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

Trevisani, Davide; López-Salas, José Germán; Vázquez, Carlos; García Rodríguez, José Antonio

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http://hdl.handle.net/2183/39723

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

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LopezSalas_JoseGerman_2024_Mathematical_models_and_numerical_methods_for_a_capital_valuation_adjustment_KVA_problem.pdf (1.13 MB)

Identifiers

URI: http://hdl.handle.net/2183/39723

DOI: 10.1016/j.amc.2024.129105

Publication date

2025-03

Authors

Trevisani, Davide

López-Salas, José Germán

Vázquez, Carlos

García Rodríguez, José Antonio

Bibliographic citation

D. Trevisani, J. G. López-Salas, C. Vázquez, and J. A. García-Rodríguez, "Mathematical models and numerical methods for a capital valuation adjustment (KVA) problem", Applied Mathematics and Computation, Vol. 488, 1 March 2025, 129105, https://doi.org/10.1016/j.amc.2024.129105

Abstract

[Abstract]: 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.