Pricing of debt and equity in a financial network with comonotonic endowments

TL;DR

This paper develops formulas for valuing debt and equity in interconnected financial networks with comonotonic endowments, providing bounds and stress testing tools, and compares network valuation with single-firm heuristics.

Contribution

It introduces new valuation formulas under comonotonic endowments, deriving bounds and stress testing methods for financial networks with bankruptcy costs.

Findings

Comonotonic setting provides a lower bound for debt prices.

Jensen's inequality offers an upper bound for debt prices.

Numerical comparisons show differences between network valuation and single-firm heuristics.

Abstract

In this paper we present formulas for the valuation of debt and equity of firms in a financial network under comonotonic endowments. We demonstrate that the comonotonic setting provides a lower bound and Jensen's inequality provides an upper bound to the price of debt under Eisenberg-Noe financial networks with bankruptcy costs. Such financial networks encode the interconnection of firms through debt claims. The proposed pricing formulas consider the realized, endogenous, recovery rate on debt claims. Special consideration is given to the CAPM setting in which firms invest in correlated portfolios so as to provide analytical stress testing formulas. We endogenously construct the comonotonic endowment setting from a equity maximizing standpoint with capital transfers. We conclude by, numerically, comparing the network valuation problem with two single firm baseline heuristics which can, respectively, approximate the price of debt and equity.