E-backtesting

58 Pages Posted: 22 Sep 2022

See all articles by Qiuqi Wang

Qiuqi Wang

University of Waterloo - Department of Statistics and Actuarial Science

Ruodu Wang

University of Waterloo - Department of Statistics and Actuarial Science

Johanna Ziegel

University of Bern

Date Written: September 1, 2022

Abstract

In the recent Basel Accords, the Expected Shortfall (ES) replaces the Value-at-Risk (VaR) as the standard risk measure for market risk in the banking sector, making it the most important risk measure in financial regulation. One of the most challenging tasks in risk modeling practice is to backtest ES forecasts provided by financial institutions. Ideally, backtesting should be done based only on daily realized portfolio losses without imposing specific models. Recently, the notion of e-values has gained attention as potential alternatives to p-values as measures of uncertainty, significance and evidence. We use e-values and e-processes to construct a model-free backtesting procedure for ES using a concept of universal e-statistics, which can be naturally generalized to many other risk measures and statistical quantities.

Keywords: E-values, e-processes, Expected Shortfall, Value-at-Risk, martingales

Suggested Citation

Wang, Qiuqi and Wang, Ruodu and Ziegel, Johanna, E-backtesting (September 1, 2022). Available at SSRN: https://ssrn.com/abstract=4206997 or http://dx.doi.org/10.2139/ssrn.4206997

Qiuqi Wang (Contact Author)

University of Waterloo - Department of Statistics and Actuarial Science ( email )

Waterloo, Ontario N2L 3G1
Canada

Ruodu Wang

University of Waterloo - Department of Statistics and Actuarial Science ( email )

Waterloo, Ontario N2L 3G1
Canada

Johanna Ziegel

University of Bern

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