KVA pricing and management, which are roughly in line with the three proposals in Section 19.3.2. Consider that a five-year transaction has KVA of 50 units (in excess of any other xVA cost). Broadly, there are three ways in which this KVA could be released as profit, as illustrated in Table 21.10.

Table 21.10 Different approaches for releasing a KVA profit of 50 units on a five-year transaction.

			Method C
	Method A	Method B	Scenario 1	Scenario 2
Year 1	50	10	30	5
Year 2	0	10	50	3
Year 3	0	10	40	2
Year 4	0	10	20	1
Year 5	0	10	10	0
Total	50	50	150	11

Figure 21.10 P&L for KVA hedges in the three scenarios shown in Figure 19.11.

Method A is – more or less – the approach still used at most banks, since there is no accounting adjustment for KVA and so any capital charge will automatically be released as profit immediately. This has obvious problems, such as creating the wrong incentives, as illustrated previously in Figure 19.8. Method B releases KVA in some defined way, which has the advantage of aligning revenue more with capital and risk. However, the arbitrary nature of the release is not in line with the definition of KVA and so would need to form some accounting adjustment, such as retained earnings. Method C is a full KVA approach, with the profit being driven by the time decay of the KVA term, together with the P&L from any associated hedges. The reason that this approach does not return a total profit of 50 is due to the KVA hedging.

A more real example will be provided by returning to the previous case in Figure 19.11, which considered the change in KVA in different market scenarios. Figure 21.10 shows the P&L for the KVA hedges in the three scenarios considered previously. In scenarios when the derivatives move OTM (ITM), there will be losses (gains) on KVA hedges so as to produce the desired ROC. The 95% and 5% potential future exposure (PFE) examples are roughly in line with scenarios 1 and 2 under method C in Table 21.10.

Method A in Table 21.10 locks in the P&L of the transaction but shows a variable ROC over the lifetime (as previously illustrated in Figure 19.13). Method C locks in the ROC and shows a variable P&L (including KVA hedges). Method B achieves neither and is probably more of an intermediate step towards method C and active KVA management.

Whether and how quickly banks might transition towards method C and the management of KVA in line with other valuation adjustments such as CVA and FVA remains to be seen.

21.3.3 Systems and Quantification

The quantification of xVA is a challenging task in terms of architecture and computational requirements due to a number of aspects, such as:

• the underlying data requirements;
• the high dimensionality and non-linearities;
• the need for real-time calculations;
• data aggregation at different levels (trade, counterparty, full portfolio); and
• the requirement for sensitivities and scenario analysis.

This has led banks, other financial institutions, and software vendors to invest heavily in xVA systems and infrastructure. The building blocks of an xVA system are:

• Data. Most institutions have multiple systems for legal, trade, market, and historical data. Data collection and storage is substantial and must be obtained from various front-office trading and back-office systems and external sources. Having a ‘golden source’ of market data, counterparty data, trade data, netting information, and margin terms can be useful. Data requirements cover the following aspects:
  • trade population (including hedges);
  • legal entities;
  • netting agreements;
  • margin agreements;
  • market data;
  • historical data;
  • credit ratings, default probabilities, and LGDs (internal and external); and
  • credit spreads.
• Simulation engines. The heart of the xVA calculation is typically a Monte Carlo simulation that must be able to efficiently generate the evolution of all relevant risk factors with an underlying correlation structure. It may also be necessary to generate additional scenarios, maintaining ‘scenario consistency’ – for example, in order to run an intraday calculation without rerunning an entire netting set or portfolio.
• Revaluation functionality. After generating a large number of scenarios, it is necessary to revalue every single transaction in each scenario. Whilst most common products are fast to value, the scale is huge, with potentially trillions of valuation calls required. Valuations can be speeded up significantly by applying both financial and computational optimisations.
• Collateralisation. It must be possible to track existing margin, whether this is in cash or other securities, calculate the projected future margin in each simulation, and calculate the impact of this (together with current margin) on exposure. This must include impacts such as segregation, and must also be able to simulate future initial margin.
• Reporting. Reporting functionality such as xVA for financial statements, limit breaches, P&L explain, and scenario analysis should be available.
• Greeks. Hedging and P&L explain require Greeks for all relevant risk factors, covering both market and credit risk. Due to the number of Greeks, calculation by finite-difference (‘bump-and-run’) methods may be extremely time consuming.
• Scenario analysis and stress-testing tools. The ability to run scenarios to test the behaviour of xVA in extreme scenarios.

