Financial Networks, Cross Holdings, and Limited Liability

Posted: 17 Jul 2006 Last revised: 10 Aug 2008

See all articles by Helmut Elsinger

Helmut Elsinger

Austrian National Bank - Economic Studies Division

Date Written: February 23, 2007

Abstract

I discuss a network of banks which are linked by financial obligations and cross holdings. Given an initial endowment the value of the obligations and the equity values of the banks are determined endogenously in a way consistent with the priority of debt and the limited liability of equity. Neither equity values nor debt values are necessarily unique. But banks with non-unique equity values are ultimately owned by banks with a zero equity value. If the value of debt claims is non-unique the obligee himself is either in default or has a non-unique equity value. I derive rather mild conditions that guarantee unique equity and debt values. Due to the cross holdings equity is not necessarily a convex and debt is not necessarily a concave function of the given endowment. An algorithm to calculate debt and equity values is developed.

Keywords: Financial Network, Credit Risk, Systemic Risk

JEL Classification: G21, G33

Suggested Citation

Elsinger, Helmut, Financial Networks, Cross Holdings, and Limited Liability (February 23, 2007). Available at SSRN: https://ssrn.com/abstract=916763

Helmut Elsinger (Contact Author)

Austrian National Bank - Economic Studies Division ( email )

POB 61
Vienna, A-1011
Austria

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