Mathematical models and numerical methods for a capital valuation adjustment (KVA) problem

In this work we rigorously establish mathematical models to obtain the capital valuation adjustment (KVA) as part of the total valuation adjustments (XVAs). For this purpose, we use a semi-replication strategy based on market theory. We formulate single-factor models in terms of expectations and PDE...

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Bibliographic Details
Published in:arXiv.org 2024-10
Main Authors: Trevisani, D, López-Salas, J G, Vázquez, C, García-Rodríguez, J A
Format: Article
Language:English
Subjects:
Numerical methods
Partial differential equations
Online Access:Get full text
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Summary:In this work we rigorously establish mathematical models to obtain the capital valuation adjustment (KVA) as part of the total valuation adjustments (XVAs). For this purpose, we use a semi-replication strategy based on market theory. We formulate single-factor models in terms of expectations and PDEs. For PDEs formulation, we rigorously obtain the existence and uniqueness of the solution, as well as some regularity and qualitative properties of the solution. Moreover, appropriate numerical methods are proposed for solving the corresponding PDEs. Finally, some examples show the numerical results for call and put European options and the corresponding XVA that includes the KVA.
ISSN:2331-8422
DOI:10.48550/arxiv.2410.16825