3
Counterparty Risk and Beyond

3.1 COUNTERPARTY RISK

Counterparty credit risk (often known just as counterparty risk) is the risk that the entity with whom one has entered into a financial contract (the counterparty to the contract) will fail to fulfil their side of the contractual agreement (e.g. they default).

Counterparty risk is primarily associated with the following situation:

over-the-counter (OTC) derivatives;
bilaterally cleared; and
uncollateralised.

However, it is also important to consider the following cases, where some form of margining or collateralisation is always present:¹

exchange-traded derivatives (which are always centrally cleared and typically margined on a daily basis);
securities financing transaction (e.g. repos), which are margined on a daily basis and sometimes centrally cleared;
centrally-cleared OTC derivatives, which are margined on a daily basis; and
collateralised OTC derivatives, where margining is reflected via some bespoke collateral agreement.

The above cases have less counterparty risk due to a combination of collateralisation, central clearing, and maturity dates (for example, exchange-traded derivatives and securities financing transactions are typically short-dated). Whilst some of the above cases may be thought to have relatively minor counterparty risks, this may relate to a large underlying position. The obvious example of this is centrally-cleared OTC derivatives which are generally believed to represent a small counterparty risk, but where the notional position of a bank to a central counterparty could be extremely large.

3.1.1 Counterparty Risk Versus Lending Risk

Traditionally, credit risk can generally be thought of as a lending risk. One party owes an amount to another party and may fail to pay some or all of this due to insolvency. This can apply to loans, bonds, mortgages, credit cards, and so on. Lending risk is characterised by two key aspects:

The notional amount at risk at any time during the lending period is usually known with a degree of certainty. Market variables such as interest rates will typically create only moderate uncertainty over the amount owed. For example, in buying a bond, the amount at risk for the life of the bond is close to par. A repayment mortgage will amortise over time (the notional drops due to the repayments), but one can predict with good accuracy the outstanding balance at some future date. A loan or credit card may have a certain maximum usage facility, which may reasonably be assumed fully drawn for the purpose of credit risk.²
Only one party takes lending risk. A bondholder takes considerable credit risk, but an issuer of a bond does not face a loss if the buyer of the bond defaults.³

With counterparty risk, as with all credit risk, the cause of a loss is the obligor being unable or unwilling to meet contractual obligations. However, two aspects differentiate contracts with counterparty risk from traditional credit risk:

The value of the contract in the future is uncertain, in most cases significantly so. The value of a derivative at a potential default date will be the net value of all future cash flows required under that contract. This future value can be positive or negative and is typically highly uncertain (as seen from today).
Since the value of the contract can be positive or negative, counterparty risk is typically bilateral. In other words, in a derivatives transaction, each counterparty has risk to the other. Note that this counterparty risk may be asymmetric (if the transaction has an asymmetric profile,⁴ or if the counterparties have significantly different credit quality and/or margining/collateralisation terms).⁵

3.1.2 Settlement, Pre-settlement, and Margin Period of Risk

A derivatives portfolio contains a number of settlements equal to multiples of the total number of transactions (for example, a swap contract will have a number of settlement dates as cashflows are exchanged periodically). There may also be a contractual exchange of collateral which is partly related to settlements because a cash flow payment may trigger a margin requirement. Historically, this led to the definition of two components covering the risk of default of the counterparty prior to expiration (settlement) of the contract and the risk of a counterparty default during the settlement process.

Pre-settlement risk. This is the risk that a counterparty will default prior to the final settlement of the transaction. This is what counterparty risk usually refers to, and it is rarely referred to as pre-settlement risk nowadays (which somewhat understates its importance).
Settlement risk. This arises at settlement times (and is often especially relevant at the maturity date) due to timing differences between when each party performs its obligations under the contract.

The difference between pre-settlement and settlement risk is illustrated in Figure 3.1.

Graph depicts the pre-settlement and settlement risk. — **Figure 3.1** Illustration of pre-settlement and settlement risk. Note that the settlement period is normally short (e.g. hours) but can be much longer in some cases. Also shown is the margin period of risk (MPoR), which is discussed below.

Unlike counterparty risk, settlement risk is characterised by a very large exposure, potentially 100% of the notional of the transaction. Whilst settlement risk gives rise to much larger exposures, default prior to the expiration of the contract is substantially more likely than default at the settlement date. However, settlement risk can be more complex when there is a substantial delivery period (for example, a commodity contract settled in cash against receiving a physical commodity over a specified time period).

Whilst all derivatives technically have both settlement and pre-settlement risk, the balance between the two will be different depending on the contract. Spot contracts have mainly settlement risk, whilst long-dated OTC derivatives have mainly pre-settlement (counterparty) risk. Furthermore, various types of netting (see Chapter 6) provide mitigation against settlement and pre-settlement risks. From now on, the term ‘counterparty risk’ will be used instead of ‘pre-settlement risk’.

Settlement risk typically occurs for only a small amount of time (often just days or even hours). It is therefore clearly more relevant for shorter maturity transactions such as those that are exchange-traded. Indeed, spot transactions essentially have only settlement risk. In long-dated OTC derivatives, the length of time for the settlement is very short compared to the remaining maturity, although it is important to remember that the exposure for settlement risk can be significantly higher, as illustrated in the FX example above.

