Individual and flexible expected shortfall backtesting

Marcelo Brutti Righi and Paulo Sergio Ceretta

Journal of Risk Model Validation

Abstract: ABSTRACT In this paper we propose an expected shortfall (ES) backtesting approach that uses the dispersion of a truncated distribution by the estimated value-at-risk (VaR) upper limit, does not limit the approach to the Gaussian case and allows us to test if each individual VaR violation is significantly different from the ES. Moreover, we present a Monte Carlo simulation algorithm to determine the significance of the backtest. We provide an empirical illustration that demonstrates the advantages that our backtests provide, especially the fact that there is no need to wait for a whole backtest period in order to prove the prediction that the ES test is inefficient.

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