The xVA Challenge. Gregory Jon

in more detail in Section 12.2.5.

      4.3 Control and quantification

      To control and quantify counterparty risk, one must first 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 collateral) that may be relevant. Control of counterparty risk has traditionally been the purpose of credit limits, used by most banks for well over a decade.

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

      Below we analyse credit limits and CVA, and how they complement one another.

4.3.1 Credit limits

      Let us consider the first and most basic use of exposure, which is as a means to control the amount of risk to a given counterparty over time. Counterparty risk can be diversified by limiting exposure to any given counterparty, broadly in line with the perceived default probability of that counterparty. This is the basic principle of credit limits (or credit lines). By trading with a greater number of counterparties, a party is not so exposed to the failure of any one of them. Diversification across counterparties is not always practical due to the relationship benefits from trading with certain key clients. In such cases, exposures can become excessively large and should be, if possible, mitigated by other means.

Credit limits are generally specified at the counterparty level, as illustrated in Figure 4.6. The idea is to characterise the potential future exposure (PFE) to a counterparty over time and ensure that this does not exceed a certain value (the credit limit). The PFE represents a worst-case scenario and is similar to the well-known VAR measure described in Section 3.3.1. The credit limit will be set subjectively according to the risk appetite of the party in question. It may be time-dependent, reflecting the fact that exposures at different times in the future may be considered differently. PFE will be described in more detail in Section 7.2.2 but, broadly, the follow aspects must be accounted for in its quantification:

Figure 4.6 Illustration of the use of PFE and credit limits in the control of counterparty risk.

      • the transaction in question;

      • the current relevant market variables (e.g. interest rates and volatilities);

      • netting of the new transaction with existing transactions with the same counterparty;

      • collateral terms with the counterparty (if any); and

      • hedging aspects.

      Credit limits will often be reduced over time, effectively favouring short-term exposures over long-term ones. This is due to the chance that a counterparty’s credit quality may deteriorate over a long time 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. The credit limit of a counterparty with poor credit quality (sub-investment grade) should arguably increase over time, because if the counterparty does not default then its credit quality will be expected to improve eventually. 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 that would breach a credit limit at any point in the future is likely to be refused unless specific approval is given. Limits could be breached for two reasons: either due to new transactions or market movements. The former case is easily dealt with by refusing transactions that would cause a limit breach. The latter is more problematic, and banks sometimes have concepts of hard and soft limits: the latter may be breached through market movements rather than 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 would be approved. Due to the directional nature of end-users activity in OTC derivatives, this is a challenge.25

      Credit limits allow a consolidated view of exposure with each counterparty and represent a 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 that are close to (but not breaching) a limit, requiring them to be more profitable, but these are generally quite ad hoc.

4.3.2 Credit value adjustment

      Traditional counterparty risk management, as described above, works in a binary fashion. The problem with this is that the risk of a new transaction is the only consideration, whereas the return (profit) should surely be a factor also. By pricing counterparty risk through CVA, the question becomes whether it is profitable once the counterparty risk component has been “priced in”. The calculation of CVA (and DVA) will be discussed in more detail in Chapter 14, but in addition to the components required for PFE quantification mentioned above, the following are also important:

      • the default probability and expected LGD of the counterparty; and

      • the parties’ own default probability (in the case of bilateral pricing and DVA).

      An important aspect of CVA is that it is a counterparty level calculation.26 CVA should be calculated incrementally by considering the increase (or decrease) in exposure, taking into account 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).

      1

      This occurs when a large number of customers withdraw their deposits because they believe the bank is, or might become, insolvent.

      2

      AIG would receive further bailouts.

      3

      Hundreds of billions of pounds were provided in the form of loans and guarantees.

26

Strictly speaking, it is a netting set level calculation, as there can possibly be more than one netting agreement with a given counterparty.