Estimation of Systemic Shortfall Risk Measure using Stochastic Algorithms

TL;DR

This paper develops stochastic algorithms to estimate systemic shortfall risk measures, demonstrating their consistency, asymptotic normality, and effectiveness through numerical testing on various examples.

Contribution

It introduces stochastic algorithms for estimating systemic risk measures and proves their statistical properties, addressing a gap in numerical methods for this area.

Findings

Algorithms are consistent and asymptotically normal.

Numerical tests show effective estimation of systemic risk.

Provides practical tools for risk assessment in interconnected financial systems.

Abstract

Systemic risk measures were introduced to capture the global risk and the corresponding contagion effects that is generated by an interconnected system of financial institutions. To this purpose, two approaches were suggested. In the first one, systemic risk measures can be interpreted as the minimal amount of cash needed to secure a system after aggregating individual risks. In the second approach, systemic risk measures can be interpreted as the minimal amount of cash that secures a system by allocating capital to each single institution before aggregating individual risks. Although the theory behind these risk measures has been well investigated by several authors, the numerical part has been neglected so far. In this paper, we use stochastic algorithms schemes in estimating MSRM and prove that the resulting estimators are consistent and asymptotically normal. We also test numerically the performance of these algorithms on several examples.