In this paper, we offer a network model that derives the expected counterparty risk of an arbitrary market after netting in a closed-form expression. Graph theory is used to represent market participants and their relationship among each other. We apply the powerful theory of characteristic functions (c.f.) and Hilbert transforms to determine the expected counterparty risk. The latter concept is used to express the c.f. of the random variable (r.v.) [Formula: see text] in terms of the c.f. of the r.v. [Formula: see text]. This paper applies this concept for the first time in mathematical finance in order to generalize results of Duffie & Zhu (2011), in several ways. The introduced network model is applied to study the features of an over-the-counter and a centrally cleared market. We also give a more general answer to the question of whether it is more advantageous for the overall counterparty risk to clear via a central counterparty or classically bilateral between the two involved counterparties.

中文翻译：

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清算网络中的交易对手信用风险

在本文中，我们提供了一个网络模型，该模型在以封闭式表达式进行净额计算后得出任意市场的预期交易对手风险。图论用于表示市场参与者及其相互之间的关系。我们应用强大的特征函数 (cf) 和希尔伯特变换理论来确定预期的交易对手风险。后一个概念用于根据 rv [公式：见文本] 的 cf 来表示随机变量 (rv) [公式：见文本] 的 cf。本文首次将这一概念应用于数学金融，以便从几个方面概括 Duffie & Zhu (2011) 的结果。引入的网络模型用于研究场外交易和集中清算市场的特征。