To measure settlement risk to a reasonable degree of accuracy would mean considering the contractual payment dates, the time zones involved, and the time it takes for the bank to perform its reconciliations across accounts in different currencies. Any failed trades should also continue to count against settlement exposure until the trade actually settles. Institutions typically set separate settlement risk limits and measure exposure against this limit rather than including settlement risk in the assessment of counterparty risk. It may be possible to mitigate settlement risk, for example, by insisting on receiving cash before transferring securities.

Settlement risk is a major consideration in FX markets, where the settlement of a contract involves payment of one currency against receiving the other. Most FX now goes through continuous linked settlement (CLS),⁶ and most securities settle using delivery versus payment (DVP),⁷ but there are exceptions such as cross-currency swaps, and settlement risk should be recognised in such cases.

Another important and related component is the margin period of risk (MPoR). This refers to the risk horizon when collateralised/margined (due to the imperfect nature of this process). The standard assumption used for this value in collateralised bilateral OTC derivatives is 10 business days. Centrally-cleared OTC derivatives (which are subject to daily margining) have a shorter value of five days (see Section 9.1.2). This reduces counterparty risk because the MPoR will typically be significantly shorter than the remaining maturity of the portfolio. However, collateralised/margined portfolios still have material counterparty risk. Furthermore, there is an important interaction between settlement risk and the counterparty risk on a collateralised portfolio since each (net) settlement will change the underlying value of the portfolio. If this valuation change is positive, then the portfolio value increases, which will be uncollateralised until collateral can be received. This, therefore, can intuitively create a ‘collateral spike’ for the duration of the MPoR (Figure 3.2). If the cash flow and collateral payments were netted, then this would not be a problem. Whilst this netting is common in exchange-traded markets, it does not occur in OTC derivatives markets, where historically the collateral has not needed to be paid in cash.

Graph depicts the spike in exposure created by a cash flow payment and subsequent delay before collateral is received. — **Figure 3.2** Illustration of the spike in exposure created by a cash flow payment and subsequent delay before collateral is received (or the derivative is closed out in the event of a default).

Note that, by convention, the above risk is typically characterised as counterparty risk even though it has features which are similar to settlement risk.

Certain features of margining/collateralisation can also create settlement risk. For example, central counterparties typically require margin to be posted in cash in each relevant currency. This creates currency silos across a multicurrency portfolio, which can lead to more settlement risk and associated liquidity problems, as parties have to post and receive large cash payments in different currencies.

3.1.3 Mitigating Counterparty Risk

There are a number of ways of mitigating counterparty risk. Some are relatively simple contractual risk mitigants, whilst other methods are more complex and costly to implement. Obviously no risk mitigant is perfect, and there will always be some residual counterparty risk, however small. Furthermore, quantifying this residual risk may be more complex and subjective than the counterparty risk itself. In addition to the residual counterparty risk, it is important to keep in mind that risk mitigants do not remove counterparty risk per se, but instead convert it into other forms of financial risk, some obvious examples being:

Netting. Netting allows components such as cash flows, values, and margin or collateral payments to be offset across a given portfolio. There are a number of forms of netting, such as cash flow netting, close-out netting, and multilateral trade compression, which may be applied bilaterally or multilaterally, as explained in more detail in Section 6.2.4. However, netting creates legal risk in cases where a netting agreement cannot be legally enforced in a particular jurisdiction.
Collateralisation. Collateral or margin agreements (Section 7.3) specify the contractual posting of cash or securities against mark-to-market (MTM) losses. Margining terms are similar but are usually associated with a cash settlement or posting. There is still a residual market risk since exposure exists in the time taken to receive the relevant collateral amount (the MPoR defined in Section 3.1.2). Furthermore, taking collateral to minimise counterparty risk creates operational risk due to the necessary logistics involved, and leads to liquidity risk since the posting of collateral needs to be funded, and collateral itself may have price and FX volatility. Aspects such as rehypothecation (reuse) and segregation of collateral are important considerations here. Taking certain types of collateral – even cash – can create wrong-way risk (Section 17.6.6).
Other contractual clauses. Other features, such as resets or additional termination events (Section 7.1.1), aim to reset MTM values periodically or terminate transactions early. Like margining/collateral, these can create operational and liquidity risks.
Hedging. Hedging counterparty risk with instruments such as credit default swaps (CDSs) aims to protect against potential default events and adverse credit spread movements. Hedging creates operational risk and additional market risk through the MTM volatility of the hedging instruments. Hedging may lead to systemic risk through feedback effects (see the statement from the Bank of England in Section 13.3.6).
Central counterparties (CCPs). CCPs guarantee the performance of transactions cleared through them and aim to be financially safe themselves through the margin and other financial resources they require from their members. CCPs act as intermediaries to centralise counterparty risk between market participants. Whilst offering advantages such as risk reduction and operational efficiencies, they require the centralisation of counterparty risk, significant collateralisation, and mutualisation of losses. They can therefore potentially create operational and liquidity risks, and also systemic risk since the failure of a CCP could amount to a significant systemic disturbance. This is discussed in more detail in Chapter 8.

