XVA. Green Andrew

      Reference close-out

      The reference close-out value is the final factor in determining the choice of unsecured discounting model. To be consistent with the CVA model the unsecured reference valuation should match that used in the CVA model so that in the event of default the risk-neutral valuation matches the claim value made against the administrators of the defaulted counterparty and the CVA becomes the realised loss on the trade once the actual recovery rate is known. Note that the use of funding discounting models implies that the CVA model has to be changed to be consistent with this choice of FVA model.5

      CSA

      CSA and OIS discounting will be discussed in detail in Chapter 8; however, it should be noted here that the implications of Piterbarg (2010) and Piterbarg (2012) are that the appropriate discount rate for fully collateralised counterparties is the rate of interest received on the posted collateral. Hence the discount curve depends on the terms of the CSA agreement. In the simplest case where collateral can only be posted in cash in a single currency then the rate of interest received on posted collateral is normally the overnight rate in that currency. Hence the appropriate discount curve is the OIS curve in the same currency as this curve represents the market expected overnight rate extended out to longer maturities. In the case where cash in multiple currencies can be posted the appropriate discount curve is a blended curve which represents the rate earned on the cheapest-to-deliver currency.6 Many CSAs allow a variety of securities to be posted as collateral and in this case the choice of appropriate discount curve becomes more complex.

      CCP

      The discount curve used by CCPs to determine the value for the purposes of margin calls is determined by the internal models of the CCP. For single currency interest rate swaps cleared through LCH.Clearnet SwapClear this is currently a single currency OIS discounting methodology, having switched over from a LIBOR methodology during 2010 (LCH, 2010a). This can be viewed as the risk-neutral valuation of the interest rate swap, but there is no guarantee that a clearing member’s own risk-neutral valuation will match that of SwapClear and this could become problematic because of the privileged position held by CCPs (Kenyon and Green, 2013c).

      1.3.3 Hedging and Management Costs

      The bid-offer spread quoted by trading desks has always been included in prices and reflects the trading desk cost of managing the trade. This is normally considered to include the cost of hedging the market risk on the trade at inception and any future re-hedging costs due to market movements and embedded nonlinear risk. There are however other elements that should be considered:

      • Staff costs are a very significant fraction of the cost base of any bank. This includes trading and sales staff with primary responsibility for managing market risk and interacting with the customer. However, there are many other support functions involved including quantitative analysts, finance professionals and business controllers, risk managers, audit and operations staff.

      • Legal and other professional fees are also a cost. Over-the-counter (OTC) derivatives are traded under the legal framework provided by ISDA (1992; 2002), which requires set-up and maintenance costs. Some transactions require external ratings, which means engagement with rating agencies and the payment of fees.

      • IT and other infrastructure costs are also a significant part of the cost base of a bank. This covers everything from buildings, lighting and air conditioning through to the cost of IT system development, maintenance and hardware. For complex derivative products, even the cost of running the valuation and risk on a daily basis can be expensive due to hardware and the energy required to both power and cool it. Of course it is not just trading systems themselves, there are huge numbers of other risk systems for CVA, PFE, VaR etc that also consume resources.

      1.3.4 Credit Risk: CVA/DVA

      Part I of this book discusses CVA and DVA in detail, including models for unsecured and secured portfolios. Here I examine the CVA impact on pricing in each of the three cases.

      Unsecured

      Unsecured portfolios represent the standard case for CVA as both counterparties are fully exposed to each other. In most cases, close-out netting will apply meaning that the exposure on default will be to the netted value of the portfolio. If unilateral models are used then the CVA is only calculated on the exposure to the counterparty. In theory this would give rise to asymmetry in the price obtained by both counterparties as each would only charge for the credit risk of the other and take no account of their own risk of default. It is this theoretical asymmetry that has been one of the key drivers behind the introduction of bilateral CVA models and DVA. If bilateral models are used then both counterparties can agree on the credit valuation adjustment as the two terms in the calculation, CVA and DVA, are mirror images of each other. Counterparty A calculates CVAA and DVAA, while B calculates CVAB and DVAB with the following symmetry holding:

      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.

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