  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, i.e. Kapital Valuation Adjustment to
distinguish from CVA.) The utilization of the capital for funding purposes is
also considered. The use of the semi-replication approach means that the
flexibility 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) and Basel III (BCBS-189) capital regimes
and their implementation via CRD IV. 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.
