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ESTIMATION OF HIGH CONDITIONAL TAIL RISK BASED ON EXPECTILE REGRESSION

Published online by Cambridge University Press:  15 February 2021

Jie Hu Open the ORCID record for Jie Hu [Opens in a new window] ,
Yu Chen Open the ORCID record for Yu Chen [Opens in a new window]  and
Keqi Tan
Jie Hu
Affiliation:
Department of Statistics and Finance, School of Management University of Science and Technology of China, Hefei, China
Yu Chen*
Affiliation:
Department of Statistics and Finance, School of Management University of Science and Technology of China, Hefei, China E-Mail: [email protected]
Keqi Tan
Affiliation:
Department of Statistics and Finance, School of Management University of Science and Technology of China, Hefei, China
*
E-Mail: [email protected]
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Abstract

Assessing conditional tail risk at very high or low levels is of great interest in numerous applications. Due to data sparsity in high tails, the widely used quantile regression method can suffer from high variability at the tails, especially for heavy-tailed distributions. As an alternative to quantile regression, expectile regression, which relies on the minimization of the asymmetric l2-norm and is more sensitive to the magnitudes of extreme losses than quantile regression, is considered. In this article, we develop a new estimation method for high conditional tail risk by first estimating the intermediate conditional expectiles in regression framework, and then estimating the underlying tail index via weighted combinations of the top order conditional expectiles. The resulting conditional tail index estimators are then used as the basis for extrapolating these intermediate conditional expectiles to high tails based on reasonable assumptions on tail behaviors. Finally, we use these high conditional tail expectiles to estimate alternative risk measures such as the Value at Risk (VaR) and Expected Shortfall (ES), both in high tails. The asymptotic properties of the proposed estimators are investigated. Simulation studies and real data analysis show that the proposed method outperforms alternative approaches.

Keywords

Quantile regressionexpectile regressionasymptoticheavy-tailed distributiontail index
Type
Research Article
Information
ASTIN Bulletin: The Journal of the IAA , Volume 51 , Issue 2 , May 2021 , pp. 539 - 570
Copyright
© 2021 by Astin Bulletin. All rights reserved

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