Before revision:  This paper formalises the addition of cost of capital by extending the Burgard-Kjaer  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 . Two approaches are considered, one where the (regulatory) capital is released back to shareholders upon counterparty default and one where the capital can be used to offset losses in the event of counterparty default  .
After revision:  This paper formalises the addition of cost of capital by extending the Burgard-Kjaer 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 and to offset losses in the event of counterparty default .