Mitigation of counterparty risk is a double-edged sword. On the one hand, it may reduce existing counterparty risks and contribute to improving financial market stability. On the other hand, it may lead to a reduction in constraints such as capital requirements and credit limits and therefore lead to a growth in volumes. Indeed, without risk mitigants such as netting and collateralisation, the OTC derivatives market would never have developed to its current size. Furthermore, risk mitigation should really be thought of as risk transfer since new risks and underlying costs are generated.

3.1.4 Product Type

As already mentioned, most counterparty risk arises from bilateral OTC derivatives. In terms of asset classes, Figure 2.5 in Chapter 2 gave a breakdown of the size of this market in notional terms but commented that this could be potentially misleading in terms of defining the magnitude of counterparty risk faced in each asset class.

The above can be seen when looking at the averaged response from banks on their counterparty risk (measured by credit value adjustment, CVA) broken down by asset class in Figure 3.3. Whilst interest rate products make up a significant proportion of the counterparty risk in the market, the important (and sometimes more subtle) contributions from other products must not be underestimated. In particular, FX products have a reasonably large contribution (due to the large volatility of FX rates and potentially long maturity dates, especially of cross-currency swaps) as do CDSs (potentially due to wrong-way risk).

Bar chart depicts the split of CVA by asset class. — **Figure 3.3** Split of CVA by asset class (average across all respondents).

Source: Deloitte/Solum CVA Survey (2013).

Note that the above breakdown contains counterparty risk from OTC derivatives that are collateralised (bilaterally, at least) since, for example, all credit derivatives will be transacted under collateral agreements. It is also important to note that, whilst large global banks have exposure to all asset classes, smaller banks may have more limited exposure (for example, mainly interest rate and some FX products). End users may also have limited exposure: for example, a corporation may use only interest rate and cross-currency swaps.

Most banks do not give a breakdown of their counterparty risk, but one exception is shown in Figure 3.4, which gives a useful decomposition (of CVA) by rating and sector (i.e. counterparty type). The counterparty risk faced with high-quality credits is generally small due to the low default probability. Financial institutions also represent a relatively small part due to relatively good credit quality and the fact that most of these transactions are probably collateralised. The majority of the counterparty risk is faced with respect to medium credit ratings (BBB to A-) and corporates and governments, most of which is likely to be uncollateralised. The reasonably small exposure (given their high default probability) to non-investment-grade counterparties is probably due to a partial reluctance to trade with such entities.

Schematic illustration of an example of CVA breakdown by rating and sector. — **Figure 3.4** Example of CVA breakdown by rating and sector.

Source: Royal Bank of Scotland Annual Report (2016). www.rbs.com.

Over the years, the quantification of counterparty risk has developed, with one aspect being the coverage of different situations. For example, in the past a bank may have focused only on relatively poor credits and uncollateralised counterparties, ignoring the remainder for materiality reasons. This is clearly not the case in Figure 3.4. However, some aspects may receive attention over the coming years, one obvious example being the counterparty risk faced with CCPs.

3.1.5 Credit Limits

To control and quantify counterparty risk, it is first important to recognise that it varies substantially depending on aspects such as the transaction and counterparty in question. In addition, it is important to give the correct benefit arising from the many risk mitigants (such as netting and margining/collateral) that may be relevant. Control of counterparty risk has traditionally been the purpose of credit limits.

However, credit limits only limit counterparty risk and, whilst this is clearly the first line of defence, there is also a need to correctly quantify and ensure that an institution is being correctly compensated for the counterparty risk they take. This is achieved via CVA, which has been used increasingly in recent years as a means of assigning an economic value to the counterparty risk and/or complying with accounting requirements. In some cases, this CVA is actively managed, such as through hedging.

Broadly speaking, there should be three levels to assessing the counterparty risk of a transaction:

Trade level. Incorporating all characteristics of the trade and associated risk factors such as the precise cash flows. This defines the counterparty risk of a trade at a ‘standalone’ level.
Counterparty level. Incorporating the impact of risk mitigants such as netting and margining/collateral for each counterparty (or netting set) individually. This defines the incremental impact a transaction has with respect to the existing portfolio.
Portfolio level. Consideration of the risk to all counterparties, knowing that only a small fraction may default in a given time period. This defines the impact a trade has on the total counterparty risk faced by an institution.

Credit limits (or credit lines) are a traditional tool to control the amount of counterparty risk taken over time. Counterparty risk can be diversified by limiting exposure to any given counterparty, sector, or region. This limit would naturally consider elements such as the underlying credit risk. By trading across a greater number of counterparties, sectors, and regions, an institution is less exposed. Such diversification across counterparties is not always practical due to the specialisation and relationships within an institution. In such cases, exposures can become excessively large and should be, if possible, mitigated by other means.

The basic idea of credit limits is illustrated in Figure 3.5. The idea is to characterise the potential future exposure (PFE) over time and compare this with a pre-determined limit. The PFE represents a bad scenario at a certain statistical confidence level. The credit limit will be set subjectively according to the risk appetite of the institution in question. It may be time-dependent, reflecting the fact that exposures at different times in the future may be considered differently.

Schematic illustration of the use of PFE and credit limits in the control of counterparty risk. — **Figure 3.5** Illustration of the use of PFE and credit limits in the control of counterparty risk.

