Funding, Collateral and Hedging: Uncovering the mechanics and the subtleties of funding valuation adjustments
by Andrea Pallavicini of Banca IMI, Milan,
December 13, 2012
Abstract: The main result of this paper is a collateralized counterparty valuation adjusted pricing equation, which allows to price a deal while taking into account credit and debit valuation adjustments (CVA, DVA) along with margining and funding costs, all in a consistent way. Funding risk breaks the bilateral nature of the valuation formula. We find that the equation has a recursive form, making the introduction of a purely additive funding valuation adjustment (FVA) difficult. Yet, we can cast the pricing equation into a set of iterative relationships which can be solved by means of standard least-square Monte Carlo techniques. As a consequence, we find that identifying funding costs and debit valuation adjustments is not tenable in general, contrary to what has been suggested in the literature in simple cases. The assumptions under which funding costs vanish are a very special case of the more general theory.
Keywords: Funding Cost, Cost of Funding, Bilateral Counterparty Risk, Credit Valuation Adjustment, Debit Valuation Adjustment, Collateral Modeling, Margining Cost, Close-Out, Re-hypothecation, Default Correlation, Gap Risk, Central Counterparty.