Funding, Collateral and Hedging: Arbitrage-Free Pricing with Credit, Collateral and Funding Costs

Andrea Pallavicini, Daniele Perini and Damiano Brigo

This chapter refines the original comprehensive valuation framework introduced in Pallavicini et al (2011), in which we discuss a collateralised counterparty valuation adjusted pricing equation, which allows us to price a deal while consistently taking into account credit and debit valuation adjustments (CVA and DVA) and margining and funding costs. Since 2011 the literature has grown considerably, as the understanding of funding costs and their relationship with credit risk has evolved. Here, we review the results of Pallavicini et al (2011), one of the first papers on the subject, to illustrate the initial stages of this research, though we do not aim to compare these results with more recent literature; we refer the reader to Brigo et al (2013) for a discussion of the literature prior to 2013, and to other chapters in the present volume for the latest developments.

Funding costs are linked to collateral modelling, which in turn has a strong impact on CVA and DVA, so an arbitrage-free pricing framework cannot include these effects separately. An initial stylised analysis of the problem of replicating derivative transactions under collateralisation but without default risk and