It is inevitable that some optimisation will be required in order to manage the volume of calculations and likely requirements for near real-time xVA. Such optimisations can be in relation to hardware, software, or numerical methods. Typical methods used are:

• Pre-calculations. Pre-calculations on the existing portfolio can speed up pre-deal pricing of xVA. This does, however, require significant data storage and rapid retrieval, and will probably become less common as processing power and other optimisations become more common.
• Numerical optimisations. Relatively straightforward numerical approximations such as random number generation (low discrepancy sequences and using the same random numbers each day to avoid unnecessary noise) and cash flows bucketing (Section 15.3.2).
• Fast revaluations. Methods that speed up the revaluation of the portfolio, which is generally the major bottleneck of the xVA calculation. See, for example, Laris and Ruiz (2018) and Ferguson and Green (2018).
• American Monte Carlo. As mentioned in Section 15.3.2, American Monte Carlo (AMC) is an approach to optimisation quite commonly used in the industry (e.g. Cesari et al. 2009). This produces speed improvement, since the pricing overhead is absorbed within the simulation via regressing with respect to the relevant market variables. There is significant implementation work involved in AMC, and the specification of the regressions is not trivial. AMC can be particularly advantageous for portfolios with significant numbers of exotics (especially those with embedded Bermudan-style optionality).
• Adjoint algorithmic differentiation (AAD). One of the more recent but increasingly popular applications to xVA, AAD is specific to the generation of sensitivities (Greeks) and requires significant implementation and architecture design. However, AAD allows the calculation of an arbitrary number of Greeks at a cost that is a small fixed multiple, often claimed to be in the region of four (see Capriotti and Lee 2014). For large portfolios where the number of required sensitivities is large (potentially in the hundreds), the additional overhead in implementing AAD is possibly worthwhile. However, it is important to bear in mind that AAD will probably result in all xVA calculations being slower, even when sensitivities are not required. It should be considered that all future developments of the xVA system (e.g. adding new products) will need to be done in an AAD-compliant way.
• Processors. The use of parallel processing involves splitting xVA computations across different processors. However, it is important to balance splitting calculations evenly and avoiding repeating calculations (such as calibrations). Additionally, some implementations have relied on more specialised hardware solutions such as graphics processing units (GPUs), which offer potential speed-up of traditional CPUs but with more implementation effort and additional expense.

Different xVA calculations also require varying amounts of complexity. First-generation xVAs such as CVA and FVA require only the calculation of the portfolio value in each scenario. However, more recent terms such as KVA and MVA often require more complex calculations, such as portfolio sensitivities, in each scenario. This additional complexity makes methods such as AMC and AAD even more important for dealing with computation demands.

Within an institution, there may be a number of different areas with xVA-related requirements, notably:

• Front-office. The calculation of xVA for pricing purposes.
• Finance. Daily valuation of transactions and the representation of this both internally for management purposes and externally for financial reporting (accounting) purposes.
• Risk and regulatory. The measurement of xVA against risk limits and the calculation of regulatory capital.

In an ideal world, the above would be addressed via a single holistic solution but, in practice, it is not uncommon to see separate implementations. Given the general convergence of standards and regulations such as SA-CVA (where accounting and regulatory CVA must be aligned), it would seem more likely that a greater amount of systems unification would occur. This is not always completely optimal (e.g. it is desirable to be able to modify front-office systems rapidly with a fast release cycle, but this is not possible when they have a strong regulatory role).

One area that may remain distinct is for banks with an internal model method (IMM) approval (Section 13.4.5). Such implementations calculate metrics such as PFE and effective EPE (EEPE), often use historical calibrations (including stress periods), and require backtesting. However, a few banks have aligned their CVA and IMM implementations (see Section 15.3.3).

Over the past decade, a number of software vendors have invested significantly in the development of counterparty risk and xVA solutions. Some of the significant vendors in this respect are CompatibL, Fincad, IBM (previously known as Algorithmics), IHS Markit (previously known as QuIC), Murex, Numerix, Pricing Partners, Quantifi, FIS Global (previously SunGard), and TriOptima. Not surprisingly, vendor solutions differ significantly, with two clear axes of differentiation being:

• Sophistication. Some vendors offer cheaper and less sophisticated solutions, whereas others offer greater sophistication at a higher cost.
• Application. Vendors are more focused on a particular implementation (e.g. front-office or risk).