Note that for simple lending transactions such as loans, the definition of PFE is relatively trivial since it will be approximately equal to the size of the transaction. However, for more complex transactions such as derivatives, the definition is much more complicated and will require quantitative modelling. PFE will be described in more detail in Chapter 11 but, broadly speaking, the following aspects must be accounted for in its quantification:

the transaction(s) in question;
the relevant portfolio being considered (typically credit limits are defined by the counterparty, but sector and regional views may also be used);
the current relevant market variables (e.g. interest rates and volatilities); and
contractual risk mitigants (for example, netting, collateral, and hedges).

Credit limits will often be reduced over time (as shown), effectively favouring short-term over long-term PFE. This is due to the chance that credit quality may deteriorate over a long horizon. Indeed, empirical and market-implied default probabilities for good-quality (investment-grade) institutions tend to increase over time, which suggests the reduction of a credit limit. Note that credit limits should be conditional on non-default before the point in question because the possibility of an earlier default is captured via a limit at a previous time.

Credit limits are typically used to assess trading activity on a dynamic basis. Any transaction activity (new trades, unwinding or restructuring trades) that would breach a credit limit at any point in the future is likely to be refused unless specific approval is given. From this point of view, it is the incremental change in the PFE that is relevant. The incremental PFE is the value after the new transaction is added minus the value before. Due to portfolio effects, this is smaller than the standalone PFE for the transaction in question. Indeed, for risk-reducing trades, the overall impact can be to reduce the portfolio PFE.

Note that limits could be breached for two reasons: due to either a new transaction or market movements. The former case is easily dealt with by refusing transactions that would cause a limit breach (unless special approval is given via an escalation). The latter is more problematic, and banks sometimes have concepts of hard and soft limits; the latter may be breached through market movements (but not new transactions), whereas a breach of the former would require remedial action (e.g. transactions must be unwound or restructured, or hedges must be sourced). For example, a credit limit of $10m (‘soft limit’) might restrict trades that cause an increase in PFE above this value and may allow the PFE to move up to $15m (‘hard limit’) as a result of changes in market conditions. When close to a limit, only risk-reducing transactions may be approved. Due to the directional nature of end users' activity in OTC derivatives, this is often a challenge.⁸

Credit limits allow a consolidated view of exposure with each counterparty and represent the first step in portfolio counterparty risk management. However, they are rather binary in nature, which is problematic. Sometimes a given limit can be fully utilised, preventing transactions that may be more profitable. Banks have sometimes built measures to penalise transactions (requiring them to be more profitable) close to (but not breaching) a limit, but these are generally quite ad hoc.

3.1.6 Credit Value Adjustment

Traditional counterparty risk management via credit limits works in a relatively binary fashion: the incremental risk of a new transaction is of primary importance, and its relative profitability is a secondary consideration. This can lead to the incorrect incentives being given: for example, a transaction with low (high) profitability may be accepted (rejected) because the existing credit limit utilisation is small (large).

CVA represents the actual price of counterparty risk and is, therefore, a step forward since, from an approval point of view, the question becomes whether or not it is profitable once the counterparty risk component has been ‘priced in’. Put another way, CVA directly incorporates the credit risk of the counterparty and so defines a minimum revenue that should be achieved. In some sense, with credit limits, the CVA is either zero (transaction accepted) or infinity (transaction rejected).

Like PFE, an important aspect of CVA is that it is a portfolio-level – specifically counterparty-level – calculation.⁹ CVA should be calculated incrementally by considering the increase (or decrease) in exposure capturing netting effects due to any existing trades with the counterparty. This means that CVA will be additive across different counterparties and does not distinguish between counterparty portfolios that are highly concentrated. Such concentration could arise from a very large exposure with a single counterparty, or exposure across two or more highly-correlated counterparties (e.g. in the same region or sector).

Traditional credit limits and CVA have their own weaknesses. CVA focuses on evaluating counterparty risk at the trade level (incorporating all specific features of the trade) and counterparty level (incorporating risk mitigants). In contrast, credit limits essentially act at the portfolio level by limiting exposures to avoid concentrations. When viewed like this, we see that CVA and credit limits act in a complementary fashion, as illustrated in Figure 3.6. Indeed, CVA encourages minimising the number of trading counterparties since this maximises the benefits of netting, whilst credit limits encourage maximising this number to encourage smaller exposures and diversification. Hence, CVA and credit limits are typically used together as complementary ways to quantify and manage counterparty risk. In practice, this means that the credit risk department in a bank will approve a trade (or not) and then (if approved) the ‘xVA desk’ will price in the CVA component before transacting.

Schematic illustration of the complementary use of CVA and credit limits to manage counterparty risk. — **Figure 3.6** High-level illustration of the complementary use of CVA and credit limits to manage counterparty risk.

3.1.7 What Does CVA Represent?

The price of a financial product can generally be defined in one of two ways:

The price represents an expected value of future cash flows, incorporating some adjustment for the risk being taken (the risk premium). We will call this the actuarial price.
The price is the cost of an associated hedging strategy. This is the risk-neutral (or market-implied) price.

The latter is a well-known concept for banks in pricing derivatives, whereas the former is more common in other areas, most obviously insurance.

