Valuation Algorithms for Structural Models of Financial Interconnectedness

TL;DR

This paper compares valuation algorithms for interconnected financial systems, introduces new finite-step algorithms for exact solutions, and evaluates their efficiency through simulations across various system designs.

Contribution

It develops a class of new algorithms that find exact solutions in finitely many steps, improving computational efficiency in structural models.

Findings

New algorithms achieve exact solutions in finite steps.

Simulation results compare efficiency of methods under different parameters.

Insights into algorithm performance for various financial system structures.

Abstract

Much research in systemic risk is focused on default contagion. While this demands an understanding of valuation, fewer articles specifically deal with the existence, the uniqueness, and the computation of equilibrium prices in structural models of interconnected financial systems. However, beyond contagion research, these topics are also essential for risk-neutral pricing. In this article, we therefore study and compare valuation algorithms in the standard model of debt and equity cross-ownership which has crystallized in the work of several authors over the past one and a half decades. Since known algorithms have potentially infinite runtime, we develop a class of new algorithms, which find exact solutions in finitely many calculation steps. A simulation study for a range of financial system designs allows us to derive conclusions about the efficiency of different numerical methods under different system parameters.