英文标题：
《Network Structure and Counterparty Credit Risk》
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作者：
Alexander von Felbert
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最新提交年份：
2015
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英文摘要：
  In this paper we offer a novel type of network model which can capture the precise structure of a financial market based, for example, on empirical findings. With the attached stochastic framework it is further possible to study how an arbitrary network structure and its expected counterparty credit risk are analytically related to each other. This allows us, for the first time, to model the precise structure of an arbitrary financial market and to derive the corresponding expected exposure in a closed-form expression. It further enables us to draw implications for the study of systemic risk. We apply the powerful theory of characteristic functions and Hilbert transforms. The latter concept is used to express the characteristic function (c.f.) of the random variable (r.v.) $\\max(Y, 0)$ in terms of the c.f. of the r.v. $Y$. The present paper applies this concept for the first time in mathematical finance. We then characterise Eulerian digraphs as distinguished exposure structures and show that considering the precise network structures is crucial for the study of systemic risk. The introduced network model is then 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 credit risk to clear via a central counterparty or classically bilateral between the two involved counterparties. We then show that the exact market structure is a crucial factor in answering the raised question.
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中文摘要：
在本文中，我们提供了一种新型的网络模型，可以捕捉金融市场的精确结构，例如基于实证结果。借助所附的随机框架，可以进一步研究任意网络结构及其预期的交易对手信用风险如何在分析上相互关联。这使我们首次能够对任意金融市场的精确结构进行建模，并在封闭形式的表达式中推导出相应的预期风险敞口。它进一步使我们能够对系统性风险的研究得出启示。我们应用了强大的特征函数理论和希尔伯特变换。后一个概念用于表示随机变量$\\max（Y，0）$的特征函数（c.f.），即r.v.$Y$的c.f。本文首次将这一概念应用于数学金融领域。然后，我们将欧拉有向图描述为不同的暴露结构，并表明考虑精确的网络结构对于系统性风险的研究至关重要。然后，将引入的网络模型应用于研究场外交易和集中清算市场的特征。对于通过中央交易对手或两个相关交易对手之间的典型双边交易对手清算整体交易对手信用风险是否更有利的问题，我们也给出了更一般的答案。然后，我们证明了准确的市场结构是回答上述问题的关键因素。
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分类信息：

一级分类：Quantitative Finance        数量金融学
二级分类：Mathematical Finance        数学金融学
分类描述：Mathematical and analytical methods of finance, including stochastic, probabilistic and functional analysis, algebraic, geometric and other methods
金融的数学和分析方法，包括随机、概率和泛函分析、代数、几何和其他方法
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