On one hand, CVA is associated mainly with derivatives for which risk-neutral pricing is standard, and there are ways in which CVA can be hedged. On the other hand, credit risk in banks is often assessed in more of an actuarial framework, due to being often illiquid and unhedgeable. Historically, the practices of banks have reflected this dichotomy: in the past, it was common to see the actuarial approach being followed, where CVA was interpreted as a statistical estimate of the expected future losses from counterparty risk and held as a reserve (analogous to a loan loss reserve in a bank). More recently, CVA is typically defined in a risk-neutral fashion, interpreted as the market cost of counterparty risk and closely associated with hedging strategies. The more sophisticated and larger banks were much quicker to adopt this risk-neutral approach.

In recent years, the risk-neutral approach to CVA has become dominant. The drivers for this have been:

Market practice. Larger banks, in particular those in the US, were early adopters of the risk-neutral CVA approach. This would then be seen by other banks via aspects such as prices for ‘novations’ (where one party contractually replaces another in a transaction). In practical terms, this could mean that a bank stepping into another bank's shoes on a given client portfolio would price the CVA differently, which in turn would lead the original bank to question whether their CVA calculation was market standard.
Accounting. FAS 157 and IFRS 13 accounting standards (Section 5.3.3) clearly reference an exit price concept and imply the use of risk-neutral default probabilities, and this has increasingly been the interpretation of auditors. Note that US and Canadian banks reporting under FAS 157 were early adopters of risk-neutral CVA at a time when many European banks (then under IAS 39 accounting standards) still used actuarial CVA. The introduction of IFRS 13 (outside the US) from 2013 has tended to create convergence here. However, the exit price concept also generally requires an institution's own credit spread to be recognised via debt value adjustment (DVA), which is generally seen as problematic (Section 17.3).
Basel III. Capital rules (Section 13.3) clearly define CVA with respect to credit spreads and therefore advocate the risk-neutral approach. However, these do not permit DVA, which creates a conflict with accounting standards.
Regulators opinions. Local regulators have also commented on the need to use credit spreads when calculating CVA. A typical statement is: ‘it is not acceptable to have CCR [counterparty credit risk] models based on expected loss or historical calculations ignoring risk premia’ and ‘market-implied credit risk premia can be observed from active markets like CDSs and bonds’.¹⁰

The result of the above is that it is now increasingly uncommon to see historical default probabilities used in the calculation of CVA (although other historical parameters are still more commonly used). For example, even as far back as 2012, a survey by Ernst and Young commented:

Two banks use a blended approach, combining market and historical data, and four banks use primarily historical data, which is generally consistent with their Basel II reporting. Given the requirements of IFRS 13, these six banks are preparing for a potential move to a more market-driven methodology for CVA, recording a DVA on derivative liabilities, and amending their hedging policies in the near future.¹¹

This does raise the question of how to define risk-neutral default probabilities when no traded credit spread is observed. This is discussed in Section 12.3.

3.1.8 Hedging Counterparty Risk and the CVA Desk

The growth of the credit derivatives market facilitated the potential hedging of counterparty credit risk. A single-name CDS is essentially an insurance contract against a certain notional value of credit risk which pays out in the event of a pre-defined credit event. One very straightforward use of hedging (Figure 3.7) could be to buy CDS protection on the counterparty in question so as to increase the credit limit.¹² This is often known as a ‘jump-to-default’ hedge. More tailored credit derivative products such as contingent CDSs (CCDSs) and risk participation agreements (RPAs) have been designed to hedge counterparty risk even more directly. CCDSs and RPAs are essentially CDSs but with the notional of protection indexed to the exposure on a contractually-specified derivative (or even portfolio of derivatives). They allow the synthetic transfer of counterparty risk linked to a specific trade and counterparty to a third party. However, whilst CCDSs and RPAs are used to share the risk of new transactions, the underlying market has never developed any significant liquidity. Even the single-name CDS market is relatively illiquid and covers only a relatively small population of reference entities.

Graph depicts the CDS hedging in order to increase a credit limit. — **Figure 3.7** Illustration of CDS hedging in order to increase a credit limit.

More practically, hedging of CVA is done on a dynamic basis with reference to credit spreads (often via CDS indices, which are more liquid than single-name CDSs) and other dynamic market variables (interest rates, FX rates, etc.). This will be discussed in more detail in Section 21.2.

As CVA has become a more central concept from an accounting and regulatory point of view, and as hedging has become more practical via credit derivatives, the concept of a CVA desk in banks has emerged. Indeed, in the largest banks, this can be traced back to as early as the late 1990s. The general role of a CVA desk in a bank (Figure 3.8) is to price and potentially own the underlying counterparty risk from the originating trading or sales desk, although the precise set-up differs across different banks, especially between larger and smaller ones. Not surprisingly, this has broadened in recent years to consider other aspects such as collateral, funding, and capital, and so the term ‘xVA desk’ or ‘central desk’ has become more common.

Schematic illustration of the role of a CVA desk in a bank. — **Figure 3.8** Illustration of the role of a CVA desk (xVA desk) in a bank.

3.2 BEYOND COUNTERPARTY RISK

3.2.1 Overview

In the aftermath of the global financial crisis (GFC), the perceived problems with derivatives and counterparty risk led to a significantly-increased interest in CVA, especially from regulators. At around the same time, accounting changes made CVA more of a key component of the valuation.

