XVA. Green Andrew

under other CSAs.

      CCP – Variation Margin

      Given the degree of overcollateralisation for trades cleared through CCPs any residual exposure is likely to be small to zero. With this in mind the FVA component due to a mismatch between valuation and variation margin is likely to be close to zero.

      Other Sources of FVA

      Central counterparties also require that initial margin be posted in addition to variation margin. Large net risk positions can give risk to volatility buffers and all members of the CCP are required to contribute to a default fund that will be used to cover any losses in the event of the default of a member. All of this additional collateral needs to be funded through unsecured borrowing and hence gives rise to Margin Valuation Adjustment (MVA). Modelling the exposure at future times arising from these collateral buffers is complex. Initial margin is generally calculated using VaR models which means estimating expected future VaR. The volatility buffers use risk multipliers based on estimates of market depth so that large risk positions that cannot be quickly closed are penalised. The default fund, in the case of LCH, is based on all positions of all clearing members and so is very difficult to estimate as the positions of other members are unknown. In addition the methodology used by central counterparties is not always public, making models difficult to build.

      The Basel Committee proposal on bilateral margin for financial counterparties BCBS 226 (2012h) and BCBS 242 (2013e) would similarly give rise to a funding requirement to maintain the initial margin collateral buffer.

      Regulatory liquidity frameworks including FSA047/048 as applied in the UK (Financial Conduct Authority, 2014, section 12) and the liquidity framework under Basel III (BCBS, 2013b) also require the maintenance of an internal liquidity buffer to protect an institution from outflow in the event of a credit downgrade. This liquidity buffer has to be held in liquid assets by the bank against a two-notch downgrade of long-term rating by credit rating agencies. Many CSAs and ISDAs contain provisions for additional collateral in the event one or more rating agencies downgrade the counterparty below certain certain rating levels. In addition non-derivative products such as deposits may contain provisions to allow the counterparty to withdraw the deposit if the bank's credit rating falls below a certain level. The liquidity buffer must be funded through unsecured borrowing and hence is a type of FVA. Trades with counterparties that have embedded downgrade triggers in their documentation should include the cost of funding any additional liquidity buffer in the price of a new transaction.

      1.3.6 Regulatory Capital and KVA

      Under the Basel III framework (BCBS, 2011b) there are three key contributors to regulatory capital requirements:

      • Market risk

      • Counterparty Credit Risk (CCR)

      • Regulatory CVA.

      In addition some transactions will be subject to other capital provisions through Specific Risk, Incremental Risk Charge (IRC) and Wrong-way Risk. The incremental cost of capital due to a new trade is significant and has to be included in the price of a new derivative. This is not a funding cost, however, as there is no requirement to hold collateral or an asset return, rather there is a requirement to hold shareholders’ capital against the risk of loss on the derivative portfolio. This capital is not free and shareholders require a return on this capital. Often bank management will state a target return on capital or direct staff within the bank to accept transactions that exceed a minimum return on capital. The Basel framework requires an amount of capital to be held based on the application of the capital rules to the current portfolio, giving a spot capital requirement.9 However, the spot capital requirement is not necessarily a good measure of the expected capital requirement throughout the life of a transaction. An interest rate swap, for example, will be entered at close to zero value but will then diverge away from it, given additional CCR and CVA capital requirements during its lifetime. Hence the cost that needs to be priced into to new derivatives is the lifetime cost of capital which measures the cost of all future capital requirements. Part III discusses approaches to how this lifetime cost of capital can be estimated.

      Once we have a measure of the lifetime cost of capital, KVA, then new transactions can be priced in such a way as to achieve the desired minimum profit to achieve the desired return for shareholders. However, this will not remain constant as market moves can lead to higher or lower capital requirements. Both the CCR and CVA terms are driven by the portfolio mark-to-market and so the lifetime cost of capital will have market risk sensitivities in a similar way to CVA and FVA. This leads to the question as to whether or not capital can be managed in a manner similar to CVA and FVA. It certainly can be managed passively through managing the back book of trades through novation and trade cancellation. Counterparties with large trade portfolios between them may find that capital as well as operational costs and risks can be reduced through compression trades that seek to replace a large portfolio with a smaller number of trades with the same risk profile. Active management of the CVA and CCR terms is embedded into Basel III through the capital mitigation that is available from the use of single name and index CDS trades to hedge counterparty risk. In theory trades could be used to hedge the market risk sensitivities of the lifetime cost of capital. Such trades would be in place to generate retained profits at exactly the time additional capital would be needed. In reality, however, these transactions would likely attract additional capital themselves making hedging involve iteration/optimisation rather than simply constructing a trade to offset the risk directly.

One further point to note here is that the amount of capital required depends on the regulatory approvals that the institution has in place. For each of three main contributors to regulatory capital listed above, the calculation method depends on status, with more advanced institutions allowed to use internal modelling subject to appropriate approvals and oversight. The different approaches are illustrated in Figure 1.1.

Figure 1.1 The different calculation methodologies available for market risk, counterparty credit risk and CVA under the Basel III framework. The more complex methodologies requiring regulatory approval are lower down the figure.

      It should be immediately clear that regulatory capital will not be the same for all market participants because the methodology in use in each institution is different. The cost of capital of each institution will also be different as each will set individual target returns. Even in the absence of book-specific effects, such as netting, the cost of capital embedded in the derivative price can be significantly different between different banks.

      Regulatory uncertainty and regulatory divergence are also major issues. Further regulatory proposals have been made by the Basel Committee and more will be made in the future. For example, under the “ review of the trading book” fundamental (2012g; 2013c) major changes will be made to the market risk capital framework, with the standardised approach revised and changes to IMM including a switch to expected shortfall from VaR. The two non-IMM approaches to counterparty credit risk will be replaced in 2017 with the standardised approach (BCBS, 2014b). The cost of future regulation is unknown but it will certainly apply to long-dated derivatives that are transacted today.

      1.4 Post-Crisis Derivative Valuation or How I Learned to Stop Worrying and Love FVA

      1.4.1 The FVA Debate and the Assault on Black-Scholes-Merton

      As noted earlier, bank CDS spreads were very narrow prior to the start of the credit crisis in 2007. AA or better rated banks were able to fund themselves at the rate implied by the LIBOR discounting curve or in some cases below. FVA adjustments were not made as they were not needed. After the default of Lehman brothers as credit spreads widened sharply so did funding costs. The spread between overnight rates and rates of longer tenors widened significantly with the US Dollar OIS-3M LIBOR spread reaching 365bp just after the collapse of Lehman Brothers in September 2008 (Sengupta and Tam, 2008). Unsecured funding costs became very significant for the first time in the history of derivative markets.

      Initially unsecured

9

Note that sometimes this spot capital requirement is referred to in terms of RWA or Risk-Weighted Assets as this is the regulatory asset value against which the capital must be held. In reality the Basel framework is written partially in terms of RWA and partly in terms of direct capital requirements but RWA is frequently used in finance as a shorthand way of describing all capital requirements.