Nonlinear Valuation with XVAs: Two Converging Approaches

Damiano Brigo, Cristin Buescu, Marco Francischello, Andrea Pallavicini and Marek Rutkowski
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Cristin Buescu: Department of Mathematics, King’s College London, London WC2R 2LS, UK
Marco Francischello: Department of Mathematics, Imperial College London, London SW7 2AZ, UK
Marek Rutkowski: School of Mathematics and Statistics, University of Sydney, Sydney 2006, Australia

Mathematics, 2022, vol. 10, issue 5, 1-31

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

Keywords: risk-neutral valuation; replication; funding costs; default; collateral (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2022
References: View references in EconPapers View complete reference list from CitEc
Citations: View citations in EconPapers (1)

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