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

IF 4.3 3区 材料科学 Q1 ENGINEERING, ELECTRICAL & ELECTRONIC ACS Applied Electronic Materials Pub Date : 2024-10-21 DOI:10.1016/j.amc.2024.129105
Davide Trevisani, José Germán López-Salas, Carlos Vázquez, José Antonio García-Rodríguez
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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.
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资本估值调整 (KVA) 问题的数学模型和数值方法
在这项工作中,我们严格地建立了数学模型,以获得作为总估值调整(XVAs)一部分的资本估值调整(KVA)。为此,我们采用了基于市场理论的半复制策略。我们用预期和 PDEs 来制定单因素模型。对于 PDEs 的表述,我们严格获得了解的存在性和唯一性,以及解的一些规律性和定性属性。此外,我们还提出了求解相应 PDE 的适当数值方法。最后,一些实例展示了看涨和看跌欧式期权的数值结果,以及包括 KVA 的相应 XVA。
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CiteScore
7.20
自引率
4.30%
发文量
567
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