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 defaulting21 over a certain time horizon?
• 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 those due to ratings 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 probability22 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 expectation23 of deterioration in credit quality will have an increasing probability of default over time (although at some point the above phenomenon will reverse this).
• 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.
Spreadsheet 4.1 Counterparty risk for a forward contract-type exposure.
There is a well-known empirical mean-reversion in credit quality, as evidenced by historical credit ratings changes. This means that good (above-average) credit quality firms tend to deteriorate and vice versa. So a counterparty of good credit quality will tend to have an increasing default probability over time, whereas 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.
Finally, we note that default probability may be defined as real-world or risk-neutral. In the former case, we ask ourselves what the actual default probability of the counterparty is, which is often estimated via historical data. In the latter case, we calculate the risk-neutral (or market-implied) probability from market credit spreads. The difference between real-world and risk-neutral default probabilities is discussed in detail in Chapter 12, but it is worth emphasising now that risk-neutral default probabilities have become virtually mandatory for CVA calculations in recent years due to a combination of accounting guidelines, regulatory rules and market practice.
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, so LGD is therefore highly uncertain. Credit exposure is traditionally measured independently, but LGD is relevant in the quantification of CVA.
In the event of a bankruptcy, the holders of OTC derivatives contracts with the counterparty in default would generally be pari passu24 with the senior bondholders. OTC derivatives, bonds and CDSs generally reference senior unsecured credit risk and may appear to relate to the same LGD. However, there are timing issues: 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 that likewise defines the LGD. However, OTC derivatives 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, which were very important in the Lehman Brothers bankruptcy of 2008 (see Figure 3.3 in the previous chapter), are discussed 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.
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,
We will generally use the term “default” to refer to any “credit event” that could impact the counterparty.
Here we refer to default probabilities in a specified period, such as annual.
This can refer to a real expectation (historical) or one implied from market spreads (risk-neutral) as discussed below.
This means they have the same seniority and therefore should expect to receive the same recovery value.
