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in market risk VAR models used by banks, regulators allow the ten-day VAR to be defined as √10=3.14 multiplied by the one-day VAR. VAR models can also be “backtested” to check their predictive performance empirically. Backtesting involves performing an ex-post comparison of actual outcomes with those predicted by the model. VAR lends itself well to backtesting since a 99 % number should be exceeded once every hundred observations.

      It is important to note that the use of historical simulation and backtesting are relatively straightforward to apply for VAR and ES due to the short time horizon (ten days) involved. For counterparty risk assessment (and xVA in general), much longer time horizons are involved and quantification is therefore much more of a challenge.

3.3.2 Models

      The use of metrics such as VAR relies on quantitative models in order to derive the distribution of returns from which such metrics can be calculated. The use of such models facilitates combining many complex market characteristics such as volatility and dependence into one or more simple numbers that can represent risk. Models can compare different trades and quantify which is better, at least according to certain predefined metrics. All of these things can be done in minutes or even seconds to allow institutions to make fast decisions in rapidly moving financial markets.

      However, the financial markets have something of a love/hate relationship with mathematical models. In good times, models tend to be regarded as invaluable, facilitating the growth in complex derivatives products and dynamic approaches to risk management adopted by many large financial institutions. The danger is that models tend to be viewed either as “good” or “bad” depending on the underlying market conditions. Whereas, in reality, models can be good or bad depending on how they are used. An excellent description of the intricate relationship between models and financial markets can be found in MacKenzie (2006).

      The modelling of counterparty risk is an inevitable requirement for financial institutions and regulators. This can be extremely useful and measures such as PFE, the counterparty risk analogue of VAR, are important components of counterparty risk management. However, like VAR, the quantitative modelling of counterparty risk is complex and prone to misinterpretation and misuse. Furthermore, unlike VAR, counterparty risk involves looking years into the future rather than just a few days, which creates further complexity not to be underestimated. Not surprisingly, regulatory requirements over backtesting of counterparty risk models15 have been introduced to assess performance. In addition, a greater emphasis has been placed on stress testing of counterparty risk, to highlight risks in excess of those defined by models. Methods to calculate xVA are, in general, under increasing scrutiny.

3.3.3 Correlation and dependency

      Probably the most difficult aspect in understanding and quantifying financial risk is that of co-dependency between different financial variables. It is well known that historically estimated correlations may not be a good representation of future behaviour. This is especially true in a more volatile market environment, or crisis, where correlations have a tendency to become very large. Furthermore, the very notion of correlation (as used in financial markets) may be heavily restrictive in terms of its specification of co-dependency.

      Counterparty risk takes difficulties with correlation to another level, for example compared to traditional VAR models. Firstly, correlations are inherently unstable and can change significantly over time. This is important for counterparty risk assessment, which must be made over many years, compared with market risk VAR, which is measured over just a single day. Secondly, correlation (as it is generally defined in financial applications) is not the only way to represent dependency, and other statistical measures are possible. Particularly in the case of wrong-way risk (Chapter 19), the treatment of co-dependencies via measures other than correlation is important. In general, xVA calculations require a careful assessment of the co-dependencies between credit risk, market risk, funding and collateral aspects.

      4

      Counterparty Risk

      Success consists of going from failure to failure without loss of enthusiasm.

Sir Winston Churchill (1874–1965)

      4.1 Background

      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 (for example, if they default). Counterparty risk is typically defined as arising from two broad classes of financial products: OTC derivatives (e.g. interest rate swaps) and securities financial transactions (e.g. repos). The former category is the more significant due to the size and diversity of the OTC derivatives market (see Figure 3.1 in the last chapter) and the fact that a significant amount of risk is not collateralised. As has been shown in the market events of the last few years, counterparty risk is complex, with systemic traits and the potential to cause, catalyse or magnify serious disturbances in the financial markets.

4.1.1 Counterparty risk versus lending risk

      Traditionally, credit risk can generally be thought of as 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 notional 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 drawn16 for the purpose of credit risk.

      • 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.17

      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 MTM value of a derivative at a potential default date will be the net value of all future cashflows 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, each counterparty in a derivatives transaction has risk to the other.

4.1.2 Settlement and pre-settlement 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. Counterparty risk is mainly associated with pre-settlement risk, which is the risk of default of the counterparty prior to expiration (settlement) of the contract. However, we should also consider settlement risk, which is the risk of 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 (at expiration). This is what “counterparty risk” usually refers to.

      • Settlement risk. This arises at settlement times due to timing differences between when each party performs on its obligations under the contract.

The difference between pre-settlement and settlement risk is illustrated in Figure 4.1.

Figure 4.1 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.

      Example

      Suppose

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