Optimal Clearing Payments in a Financial Contagion Model

IF 1.4 4区经济学 Q3 BUSINESS, FINANCE

SIAM Journal on Financial Mathematics Pub Date : 2024-06-03 DOI:10.1137/22m150294x

Giuseppe C. Calafiore, Giulia Fracastoro, Anton V. Proskurnikov

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Abstract

SIAM Journal on Financial Mathematics, Volume 15, Issue 2, Page 473-502, June 2024.
Abstract.Financial networks are characterized by complex structures of mutual obligations. These obligations are fulfilled entirely or in part (when defaults occur) via a mechanism called clearing, which determines a set of payments that settle the claims by respecting rules such as limited liability, absolute priority, and proportionality (pro-rated payments). In the presence of shocks on the financial system, however, the clearing mechanism may lead to cascaded defaults and eventually to financial disaster. In this paper, we first study the clearing model under pro-rated payments of Eisenberg and Noe, and we derive novel necessary and sufficient conditions for the uniqueness of the clearing payments, valid for an arbitrary topology of the financial network. Next, we observe that the proportionality rule is a factor that potentially concurs to the cascaded defaults effect, and that the aggregated systemic loss can be reduced if this rule is lifted. We thus shift the focus from the individual interest to the overall systemic interest to contain the adverse effects of cascaded failures, and we show that pro-rate-free clearing payments can be computed uniquely by solving suitable convex optimization problems.

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金融疫情模型中的最优清算支付

SIAM 金融数学期刊》，第 15 卷，第 2 期，第 473-502 页，2024 年 6 月。摘要：金融网络的特点是相互义务的复杂结构。这些义务通过一种称为清算的机制来全部或部分履行（当违约发生时），该机制通过遵守有限责任、绝对优先权和比例（按比例支付）等规则来确定一系列支付，以清偿债权。然而，在金融体系受到冲击的情况下，清算机制可能会导致连锁违约，并最终引发金融灾难。在本文中，我们首先研究了艾森伯格和诺伊的按比例支付下的清算模型，并推导出了新的清算支付唯一性的必要条件和充分条件，这些条件对金融网络的任意拓扑结构都有效。接下来，我们发现比例规则是可能导致连带违约效应的一个因素，如果取消这一规则，系统性损失的总量就会减少。因此，我们将关注点从个人利益转移到整体系统利益，以遏制连带违约的不利影响，并证明通过求解合适的凸优化问题，可以唯一计算出无比例清算付款。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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来源期刊

SIAM Journal on Financial Mathematics MATHEMATICS, INTERDISCIPLINARY APPLICATIONS-

CiteScore

2.30

自引率

10.00%

发文量

期刊介绍： SIAM Journal on Financial Mathematics (SIFIN) addresses theoretical developments in financial mathematics as well as breakthroughs in the computational challenges they encompass. The journal provides a common platform for scholars interested in the mathematical theory of finance as well as practitioners interested in rigorous treatments of the scientific computational issues related to implementation. On the theoretical side, the journal publishes articles with demonstrable mathematical developments motivated by models of modern finance. On the computational side, it publishes articles introducing new methods and algorithms representing significant (as opposed to incremental) improvements on the existing state of affairs of modern numerical implementations of applied financial mathematics.