Time-lagged marginal expected shortfall

TL;DR

This paper introduces the time-lagged marginal expected shortfall (TMES), a dynamic measure for systemic risk assessment that incorporates time delays, with a proposed estimator, bootstrap confidence intervals, and practical applications.

Contribution

It proposes TMES as a novel dynamic extension of MES, along with an estimator, asymptotic analysis, and bootstrap-based confidence intervals for systemic risk evaluation.

Findings

TMES effectively captures time-lagged systemic risk contributions.

The estimator shows desirable asymptotic properties in simulations.

Real data applications demonstrate TMES's practical utility.

Abstract

Marginal expected shortfall (MES) is an important measure when assessing and quantifying the contribution of the financial institution to a systemic crisis. In this paper, we propose time-lagged marginal expected shortfall (TMES) as a dynamic extension of the MES, accounting for time lags in assessing systemic risks. A natural estimator for the TMES is proposed, and its asymptotic properties are studied. To address challenges in constructing confidence intervals for the TMES in practice, we apply the stationary bootstrap method to generate confidence bands for the TMES estimator. Extensive simulation studies were conducted to investigate the asymptotic properties of empirical and bootstrapped TMES. Two practical applications of TMES, supported by real data analyses, effectively demonstrate its ability to account for time lags in risk assessment.