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      Of course in practice this symmetry would certainly not hold as both counterparties would operate different CVA models and may be operating under different accounting regimes. For example, one could be a bank with the derivative held in its trading book using mark-to-market accounting while the other might be a corporate using IAS 39 hedge accounting rules (IASB, 2004). There are also a number of other issues to be addressed when pricing unsecured derivatives such as including the impact of right-way or wrong-way risk and dealing with illiquid counterparties. Counterparties that deal on an unsecured basis are more likely to be smaller names with no traded CDS contracts, although some will be larger corporates or governmental entities.

      CSA

      In the case of perfect collateralisation, where any change in mark-to-market is instantaneously covered by a transfer of collateral to support it, there is no credit exposure and hence no CVA or DVA. In practice, of course, even the strongest of bilateral CSA agreements do not display this behaviour and have a daily collateral call. In general all CSAs have a minimum transfer amount (MTA) and many have non-zero thresholds. Many CSAs will also have asymmetric thresholds giving one-way CSAs. Some CSAs have credit-rating dependent features such as thresholds that reduce on downgrade, volatility buffers or a requirement to novate the trade if the derivative issuer falls below a certain rating. CSAs can have a much lower call frequency such as weekly or monthly and this is particularly true of non-bank counterparties who do not have the operational capacity to manage collateral on a daily basis. In general, a default is not recognised immediately and often there is a recognised cure or grace period where a counterparty that has failed to make a collateral payment is allowed time to make the payment. In general, a margin period of risk is included when modelling collateral to allow an estimate of the realistic expected exposure. In the Basel III regulatory framework this is set at ten days unless the counterparty is a significant financial institution in which case the margin period is increased to twenty days.7 During the margin period of risk no collateral is assumed to be transferred by the counterparty but often it is assumed that the bank must continue to make collateral payments, even if the counterparty has previously failed to make a collateral payment. Collateral disputes can also give rise to exposure and to the regulatory margin period of risk if more than two disputes occur in the previous two quarters (European Parliament and the Council of the European Union, 2013a; European Parliament and the Council of the European Union, 2013b).

      CSAs are imperfect and give rise to residual exposure and hence there is credit risk and so CVA can be calculated and charged. However, not all banks mark CVA on collateralised names, particularly those with low or zero thresholds and a daily call frequency.

      CCP

      CCP variation margin arrangements are very similar to a strong CSA with a daily call frequency and in some circumstances collateral can be called intraday. Given the presence of initial margin the residual expected exposure to the derivative trades themselves will be very small or zero.8 However, there remains the possibility of exposure to the CCP itself through the initial margin and the default fund. If the initial margin is bankruptcy remote then the exposure generated by posted initial margin can be excluded from CVA. However, this is not the case for the default fund contributions which are designed to be used in the event of the default of a member. The default fund certainly generates exposure and hence credit risk.

      1.3.5 FVA

      FVA was initially controversial in the quantitative finance community as is clear from the series of papers by John Hull and Alan White (2012b; 2012c; 2014b) and the responses to them by Castagna (2012), Laughton and Vaisbrot (2012), Morini (2012) and Kenyon and Green (2014c). The debate around FVA is discussed in section 1.4.1 and FVA models are presented in Part II; however, it is clear that most market practitioners believe a pricing adjustment should be made for the cost of funding unsecured derivative transactions. In this context FVA represents the costs and benefits from managing the collateral on hedges used to eliminate market risk from the unsecured transactions. FVA and CVA together can be viewed as the cost of not trading under a perfect CSA agreement. The accounting status of FVA is now in transition with increasing numbers of banks taking reserves.

      Unsecured

      As with CVA, unsecured trades are the standard case for FVA as both counterparties are fully exposed to each other. Symmetric models with both funding cost and benefits as well as asymmetric models with only funding costs have been proposed with a key determining factor being the potential overlap with DVA benefit. Broadly speaking, methodologies for FVA are either based on discounting, as noted earlier, or on exposure-based models that are extensions of CVA.

      CSA

      The discussion on residual exposure from CVA also applies in the context of FVA so that deviations from a perfect CSA could give rise to residual FVA. If we view FVA as the cost of providing an effective loan or the benefit of an effective deposit through a derivative then the residual exposure just gives rise to a residual funding cost or benefit. However, as will be discussed later, if we view the FVA as the cost of maintaining collateral on a hedge trade then the argument for residual FVA on CSA trades is much weaker, although funding costs and benefits will still arise from mismatches in collateral requirements due to differing CSA terms. What is clear is that FVA does not apply to the secured portion of the exposure unless the assets provided as collateral cannot be rehypothecated. Lack of rehypothecation may be due to legal terms within the CSA or because the asset provided as collateral may

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