From FVA to KVA: including cost of capital in derivatives pricing

Youssef Elouerkhaoui addresses the problem of pricing derivatives with credit valuation adjustment, funding, initial margin and capital costs. By extending the fundamental funding invariance principle, he shows how to compute the capital valuation adjustment (KVA) term for an IMM bank and how to tackle the issue with nested P and Q expectations. Finally, he compares the KVA approach with the standard risk-weighted asset hurdle rate analysis

With the increased capital requirements under Basel III, capital has become the main constraint for derivatives businesses; the profitability metric used has shifted from a net revenue or a market share measure to a return on equity (ROE) measure. ROE hurdle rates are now the de facto drivers of valuation (including both Basel III risk-weighted asset (RWAs) and supplementary leverage ratios (SLRs)). This is so critical to business profitability that banks are willing to take a profit and loss (P