4.4 Illustration of the classic end-user counterparty risk setup.
Figure 4.5 Illustration of the classic bank setup.
Another important feature is that end-users may hedge risks on a one-for-one basis; for example, the terms of a swap may be linked directly to those of bonds issued rather than the interest rate exposure being hedged more generically on a macro basis. End-users may find it problematic when unwinding transactions, since the original counterparty will not necessarily quote favourable terms. Furthermore, if they do execute offsetting transactions – for example, a supranational may execute receiver swaps to hedge their lending whilst also having payer swaps to hedge borrowing – the terms received will be less favourable than if they macro-hedged the overall risk. This is a consequence of hedging borrowing and lending on a one-to-one basis. For a similar reason, default situations will be problematic because an end-user may want to replace transactions on a one-for-one basis rather than macro-hedging their exposure to the defaulted counterparty. This will likely be more expensive and time-consuming.
For a bank, the classic counterparty risk situation is rather different (Figure 4.5). Banks will typically aim to run a relatively flat (i.e. hedged) book from a market risk perspective. This means that a transaction with a client will be hedged (either on a macro basis or one-for-one) with another market participant. This is likely to lead to a series of hedges through the interbank market, ending with another opposite exposure to another end-user. In this situation, the bank may have little or no MTM volatility or market risk. However, they do have counterparty risk to both counterparties A and B, because if either were to default it would leave market risk with respect to the other side of the trade.
Another important feature of this situation is that client transactions will often be uncollateralised, whereas the hedges will be collateralised (or centrally cleared). The counterparty risk problem exists mainly on the uncollateralised transactions (although there is still material risk on the hedges). Whilst the overall MTM is neutralised, this introduces an asymmetry in collateral flows that can be problematic. Dealers also suffer from the directional hedging needs of clients. For example, they may transact mainly receiver interest rate swaps with corporate clients. In a falling interest rate environment, the bank’s exposure will increase substantially and the hedges of these swaps will require significant collateral posting. Figure 4.5 is very important as a starting point for many different types of analysis and will be referred back to at several later points in this book.
4.2 Components
Counterparty risk represents a combination of market risk, which defines the exposure and credit risk that defines the counterparty credit quality. A counterparty with a large default probability and a small exposure may be considered preferable to one with a larger exposure and smaller underlying default probability – but this is not clear. CVA puts a value on counterparty risk and is one way to distinguish numerically between the aforementioned cases. CVA will be discussed in detail later, but we now define the important components that define counterparty risk and related metrics.
Mark-to-market (MTM) is the starting point for analysis of counterparty risk and related aspects. Current MTM does not constitute an immediate liability by one party to the other, but rather is the present value of all the payments that a party is expecting to receive, less those it is obliged to make. These payments may be scheduled to occur many years in the future and may have values that are strongly dependent on market variables. MTM will be positive or negative, depending on the magnitude of remaining payments and current market rates.
The MTM with respect to a particular counterparty defines the net value of all positions and is therefore directly related to what could potentially be lost today in the event of a default. However, 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.
Contractual features of transactions, such as close-out netting and termination features, refer to replacement costs. MTM 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 especially for particularly illiquid products. Note that even a standard and liquid contract might be non-standard and illiquid at the default time. In such a case, one must then decide whether to replace with an expensive non-standard derivative or with a more standard one that does not match precisely the original one. Large portfolios can be replaced one-for-one or macro-hedged. Broadly speaking, documentation suggests that default costs can effectively be passed on via the replacement cost concept, although this is discussed in more detail later via the definition of close-out amount (Section 5.2.6).
Contractual agreements generally reference replacement costs (and not MTM) in defining a surviving party’s position in a default scenario. Although this represents the economic reality in a default, it can cause further problems. By their nature, replacement costs will include CVA (and more generally xVA) components that create a recursive problem, since one cannot define xVA today without knowing the future xVA. Chapter 14 addresses this topic in more detail (Section 14.6.5). For now, we note that quantification will assume, for reasons of simplicity, that MTM is a good proxy for the real replacement cost and this is in general not a bad approximation.
Credit exposure (hereafter often simply known as exposure) defines the loss in the event of a counterparty defaulting. It is also representative of other costs such as capital and funding that appear in other xVA terms. 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, a party is still obliged to honour their contractual payments (at least to the extent that they exceed those of the defaulted counterparty). This means that if a party is owed money and their counterparty defaults then they will incur a loss, while in the reverse situation they cannot gain20 from the default by being somehow released from their liability.
Exposure is clearly a very time-sensitive measure, since a counterparty can default at any time in the future and one must consider the impact of such an event many years from now. Essentially, characterising exposure involves answering the following two questions:
• What is the current exposure (the maximum loss if the counterparty defaults today)?
• What is the exposure in the future (what could be the loss if the counterparty defaults at some point in the future)?
The second point above is naturally far more complex to answer than the first, except in some simple cases.
All exposure calculations, by convention, will ignore any recovery value in the event of a default. Hence, the exposure is the loss, as defined by the value or replacement cost that would be incurred, assuming no recovery value. Exposure is relevant only if the counterparty defaults and hence the quantification of exposure would be conditional on counterparty default. Having said this, we will often 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 Chapter 17.
Note that exposure from other points of view (most obviously funding-related) need not be conditional on counterparty default.
When
