KVA: Capital Valuation Adjustment

Risk, December 2014

25 Pages Posted: 24 Feb 2014 Last revised: 6 Nov 2014

See all articles by Andrew David Green

Andrew David Green


Chris Kenyon

MUFG Securities EMEA plc; University College London

Chris Dennis

Lloyds Banking Group

Date Written: October 23, 2014


Credit (CVA), Debit (DVA) and Funding Valuation Adjustments (FVA) are now familiar valuation adjustments made to the value of a portfolio of derivatives to account for credit risks and funding costs. However, recent changes in the regulatory regime and the increases in regulatory capital requirements has led many banks to include the cost of capital in derivative pricing. This paper formalises the addition of cost of capital by extending the Burgard-Kjaer (2013) semi-replication approach to CVA and FVA to include an addition capital term, Capital Valuation Adjustment (KVA). The utilization of the capital for funding purposes is also considered. The use of the semi-replication approach means that the exibility around the treatment of self-default is carried over into this analysis. The paper further considers the practical calculation of KVA with reference to the Basel II (BCBS-128 2006) and Basel III (BCBS-189 2011) capital regimes and their implementation via CRD IV (EU 2013b; EU 2013a). The paper also assesses how KVA may be hedged, given that any hedging transactions themselves lead to regulatory capital requirements and hence capital costs. Finally a number of numerical examples are presented to gauge the cost impact of KVA on vanilla derivative products.

Keywords: Capital, Pricing, Regulation, Basel II, Basel III, Derivative Valuation, xVA, CVA, DVA, FVA, FCA, KVA

JEL Classification: E22, G11, G12, G13, G18, G21, G28, G31, G38, H77, K23, L51, M20, M41

Suggested Citation

Green, Andrew David and Kenyon, Chris and Dennis, Chris, KVA: Capital Valuation Adjustment (October 23, 2014). Risk, December 2014, Available at SSRN: https://ssrn.com/abstract=2400324 or http://dx.doi.org/10.2139/ssrn.2400324

Andrew David Green (Contact Author)

Scotiabank ( email )

201 Bishopsgate
London, London EC2M 3NS
United Kingdom

Chris Kenyon

MUFG Securities EMEA plc ( email )

25 Ropemaker St
London, EC2Y 9AJ
United Kingdom

University College London ( email )

Gower Street
London, WC1E 6BT
United Kingdom

Chris Dennis

Lloyds Banking Group ( email )

10 Gresham Street
London, EC2V 7AE
United Kingdom

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