However, related to these changes, other aspects started to gain considerable interest, some of which are related to funding or capital costs and all of which are linked to the existence of counterparty risk:

Funding. Institutions face funding costs because they need to borrow to finance their activities. Funding costs are directly related to credit and counterparty risk because the greater the risk on the balance sheet, the greater the cost of funding it will be.
Collateral. Collateral posted contractually against products such as derivatives to mitigate counterparty risk may also create a cost or benefit depending on its type (e.g. currency, type of security).
Initial margin. Some situations, such as central clearing, require the posting of initial margin in order to mitigate counterparty risk. This initial margin represents over-collateralisation and represents a funding cost.
Regulatory capital. Banks face regulatory capital requirements for counterparty risk and CVA.

3.2.2 Economic Costs of a Derivative

We can generalise the discussion on counterparty risk to consider all relevant economic costs associated with a contract/portfolio, such as a derivative, as illustrated in Figure 3.9. In order to do this, we need to use the definition of a threshold that defines the point at which margin/collateral would be posted, and this is explained in more detail in Section 7.3.4. The explanation of the different aspects is as follows:

Positive value. When the portfolio has a positive value and is ‘in the money’ (ITM) (above the centre line), then the uncollateralised component gives rise to counterparty risk and funding costs. If some or all of the value is collateralised, the counterparty may be able to choose what type of collateral to post (with the range specified contractually).

Figure 3.9 Illustration of the lifetime cost of a portfolio in relation to xVA components. Note that this representation is general, and in reality margin/collateral thresholds are often zero or infinity.
Negative value. When the portfolio has a negative value or is ‘out of the money’ (OTM), then there is counterparty risk from the party's own default and a potential funding benefit to the extent that their counterparty is uncollateralised. If margin is required, the institution may be able to choose the type of collateral to post.
Overall. Whether or not the portfolio has a positive or negative value, there are costs from funding the capital that must be held against the transaction and any initial margin that needs to be posted.

Note that there are some inherent symmetries related to the symmetry in derivatives valuation (i.e. the fact that one party's positive value should be the other's negative value). An obvious example is that one party's CVA cost is the other's DVA benefit (Section 17.3). However, these symmetries are not always present: for example, capital and initial margin costs are always present and do not provide an equal and opposite benefit to the counterparties.

3.2.3 xVA Terms

Valuation adjustments (VAs) are given the generic term xVA (or XVA). An xVA term quantifies the cost (or benefit) of a component such as counterparty risk, collateral, funding, or capital over the lifetime of the transaction or portfolio in question (Figure 3.10). By convention, a cost will be associated with a positive value on the y-axis and benefits will, therefore, be represented by negative values. In order to compute xVA, it is necessary to integrate the profile shown against the relevant cost (or benefit) component, such as a credit spread, collateral, funding, or cost of capital curve.

Graph depicts the xVA term. An xVA term quantifies the cost of a component such as counterparty risk, collateral, funding, or capital over the lifetime of the transaction or portfolio. — **Figure 3.10** Generic illustration of an xVA term. Note that some xVA terms represent benefits and not costs and would appear on the negative y-axis.

Valuation may start from a base case which may only be relevant in certain specific cases (this will be discussed in more detail in Chapter 16). Valuation adjustments correct for components ignored in the base valuation (Figure 3.11) will be defined as follows:

CVA and DVA. Defines the bilateral valuation of counterparty risk. DVA represents counterparty risk from the point of view of a party's own default. These components will be discussed in Chapter 17.
FVA (funding value adjustment). Defines the cost and benefit arising from the funding of the transaction. It is divided into two terms: funding cost adjustment (FCA) and funding benefit adjustment (FBA). This will be discussed in Chapter 18.

Figure 3.11 Illustration of the role of valuation adjustments (xVAs). Note that some xVAs can be benefits.
ColVA (collateral value adjustment). Defines the costs and benefits from embedded optionality in the collateral agreement (such as being able to choose the currency or type of collateral to post) and any other non-standard collateral terms (compared to the idealised starting point). This will be discussed in Chapter 16.
KVA (capital value adjustment). Defines the cost of holding capital (typically regulatory) over the lifetime of the transaction. This will be discussed in Chapter 19.
MVA (margin value adjustment). Defines the cost of posting initial margin over the lifetime of the transaction. This will be discussed in Chapter 20.

Note that the above definitions are relatively standard but are not the only ones used in the industry. Note also that, even given the definitions, there are some elements that could fit into one VA or another. For example, since collateral posting must be funded, there are components that could be defined as either FVA or ColVA. This book will aim to use the most common and logical definitions.

It is also important to note that there are potential overlaps between the above terms; for example, between DVA and FBA, where own-default risk is widely seen as a funding benefit. These overlaps are important and will be discussed where relevant.

3.3 COMPONENTS OF XVA

3.3.1 Overview

Counterparty risk represents a combination of market risk, which defines the exposure, and credit risk, which defines the counterparty credit quality. More generally, any valuation adjustment term is made up of a market component (directly or indirectly related to the base portfolio value) and a cost (or benefit) component (defining the cost of bearing the market component). This is outlined in Table 3.1.

The important components that define counterparty risk and related metrics will be outlined below.

