No-arbitrage pricing under cross-ownership

TL;DR

This paper extends Merton's asset valuation model to systems of interconnected firms with cross-ownership, deriving no-arbitrage prices for equities and liabilities, and analyzing systemic risk implications.

Contribution

It introduces a generalized framework for no-arbitrage pricing in cross-ownership systems, including existence, uniqueness, and computational algorithms.

Findings

Derived equations for equity and liability prices under cross-ownership.

Proved existence and uniqueness of solutions for the pricing equations.

Discussed implications for systemic risk and capital structure irrelevance.

Abstract

We generalize Merton's asset valuation approach to systems of multiple financial firms where cross-ownership of equities and liabilities is present. The liabilities, which may include debts and derivatives, can be of differing seniority. We derive equations for the prices of equities and recovery claims under no-arbitrage. An existence result and a uniqueness result are proven. Examples and an algorithm for the simultaneous calculation of all no-arbitrage prices are provided. A result on capital structure irrelevance for groups of firms regarding externally held claims is discussed, as well as financial leverage and systemic risk caused by cross-ownership.