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OPTIMAL MODEL AVERAGING FOR JOINT VALUE-AT-RISK AND EXPECTED SHORTFALL REGRESSION

Published online by Cambridge University Press:  12 February 2025

Shoukun JiaoOpen the ORCID record for Shoukun Jiao[Opens in a new window],
Wenchao XuOpen the ORCID record for Wenchao Xu[Opens in a new window],
Wuyi YeOpen the ORCID record for Wuyi Ye[Opens in a new window] and
Xinyu Zhang
Shoukun Jiao
Affiliation:
University of Science and Technology of China
Wenchao Xu
Affiliation:
Shanghai University of International Business and Economics
Wuyi Ye*
Affiliation:
University of Science and Technology of China
Xinyu Zhang
Affiliation:
University of Science and Technology of China and Chinese Academy of Sciences
*
Address correspondence to Wuyi Ye, School of Management, University of Science and Technology of China, Hefei, China; e-mail: wyye@ustc.edu.cn.
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Abstract

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Since the implementation of the Basel III Accord, expected shortfall (ES) has gained increasing attention from regulators as a complement to value-at-risk (VaR). The problem of elicitability for ES makes jointly modeling VaR and ES a popular method to study ES. In this article, we develop model averaging for joint VaR and ES regression models that selects the two weight vectors by minimizing a jackknife criterion. We show the large sample properties of the estimators under potential model misspecification with increasing dimension of parameters and the asymptotic optimality of the selected weights in the sense of minimizing the out-of-sample excess final prediction error. Simulation studies and three empirical analyses reveal good finite sample performance.

Information

Type
ARTICLES
Information
Econometric Theory , Volume 42 , Issue 1 , February 2026, pp. 101 - 134
Copyright
© The Author(s), 2025. Published by Cambridge University Press

Footnotes

The authors would like to thank the Co-Editor, Viktor Todorov, and three anonymous referees for their guidance and insightful comments which substantially improved the article. S.J. and W.Y. thank research support by the National Natural Science Foundation of China (Grant No. 72371230) and the Anhui Provincial Natural Science Foundation (Grant No. 2208085J41). W.X. thanks research support by the National Natural Science Foundation of China (Grant No. 12101591). X.Z. thanks research support by the National Natural Science Foundation of China (Grant Nos. 71925007, 72091212, and 71988101).

S.J. and W.X. have contributed equally to this work and should be considered co-first authors.

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