3.3.2 Valuation and Mark-to-Market

A definition of valuation such as MTM is the starting point for the analysis of counterparty risk and related aspects. The current value does not constitute an immediate liability by one party to the other, but rather is the present value of all the payments an institution is expecting to receive, less those it is obliged to make. It is, therefore, the core component of valuation adjustments. With respect to the definitions in Table 3.1, the valuation defines either directly or indirectly:

Table 3.1 Components of xVA terms.

	Valuation adjustment term	Market component	Cost component
Counterparty Risk	CVA/DVA	Credit exposure	Default probability
Funding	FVA	Valuation	Funding cost
Funding	MVA	Initial margin amount	Funding cost
Collateral	ColVA	Collateral amount	Collateral cost
Capital	KVA	Capital amount	Capital cost

Credit exposure. The valuation with respect to a particular counterparty defines the net value of all positions (if positive) and is therefore directly related to what could potentially be lost today in the event of a default. This is typically defined as credit exposure.
Funding position. The valuation defines the size of the asset (if positive) or liability (if negative) position and, therefore, is linked to the funding position.
Initial margin. In the event that initial margin is posted, this is typically calculated based on the variability of the valuation.
Collateral amount. Since margin is primarily determined based on the current value, there is clearly a direct link to the cost of collateral.
Capital. Methodologies for defining capital are always based on the underlying valuation.

The payments that define the current valuation may be scheduled to occur many years in the future and may have values that are strongly dependent on market variables. The valuation will be positive or negative depending on the transaction(s) in question, the magnitude of remaining payments, and current market rates. Hence, all of the above components are relevant from both a current (spot) and future point of view. Essentially, characterising valuation adjustments requires answering the following two questions:

What is the current valuation?
What is the valuation in the future (since, for example, the counterparty can default at any point in the future)?

The first point is clearly simpler to define and needs to be done irrespective of the wish to consider valuation adjustments. The second point is naturally far more complex to answer than the first (except in some simple cases).

Valuation adjustments may also depend on risk mitigants. Where the nature of the risk mitigant is fixed through time, this may be relatively straightforward. However, when the risk mitigant itself changes over time, this is more complex. For example, margin is generally required based on a defined valuation which will change over time. It is therefore necessary to be able to calculate the future value of required margin as well as the more well-defined current margin amount. The future value of collateral securities used to fulfil margin requirements should also be quantified.

Note that there is also a potential recursive problem with the above. The valuation is an input parameter for calculating the valuation adjustments, and yet the correct valuation should include valuation adjustments. One solution to this is to consider a base value (without valuation adjustments) and add valuation adjustments linearly as a function of this base value. This is often used in practice, but it is only an approximation as the real problem is non-linear and recursive.

3.3.3 Replacement Cost and Credit Exposure

Default-related contractual features of transactions, such as close-out netting and termination features, refer to replacement costs. The base valuation is clearly closely related to replacement cost, which defines the entry point into an equivalent transaction(s) with another counterparty. However, the actual situation is more complicated. To replace a transaction, one must consider costs such as bid-offer spreads, which may be significant for highly-illiquid securities (note that even a standard and liquid contract might be non-standard and illiquid at the default time). Portfolios can be also be replaced one-for-one or macro-hedged.

Not surprisingly, documentation of derivatives in a default scenario has tended generally to aim to reference replacement costs, defined as objectively as possible, as opposed to a basic valuation. This implies that real additional costs in replacing or rehedging a portfolio can be included in the determination of the amount owed (between a surviving and defaulting party) at the default time. This will be discussed in more detail in Section 6.3.4. However, replacement costs, by their nature, may include valuation adjustment terms, such as CVA, leading to the recursive problem mentioned above.

Other aspects are important in this regard, such as the ability to net transactions in default and the possibility to adjust positions with collateral amounts. Both of these aspects are subject to legal agreements and their potential interpretation in a court of law.

Credit exposure (or simply exposure) defines the loss in the event of a counterparty defaulting. Exposure is characterised by the fact that a positive value of a portfolio corresponds to a claim on a defaulted counterparty, whereas in the event of negative value, an institution is still obliged to honour its contractual payments (at least to the extent that they exceed those of the defaulted counterparty). This means that if an institution is owed money and its counterparty defaults, then it will incur a loss, whilst in the reverse situation it cannot gain from the default by being somehow released from its liability.¹³

Exposure is relevant only if the counterparty defaults and hence the quantification of exposure is conditional on counterparty default. Having said this, it is often market practice to consider exposure independently of any default event and so assume implicitly no wrong-way risk. Such an assumption is reasonable for most products subject to counterparty risk, although the reader should keep the idea of conditional exposure in mind. We will then address wrong-way risk, which defines the relationship between exposure and counterparty default, in more detail in Section 17.6. Note that credit exposure is specific to default (and therefore CVA), and other points of view (most obviously funding-related) need not be conditional on counterparty default.

3.3.4 Default Probability, Credit Migration, and Credit Spreads

When assessing counterparty risk, one must consider the credit quality of a counterparty over the entire lifetime of the relevant transactions. Such time horizons can be extremely long. Ultimately, there are two aspects to consider:

What is the probability of the counterparty defaulting over a certain time horizon?¹⁴
What is the probability of the counterparty suffering a decline in credit quality over a certain time horizon (for example, a ratings downgrade and/or credit spread widening)?

