Nonlinear Valuation with XVAs: Two Converging Approaches

When pricing OTC contracts in the presence of additional risk factors and costs, such as credit funding collateral starting “clean price” is modified additively by valuation adjustments (XVAs) that account for each factor or cost isolation, while seemingly ignoring combined effects. Instead, costs can be jointly accounted ab initio mechanism at level cash flows, this “adjusted flow" approach leads to a nonlinear formula. While practitioners made more sense because it showed which discount used flow (recall multi-curve environment post-crisis), academics, focus was on checking resulting formula consistent with theoretical arbitrage-free “replication approach” we also analyse paper. We formulate specific reasonable assumptions, ensure formulae obtained two approaches coincide, thus reinforcing both academics’ practitioners’ confidence adopting setup.