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Nonlinear valuation with XVAs: two converging approaches

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Title: Nonlinear valuation with XVAs: two converging approaches
Authors: Brigo, D
Buescu, C
Francischello, M
Pallavicini, A
Rutkowski, M
Item Type: Journal Article
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.
Issue Date: 2-Mar-2022
Date of Acceptance: 26-Feb-2022
URI: http://hdl.handle.net/10044/1/95964
DOI: 10.3390/math10050791
ISSN: 2227-7390
Publisher: MDPI
Journal / Book Title: Mathematics
Volume: 10
Issue: 5
Copyright Statement: © 2022 by the authors. This is an open access article distributed under the Creative Commons Attribution License which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited
Sponsor/Funder: Engineering and Physical Sciences Research Council
Funder's Grant Number: EPSRC Mathematics Platform Grant EP/I019111/1
Publication Status: Published
Online Publication Date: 2022-03-02
Appears in Collections:Financial Mathematics

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