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CHAPTER 1
Introduction: The Valuation of Derivative Portfolios
1.3 Trade Economics in Derivative Pricing
1.3.1 The Components of a Price

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Table 1.1 illustrates the components of pricing before and after the financial crisis of 2007–2009. Not all of these components apply to all trades and to understand the terms under which a derivative is transacted it is useful to divide counterparties into three types: unsecured, CSA and CCP. Of course, in reality the range of counterparty arrangements is a continuum between unsecured and an idealised CSA with full instantaneous transfer of collateral but it is useful to separate them for the purpose of this discussion. Each of these three cases will have different pricing components.

Unsecured Pricing

• Risk-neutral valuation

• Hedging/management costs

• CVA

• FVA

• KVA

• Profit (Tax/TVA).

For trades that are unsecured the components of the price begin with the baseline risk-neutral valuation, although there remains industry debate about the appropriate choice of discount curve for this, with both OIS and xIBOR-based discount curves used in the market. Hedging and trading desk management costs should be charged and this includes effects such as bid-offer, lifetime re-hedging costs and cost of supporting infrastructure such as system maintenance and staff. A profit margin will also typically be charged. Given there is no collateral to mitigate the exposure to the counterparty, CVA will be calculated based on the full expected exposure profile. If a bilateral CVA model is used there will 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.

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