Large banks have tended to build xVA systems internally, driven by economies of scale and the desire to maintain full control over the framework and its development. Smaller banks and financial institutions have tended to use external vendor solutions that may offer time savings. Additionally, in-house builds are generally preferred for more bespoke front-office xVA implementations, with vendor implementations being more common for risk and regulatory functionality.

An internally-developed solution can offer greater control over the development process and future flexibility. On the other hand, internal development from a limited starting point can be a substantial undertaking and may require significant time and resources, especially with respect to aspects such as achieving a satisfactory coverage of the many underlying products. A vendor system may offer a faster implementation route without the need to ‘reinvent the wheel’.

The following is a list of the broad considerations when choosing a vendor-based xVA solution:

• modelling:
  • availability of different models and calibration across each asset class;
  • modelling of collateralisation;
  • treatment of resets and break clauses; and
  • treatment of specific and general WWR.
• calculation:
  • methodology for calculating xVA in real time;
  • approach for exotic payoffs and/or path dependency where the computation time for valuation is prohibitive (e.g. AMC);
  • what sensitivities can be calculated and how the calculation is implemented (e.g. finite difference, AAD);
  • whether a P&L explain is implemented;
  • ability to calculate terms such as MVA and KVA, and include initial margin in the calculation of CVA and KVA;
  • approach for scenario analysis and stress testing; and
  • speed and recommended hardware requirements for the portfolio in question.
• data and implementation:
  • approaches for data capture (market, legal) and data maintained by vendor (e.g. market conventions and calendars);
  • product coverage and how non-standard payoffs can be represented (e.g. generic scripting language); and
  • reporting functionality and feeding of downstream systems (e.g. accounting, general ledger).
• general:
  • other institutions that use the system and for what purposes;
  • cost structure (upfront, costs per licence, computing services, consultants cost per day); and
  • likely implementation time.

Not surprisingly, any incumbent vendor solutions for other purposes (risk, back-office) are also a major consideration in most cases.

21.3.4 xVA Optimisation

In addition to pricing and management, optimisation of xVA has been an important topic for banks. Optimisation of xVA in the interdealer market is active, with traditional portfolio compression (Section 6.2.4) and more advanced approaches seeking to reduce new components, such as bilateral initial margin. This is an area mainly limited by innovation, as all participants have similar goals and can benefit mutually.

Optimisation with respect to end users is more difficult for banks as the goals are not aligned and can only be agreed via a trade-off of benefits, such as one party making a cash payment. Some uncollateralised end users have experienced problems when hedging transactions that have moved heavily against them. Not only does this increase a bank's xVAs, but it may also cause credit limit breaches and lead to a bank being unable to transact and provide hedges any more. One potential solution in this situation is to ‘restrike’ transactions, so they are less ITM for the bank. This is similar at the outset to the effect of entering into a margin agreement, but without the uncertainty of future margin requirements and related liquidity costs. Basic, one-off optimisations such as restrikes can reduce xVA for an ITM portfolio and do not require any ongoing changes to contractual terms. Beyond this, changes to margining agreements can reduce xVA, which is advantageous for the bank but costly for the client. However, some clients have agreed to this as a means of achieving better prices and/or monetising gains from moving legacy portfolios. Moving beyond this, moving voluntarily to bilateral margining or central clearing will make xVA costs for clients smaller at the expense of initial margin posting.

Not surprisingly, a number of major end users of derivatives have actively considered the pros and cons of changing the way in which they transact, usually in the form of changing the level of collateralisation. For example, Danmarks Nationalbank (2015) gives an account of a move to two-way collateralisation and its costs and benefits. Nakashima et al. (2016) make a similar analysis and state that:

In the case of Canada, our analysis shows that an asymmetric CSA [one-way margin agreement] is unlikely to be the most desirable margining structure, because it carries the highest risk charges and pass-through of bank dealer costs. The symmetric variation margin scenarios [two-way margin agreement] have lower risk and, with rehypothecation, result in lower pass-through of both the bank dealers' funding costs and Basel capital charges. The analysis appears to be consistent with the practices of certain OIs [official institutions], some of which have moved to more symmetric structures.

There are also potential regulatory arbitrages that arise from the above, where a bank may lend money to an end user in order for them to restrike their derivative portfolio. This can be seen as converting an ITM derivative portfolio into an at-the-money (ATM) derivative portfolio plus a loan. This practice is incentivised by regulation, since a bank does not experience anything analogous to the CVA capital charge for a loan, and so essentially can reduce KVA without changing the real economic risk it faces. The EBA (2015b) comments on this as follows:¹⁵

From the point of view of the bank, there is a transformation of counterparty risk (coming from the derivatives) into credit risk (coming from the loan). But assuming the loan will roll over until the maturity of the derivative contracts, the overall level of risk has not changed. However, the net level of capital has.

