Paper: arXiv 2304.05794

Authors: Luka Klinčić, Vinko Zlatić, Guido Caldarelli, Hrvoje Štefančić

Abstract

The study of systemic risk is often presented through the analysis of several measures referring to quantities used by practitioners and policy makers. Almost invariably, those measures evaluate the size of the impact that exogenous events can exhibit on a financial system without analysing the nature of initial shock. Here we present a symmetric approach and propose a set of measures that are based on the amount of exogenous shock that can be absorbed by the system before it starts to deteriorate. For this purpose, we use a linearized version of DebtRank that allows to clearly show the onset of financial distress towards a correct systemic risk estimation. We show how we can explicitly compute localized and uniform exogenous shocks and explained their behavior though spectral graph theory. We also extend analysis to heterogeneous shocks that have to be computed by means of Monte Carlo simulations. We believe that our approach is more general and natural and allows to express in a standard way the failure risk in financial systems.

Complexity vs Empirical Score

  • Math Complexity: 7.5/10
  • Empirical Rigor: 4.5/10
  • Quadrant: Lab Rats — theoretically deep, empirically untested

Why this score: The paper introduces an innovative, inverted perspective on DebtRank by evaluating the threshold of exogenous shocks a system can absorb before distress using spectral graph theory. While the mathematical framework and theoretical formulation are strong, the paper relies heavily on simulations (Monte Carlo) rather than extensive empirical validation on real-world interbank networks.

Research Flowchart

  flowchart TD
    A[Goal: Measure Systemic Risk via Absorption Capacity of Initial Shocks] --> B[Input: Multi-Asset Financial Network Data]
    B --> C[Method: Apply Linearized DebtRank Model]
    C --> D1[Analytical Math: Compute Localized & Uniform Shocks via Spectral Graph Theory]
    C --> D2[Simulation: Compute Heterogeneous Shocks via Monte Carlo Methods]
    D1 --> E[Outcome: Standardized Metric for Systemic Resiliency & Onset of Distress]
    D2 --> E