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Expected shortfall (ES), also known as conditional value-at-risk, is a widely recognized risk measure that complements value-at-risk by capturing tail-related risks more effectively. Compared with quantile regression, which has been…

Methodology · Statistics 2025-11-13 Myeonghun Yu , Kean Ming Tan , Huixia Judy Wang , Wen-Xin Zhou

Expected Shortfall (ES), also known as superquantile or Conditional Value-at-Risk, has been recognized as an important measure in risk analysis and stochastic optimization, and is also finding applications beyond these areas. In finance, it…

Methodology · Statistics 2022-12-13 Xuming He , Kean Ming Tan , Wen-Xin Zhou

We propose an $\ell_1$-penalized estimator for high-dimensional models of Expected Shortfall (ES). The estimator is obtained as the solution to a least-squares problem for an auxiliary dependent variable, which is defined as a…

Econometrics · Economics 2024-01-25 Sander Barendse

To provide a comprehensive summary of the tail distribution, the expected shortfall is defined as the average over the tail above (or below) a certain quantile of the distribution. The expected shortfall regression captures the…

Methodology · Statistics 2026-02-24 Yuanzhi Li , Shushu Zhang , Xuming He

We introduce a novel regression framework which simultaneously models the quantile and the Expected Shortfall (ES) of a response variable given a set of covariates. This regression is based on a strictly consistent loss function for the…

Statistics Theory · Mathematics 2020-08-13 Timo Dimitriadis , Sebastian Bayer

Expected shortfall is defined as the average over the tail below (or above) a certain quantile of a probability distribution. Expected shortfall regression provides powerful tools for learning the relationship between a response variable…

Methodology · Statistics 2025-01-03 Shushu Zhang , Xuming He , Kean Ming Tan , Wen-Xin Zhou

A new semi-parametric Expected Shortfall (ES) estimation and forecasting framework is proposed. The proposed approach is based on a two-step estimation procedure. The first step involves the estimation of Value-at-Risk (VaR) at different…

Risk Management · Quantitative Finance 2021-03-16 Giuseppe Storti , Chao Wang

Expected Shortfall (ES) in several variants has been proposed as remedy for the defi-ciencies of Value-at-Risk (VaR) which in general is not a coherent risk measure. In fact, most definitions of ES lead to the same results when applied to…

Statistical Mechanics · Physics 2008-12-10 Carlo Acerbi , Dirk Tasche

This paper introduces novel backtests for the risk measure Expected Shortfall (ES) following the testing idea of Mincer and Zarnowitz (1969). Estimating a regression framework for the ES stand-alone is infeasible, and thus, our tests are…

Risk Management · Quantitative Finance 2020-08-31 Sebastian Bayer , Timo Dimitriadis

We propose an original two-part, duration-severity approach for backtesting Expected Shortfall (ES). While Probability Integral Transform (PIT) based ES backtests have gained popularity, they have yet to allow for separate testing of the…

Risk Management · Quantitative Finance 2024-05-14 Sullivan Hué , Christophe Hurlin , Yang Lu

We discuss the coherence properties of Expected Shortfall (ES) as a financial risk measure. This statistic arises in a natural way from the estimation of the "average of the 100p % worst losses" in a sample of returns to a portfolio. Here p…

Statistical Mechanics · Physics 2013-12-31 Carlo Acerbi , Dirk Tasche

Expected Shortfall (ES), the average loss above a high quantile, is the current financial regulatory market risk measure. Its estimation and optimization are highly unstable against sample fluctuations and become impossible above a critical…

Portfolio Management · Quantitative Finance 2021-05-05 Gábor Papp , Imre Kondor , Fabio Caccioli

Expected Shortfall (ES) is the average return on a risky asset conditional on the return being below some quantile of its distribution, namely its Value-at-Risk (VaR). The Basel III Accord, which will be implemented in the years leading up…

Economics · Quantitative Finance 2017-07-18 Andrew J. Patton , Johanna F. Ziegel , Rui Chen

The issue related to the quantification of the tail risk of cryptocurrencies is considered in this paper. The statistical methods used in the study are those concerning recent developments in Extreme Value Theory (EVT) for weakly dependent…

Risk Management · Quantitative Finance 2023-11-30 Andrea Teruzzi

We introduce and study the main properties of a class of convex risk measures that refine Expected Shortfall by simultaneously controlling the expected losses associated with different portions of the tail distribution. The corresponding…

Risk Management · Quantitative Finance 2021-08-19 Matteo Burzoni , Cosimo Munari , Ruodu Wang

We introduce a semiparametric approach for forecasting Value-at-Risk (VaR) and Expected Shortfall (ES) by modeling the conditional scale of financial returns, defined as the difference between two specified quantiles, via restricted…

Econometrics · Economics 2026-03-18 Xiaochun Liu , Richard Luger

A novel forecast combination and weighted quantile based tail-risk forecasting framework is proposed, aiming to reduce the impact of modelling uncertainty in tail-risk forecasting. The proposed approach is based on a two-step estimation…

Risk Management · Quantitative Finance 2021-07-20 Giuseppe Storti , Chao Wang

We introduce new forecast encompassing tests for the risk measure Expected Shortfall (ES). The ES currently receives much attention through its introduction into the Basel III Accords, which stipulate its use as the primary market risk…

Risk Management · Quantitative Finance 2020-08-31 Timo Dimitriadis , Julie Schnaitmann

In financial risk management, Value at Risk (VaR) is widely used to estimate potential portfolio losses. VaR's limitation is its inability to account for the magnitude of losses beyond a certain threshold. Expected Shortfall (ES) addresses…

Risk Management · Quantitative Finance 2024-07-10 Federico Gatta , Fabrizio Lillo , Piero Mazzarisi

Quantiles and expected shortfalls are commonly used risk measures in financial risk management. The two measurements are correlated while have distinguished features. In this project, our primary goal is to develop stable and practical…

Methodology · Statistics 2022-08-24 Xiang Peng , Huixia Judy Wang
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