Time-lagged marginal expected shortfall

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.