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of trades or posting collateral), model risk (inaccurate or inappropriately calibrated models), fraud (such as rogue traders), and legal risk (such as the inability to enforce legal agreements, for example those covering netting or collateral terms). Whilst some operational risk losses may be moderate and common (incorrectly booked trades, for example), the most significant losses are likely to be a result of highly improbable scenarios or even a “perfect storm” combination of events. Operational risk is therefore extremely hard to quantify, although quantitative techniques are increasingly being applied. Counterparty risk mitigation methods, such as collateralisation, inevitably give rise to operational risks.

      Legal risk (defined as a particular form of operational risk by Basel II) is the risk of losses due to the assumed legal treatment not being upheld. This can be due to aspects such as incorrect documentation, counterparty fraud, mismanagement of contractual rights, or unanticipated decisions by courts. Mitigating financial risk generally gives rise to legal risk due to the mitigants being challenged in some way at a point where they come into force. Defaults are particularly problematic from this point of view, because they are relatively rare and very sensitive to the jurisdiction in question.

3.2.4 Liquidity risk

      Liquidity risk is normally characterised in two forms. Asset liquidity risk represents the risk that a transaction cannot be executed at market prices, perhaps due to the size of the position and/or relative illiquidity of the underlying market. Funding liquidity risk refers to the inability to fund contractual payments or collateral requirements, potentially forcing an early liquidation of assets and crystallisation of losses. Since such losses may lead to further funding issues, funding liquidity risk can manifest itself via a “death spiral” caused by the negative feedback between losses and cash requirements. Reducing counterparty risk often comes at the potential cost of increased funding liquidity risk via mechanisms such as collateralisation or central clearing.

3.2.5 Integration of risk types

      A particular weakness of financial risk management over the years has been the lack of focus on the integration of different risk types. It has been well known for many years that crises tend to involve a combination of different financial risks. Given the difficulty in quantifying and managing financial risks in isolation, it is not surprising that limited effort is given to integrating their treatment. As noted above, counterparty risk itself is already a combination of two different risk types, market and credit. Furthermore, the mitigation of counterparty risk can create other types of risk, such as liquidity and operational. It is important not to lose sight of counterparty risk as an intersection of many types of financial risk, and that mitigating counterparty risk creates even more financial risks. This is one of the reasons that this book, since the first and second editions, has evolved to cover more material in relation to collateral, funding and capital.

3.2.6 Counterparty risk

      Counterparty risk is traditionally thought of as credit risk between OTC derivatives counterparties. Since the global financial crisis, the importance of OTC derivatives counterparty risk has been a key focus of regulation. Historically, many financial institutions limited their counterparty risk by trading only with the most sound counterparties. The size and scale of counterparty risk has always been important, but for many years has been obscured by the myth of the creditworthiness of the “too big to fail” institutions. However, the financial crisis showed that these are often the entities that represent the most counterparty risk. The need to consider counterparty risk in all OTC derivative relationships and the decline in credit quality generally has caused a meteoric rise in interest in and around the subject. Regulatory pressure has continued to fuel this interest. Whereas in the past, only a few large dealers invested heavily in assessed counterparty risk, it has rapidly become the problem of all financial institutions, big or small. At the same time, the assessment of the impact of collateral, funding and capital has become a key topic.

      3.3 Risk management of derivatives

3.3.1 Value-at-risk

      Financial risk management of derivatives has changed over the last two decades. One significant aspect has been the implementation of more quantitative approaches, the most significant probably being value-at-risk (VAR). Initially designed as a metric for market risk, VAR has subsequently been used across many financial areas as a means for efficiently summarising risk via a single quantity. For example, the concept of PFE (potential future exposure), when used to assess counterparty risk, is strongly related to the definition of VAR.

Figure 3.4 Illustration of the value-at-risk (VAR) concept at the 99 % confidence level. The VAR is 125, since the chance of a loss greater than this amount is no more than 1 %.

A VAR number has a simple and intuitive explanation as the worst loss over a target horizon to a certain specified confidence level. The VAR at the α% confidence level gives a value that will be exceeded with no more than a (1 – α)% probability. An example of the computation of VAR is shown in Figure 3.4. The VAR at the 99 % confidence level is –125 (i.e. a loss) since the probability that this will be exceeded is no more than 1 %. (It is actually 0.92 % due to the discrete13 nature of the distribution.) To find the VAR, one finds the minimum value that will be exceeded with the specified probability.

VAR is a very useful way in which to summarise the risk of an entire distribution in a single number that can be easily understood. It also makes no assumption as to the nature of distribution itself, such as that it is a Gaussian.14 It is, however, open to problems of misinterpretation since VAR says nothing at all about what lies beyond the defined (1 % in the above example) threshold. To illustrate this, Figure 3.5 shows a slightly different distribution with the same VAR. In this case, the probability of losing 250 is 1 % and hence the 99 % VAR is indeed 125 (since there is zero probability of other losses in-between). We can see that changing the loss of 250 does not change the VAR since it is only the probability of this loss that is relevant. Hence, VAR does not give an indication of the possible loss outside the confidence level chosen. Over-reliance upon VAR numbers can be counterproductive as it may lead to false confidence.

Figure 3.5 Distribution with the same VAR as Figure 3.4.

      Another problem with VAR is that it is not a coherent risk measure (Artzner et al., 1999), which basically means that in certain (possibly rare) situations it can exhibit non-intuitive properties. The most obvious of these is that VAR may not behave in a sub-additive fashion. Sub-additivity requires a combination of two portfolios to have no more risk than the sum of their individual risks (due to diversification).

      A slight modification of the VAR metric is commonly known as expected shortfall (ES). Its definition is the average loss equal to or above the level defined by VAR. Equivalently, it is the average loss knowing that the loss is at least equal to the VAR. ES does not have quite as intuitive an explanation as VAR, but has more desirable properties such as not completely ignoring the impact of large losses (the ES in Figure 3.5 is indeed greater than that in Figure 3.4) due to being a coherent risk measure. For these reasons, The Fundamental Review of the Trading Book (BCBS, 2013) has suggested that banks use ES rather than VAR for measuring their market risk (this may eventually also apply to the calculation of CVA capital, as discussed in Section 8.7).

      The most common implementation of VAR and ES approaches is using historical simulation. This takes a period (usually several years) of historical data containing risk factor behaviour across the entire portfolio in question. It then resimulates over many periods how the current portfolio would behave when subjected to the same historical evolution. For example, if four years of data were used, then it would be possible to compute around 1,000 different scenarios of daily movements for the portfolio. If a longer time horizon is of interest, then quite commonly the one-day result is simply extended using the “square

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