Many end users have not traditionally posted margin due to the liquidity implications. For example, the EBA (2015b) notes:

It is however more difficult to convince counterparties without collateral [margin] agreements to operate on a collateralised basis because most of them do not have the treasury function to exchange collateral on a frequent basis.

Nevertheless, in recent years, a number of parties have been under pressure to move towards transacting under two-way CSAs, driven by the large costs experienced by banks for uncollateralised transactions. Before entering into a margin arrangement, it would naturally be important to make an analysis of the funding implications that may arise, and to put in place a ‘liquidity buffer’ to mitigate the risk of having to post a substantial amount of liquid margin in a relatively short space of time. In sizing this liquidity buffer, there are subjective questions, such as what time horizon should be considered and what form of cash and/or securities should make up the buffer. As an example of the type of analysis that might be used, Figure 21.11 shows the worst-case quarterly margin outflow for a client's portfolio, compared to ENE and PFE. Note that, with a zero threshold assumed, ENE and PFE represent approximately the expected and unexpected (to a confidence level) cumulative amount of margin posted. For parties with low costs of funding, such as sovereigns, supranationals, and agencies (SSAs), even funding a conservatively-large liquidity buffer may be optimal compared to paying the xVA costs of banks.

Figure 21.11 Worst-case (99% quantile) quarterly outflow for a two-way margin agreement with zero threshold, compared to ENE and PFE.

One feature of the clearing mandate and bilateral margin rules are that they only impact future and not existing transactions. However, the question arises as to whether or not it may be optimal to ‘backload’ legacy transactions to a CCP and voluntarily post initial margin against bilateral transactions that were transacted before the bilateral rules, or which are within the specified €50m threshold. It may be that certain users considering posting margin actually consider such routes, rather than the middle ground of bilateral trades without initial margin.¹⁶

A final aspect of optimisation is to correctly account for any overlaps or double-counting within the hierarchy of xVA terms. Whilst assessing the true impact of a new derivative on the balance sheet of a bank is very hard to do, it can be better approximated by assessing the impact of overlaps. For example, Albanese et al. (2015) argue that banks use a lower ‘blended rate’ to account implicitly for the possibility of using capital for funding purposes and, therefore, to avoid double-counting.

NOTES

1. 1 International Association of Credit Portfolio Managers (IACPM) Survey 2018.
2. 2 Due to hedging costs.
3. 3 This may only be relevant for US banks. Non-US banks may have a TOTUS (trading outside the United States) exemption for their xVA desks.
4. 4 Usually defined in terms of a metric such as the delta of the transaction, which combines size and maturity as the key determinants.
5. 5 Except implicitly because the name happened to be referenced in the index.
6. 6 Sherif, N. (2015). CDS de-correlation a threat to CVA hedging, traders warn. Risk (3 September). www.risk.net.
7. 7 For example, only updating valuations for trades which are sensitive to a given risk factor change. This can be implemented algorithmically (e.g. if a valuation does not change in a given simulation, then other instances in other simulations are not revalued) or via a mapping of each trade to the dependent market data.
8. 8 AAD uses the chain rule to compute derivatives automatically within a computer algorithm. It has been implemented by some banks to provide an efficient calculation of many xVA Greeks at a fixed cost (see Section 21.3.3).
9. 9 Sherif, N. (2016). CVA desks suffer Brexit double whammy. Risk (30 June). www.risk.net.
10. 10 Note that this should reference the counterparty directly, but can include protection via being long an index, where the counterparty is one of the reference names.
11. 11
12. 12 Depending on calculation assumptions, such as whether survival probabilities are included, other xVA terms can have a small sensitivity to credit spread changes.
13. 13 Some more complex credit hedges such as swaptions are allowable, although they are generally very illiquid. Becker, L. (2014). CVA hedge losses prompt focus on swaptions and guarantees. Risk (28 October). www.risk.net.
14. 14 APRA (2019). Derivative valuation adjustments - frequently asked questions. Australian Prudential Regulatory Authority (8 May). www.apra.gov.au.
15. 15 Note that the comment on the loan rolling is relevant if the end user is entering into a margin agreement, rather than just restriking the derivative.
16. 16 Stafford, P. (2017). Dutch debt agency looks at derivatives clearing. Financial Times (23 June). www.ft.com.