BILATERAL CONTRACTS UNDER XVA

Abstract

We deal with bilateral contracts under XVA with emphasis on issues of funding value adjustment (FVA). First, we discuss a binary nature of funding impacts. Under some conditions, funding is either cost or benefit. Once we can guarantee that only one of the rates affects pricing, we can recover linear equations and derive analytic formulae. Moreover, as a byproduct, our results explain how debt value adjustment (DVA) and funding benefits are different. Second, we introduce a risk-sharing framework for bilateral contracts to find the optimal pair, initial price and amount of collateral. The derived optimal collateral can be used for contracts between financial firms and non-financial firms. For inter-dealers contracts, which are governed by regulations, the optimal collateral can interpret circumstances where the margin requirement is indeed optimal. We will see that absence of market frictions is an inherent assumption for the margin requirement in Basel III.