Credit migrations or discrete changes in credit quality, such as due to rating changes, are crucial since they influence the term structure of default probability. They should also be considered since they may cause issues even when a counterparty is not yet in default. Suppose the probability of default of a counterparty between the current time and a future date of (say) one year is known. It is also important to consider what the same annual default rate might be in four years; in other words, the probability of default between four and five years in the future. There are three important aspects to consider:

Future default probability,¹⁵ as defined above, will have a tendency to decrease due to the chance that the default may occur before the start of the period in question. The probability of a counterparty defaulting between 20 and 21 years in the future may be very small, not because they are very creditworthy (potentially quite the reverse), but rather because they are unlikely to survive for 20 years!
A counterparty with an expectation of deterioration in credit quality will have an increased probability of default over time (although at some point the above phenomenon will reverse this).¹⁶
A counterparty with an expectation of improvement in credit quality will have a decreasing probability of default over time, which will be accelerated by the first point above.

There is a well-known empirical mean reversion in credit quality, as evidenced by historical credit rating changes. This means that good-credit-quality (above average) firms tend to deteriorate and vice versa. Hence, a counterparty of good credit quality will tend to have an increasing default probability over time, whilst a poor-credit-quality counterparty will be more likely to default in the short term and less likely to do so in the longer term. The term structure of default is very important to consider.

We note finally that default probability may be defined as real world or risk-neutral. In the former case, the question is what is the actual default probability of the counterparty, and this is often estimated via historical data. In the latter case, we calculate the risk-neutral (or market-implied) probability from market credit spreads (for example, via CDSs). The difference between real-world and risk-neutral default probabilities is discussed in detail in Section 12.1.1, but it is worth emphasising now that risk-neutral default probabilities have become the standard for CVA calculations in recent years due to a combination of accounting guidelines, regulatory rules, and market practice (Section 3.1.7).

3.3.5 Recovery and Loss Given Default

Exposure calculations, by convention, will ignore any recovery value in the event of a default. Hence, the exposure (Section 3.3.3) is the loss, as defined by the value or replacement cost that would be incurred, assuming no recovery value.

Recovery rates typically represent the percentage of the outstanding claim recovered when a counterparty defaults. An alternative variable to recovery is loss given default (LGD), which in percentage terms is 100% minus the recovery rate. Default claims can vary significantly, and LGD is therefore highly uncertain. Whilst credit exposure is traditionally measured independently, LGD is relevant in the quantification of CVA.

In the event of a bankruptcy, the holders of bilateral derivatives contracts such as derivatives with the counterparty in default would generally be pari passu with the senior bondholders.¹⁷ OTC derivatives, bonds, and CDSs generally reference senior unsecured credit risk and may appear to relate to the same LGD. However, this is not always the case, and sometimes there are structural reasons why certain contracts would be assumed to have a lower LGD (higher recovery) or even vice versa.

There are timing issues with respect to LGD. When a bond issuer defaults, LGD is realised immediately since the bond can be sold in the market. CDS contracts are also settled within days of the defined credit event via the CDS auction which likewise defines the LGD. However, derivatives (unlike bonds) cannot be freely traded or sold, especially when the counterparty to the derivative is in default. This essentially leads to a potentially different LGD for derivatives. These aspects, very important in the Lehman Brothers bankruptcy of 2008, were discussed in more detail in Section 2.2.9.

3.3.6 Funding, Collateral, and Capital Costs

In addition to the cost of taking credit risk measured by a credit spread (and LGD), it is necessary to consider the costs associated with funding, collateral, and capital. Like credit spreads, these components are difficult to assess and may require a combination of qualitative and quantitative considerations. Ultimately, though, they will be key inputs in xVA quantification.

It may be helpful to consider examples where such costs will arise:

Funding. Suppose an institution enters into an uncollateralised transaction¹⁸ which requires them to make an upfront cash payment.¹⁹ There is clearly a need to fund this payment as it relates to cash flows that will be received later. It may be necessary to borrow money (such as by issuing a bond) in order to make this upfront payment. There will be an associated cost to this, representing the compensation that lenders will require. In collateralised transactions, this will not be the cash because the margin/collateral will offset with other payments (such as the upfront cash payment in this example). Initial margin, as overcollateralisation, will not offset with any other component and will generate a funding requirement.
Collateral (margin). Funding will normally be defined as the cost of raising cash in a base currency. If the collateral under a margining agreement is in a different currency or securities, then this will constitute a different interest rate, which should be reflected in the valuation. For example, receiving bonds may represent a funding benefit, but there will be a repo rate that defines the cost of converting these bonds into cash. There may also be optionality, where the party required to post collateral to meet margin requirements may have a contractual choice over the currencies and/or securities that can be used.
Capital. An institution enters into a transaction that causes an increase in its capital requirements. In order to raise share capital, the institution must pay an implicit return to shareholders via dividend payments. They should, therefore, consider the cost of the capital required when assessing the economics of the transactions.

Some of the above inputs are objective and quantifiable. For example, an institution may be able to observe where their bonds are trading in the secondary market and use this as an estimate of the cost of raising more funding. However, some aspects are more subjective, such as determining what maturity of funding is required against a transaction or what dividends will be required by shareholders in the future. More discussion of these inputs will be given in Chapter 14.