also be a DVA benefit term. The same expected exposure will give rise to FVA. The lifetime cost of maintaining regulatory capital, KVA, will also be included, although this might be a hurdle rate or minimum return level rather than a cash amount.
CSA Pricing
• Risk-neutral valuation: CSA-based (OIS) discounting
• Hedging/Management costs
• Residual CVA (including impact of collateralisation)
• Residual FVA (including impact of collateralisation)
• COLVA/Collateral effects
• KVA
• Bilateral Initial Margin MVA
• Profit.
For trades covered by a CSA the baseline risk-neutral valuation will be discounted using a curve appropriate to the terms of the CSA. Given that the CSA is imperfect in the sense that the collateral transferred to support the mark-to-market of the trade is done on a discrete periodic basis rather than a continuous basis, a residual counterparty exposure will remain. This residual exposure leads to residual CVA and residual FVA. There may also be a COLVA adjustment to account for collateral effects in pricing that cannot be captured by a discounting approach such as collateral optionality. Capital must be held against collateralised portfolios and this gives rise to KVA, although the presence of collateral significantly reduces the amount of capital that must be held through the counterparty credit risk and CVA capital terms. The leverage ratio comes into importance here, however, as while collateral reduces the CCR and CVA terms, it has a restricted impact on the leverage ratio. Market risk capital will be held unless there are other market risk offsetting trades. Hedging and trading desk management costs should again be charged as should the profit margin. Under BCBS 226 (2012e) and BCBS 242 (2013e), trades supported by CSA agreements will also require bilateral initial margin to be held in a similar way to the way that CCP initial margin requirements operate.
CCP Pricing
• Risk-neutral valuation: CCP methodology including CCP discount curves
• Hedging/Management costs
• Residual CVA (including impact of variation margin)
• Residual FVA (including impact of variation margin)
• COLVA/Collateral effects
• KVA
• Initial margin
• Liquidity buffers
• Default fund
• Profit.
For trades cleared through a CCP the components of a price include similar components to those of a trade supported by a CSA agreement. Residual exposure above the collateral provided as variation margin gives rise to CVA and FVA as with CSA pricing. Hedging and trading management costs are the same as is the addition of a profit margin. The lifetime cost of capital is also present although the risk-weight applied to qualifying CCPs is the relatively low value of 2 % (BCBS, 2012c). As with CSA pricing a COLVA adjustment may be needed. In addition to variation margin, three other payments are often made to CCPS: initial margin, liquidity buffers and default fund contributions. The initial margin is designed to cover exposure that might arise due to market movements during a close-out period and hence prevent loss should a counterparty subsequently default. Liquidity buffers can also be applied if the risk position of a CCP member is large. All CCP clearing members are required to post default fund contributions which are designed to be used in the event of the default of a CCP member.
1.3.2 Risk-Neutral Valuation
In all three of the cases studied in section 1.3.1 a baseline risk-neutral valuation model is still used. The risk-neutral valuation is the value as seen by the derivative trader and is the value this trader is tasked with hedging. Normally this trader will be an asset-class specialist with experience of hedging in the markets underlying the derivative and so this is where the majority of the market risk on the trade is managed. The risk-neutral trade level valuation makes the usual assumptions of no credit or funding risk so in effect this valuation assumes that a perfect CSA agreement is in place. However, in general the choice of discounting curve varies depending on the arrangements under which the derivative has been traded.
Unsecured
The choice of discount curve is still a matter of debate in the industry and depends on internal factors. Many banks have left the baseline valuation of unsecured trades using xIBOR-based discounting models (Solum Financial Partners, 2014). In many cases this will be exactly the same multi-currency discounting model that was prevalent before the credit crisis, typically where all other currencies had cross-currency basis quoted against the US dollar interest rates. Other choices are also possible including OIS discounting. The choice may be made to use a single currency discount curve for all unsecured trades, say for example Fed Funds. A further alternative might be to allow single currency derivatives to be discounted using the appropriate OIS curve for that currency and treat multi-currency trades differently. This has the advantage that single currency trading books would not be exposed to any cross-currency effects. If the bank elects to use funding discounting models for unsecured trades, then the discount rate will be the bank’s internal cost of funds curve. The possible choices and motivating factors are listed in Table 1.2.
Table 1.2 The possible choices of discounting for the baseline risk-neutral valuation of unsecured derivative trades.
The choice of discounting depends on three key factors: organisational design, internal bank modelling of funding costs and the expected reference close-out in the event of default. Note that this reflects the practical reality of what happens in banks rather than theoretical correctness of any models used.
Organisation design
Organisational design4 determines which trading desks manage which risks. Broadly there are two main choices; either each individual trading desk manages their own funding (distributed model) or there is a central management desk for funding (centralised model). In the distributed model each trading desk will need to know the funding impact of all unsecured trades on their book. This would most likely be done using a funding discounting approach, although other models could be used. In the centralised model the asset-class trading desks will either wish to measure the funding risk and lay it off with the central desk or not be exposed to it at all. If the asset-class desks hedge out funding risks with the central desk then they will measure the funding cost and hedge it out through funding basis swaps, otherwise the asset-class desk would value all their unsecured trades either at xIBOR or OIS and be oblivious to funding considerations, with the central funding desk calculating and managing FVA directly.
Bank models of funding costs
The bank model of funding costs also plays a role in determining the choice of discounting for unsecured trades. As will be discussed at length in Chapter 9 there are broadly two types of model for FVA, discounting approaches and exposure-based approaches. Discounting approaches simply adjust the discount curve, while exposure-based approaches use models similar to those used for CVA. Discounting-based approaches simply adjust the risk-neutral valuation by using the cost of funds as the discount rate and hence the risk-neutral valuation. Exposure-based approaches apply FVA as an adjustment to the portfolio valuation in the same way as CVA so the underlying risk-neutral
