Nonparametric Inference for VaR, CTE, and Expectile with High-Order Precision

Abstract

Value-at-Risk and Conditional Tail Expectation are the two most frequently applied risk measures in quantitative risk management. Recently expectile has also attracted much attention as a risk measure because of its elicitability property. This article establishes empirical likelihood–based estimation with high-order precision for these three risk measures. The superiority of the estimation is justified both in theory and via simulation studies. Extensive simulation studies confirm that our method significantly improves the coverage probabilities for interval estimation of the three risk measures, compared to three competing methods available in the literature.

Acknowledgments

The authors are grateful to the two anonymous reviewers for their valuable suggestions which have led to a significant improvement of the article in both contents and organization.

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Notes

1 The authors are grateful to an anonymous referee for suggesting that we discuss this practical aspect.

Additional information

Funding

Yukun Liu acknowledges funding support from the National Natural Science Foundation of China (No. 11771144) and the Chinese Ministry of Education 111 project (No. B14019). Chengguo Weng thanks funding support from the Natural Sciences and Engineering Research Council of Canada (RGPIN-2016- 04001) and the National Natural Science Foundation of China (No. 71671104).