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In this paper, we investigate risk measures such as value at risk (VaR) and the conditional tail expectation (CTE) of the extreme (maximum and minimum) and the aggregate (total) of two dependent risks. In finance, insurance and the other…

Risk Management · Quantitative Finance 2021-02-01 Suman Thapa , Yiqiang Q. Zhao

Value at risk (VaR) and expected shortfall (ES) are common high quantile-based risk measures adopted in financial regulations and risk management. In this paper, we propose a tail risk measure based on the most probable maximum size of risk…

Risk Management · Quantitative Finance 2025-06-17 Kan Chen , Tuoyuan Cheng

To comply with increasingly stringent international standards in risk management and regulation, several approaches have been developed in the literature for forecasting tail-risk measures such as Value-at-Risk (VaR) and Expected Shortfall…

Risk Management · Quantitative Finance 2026-03-02 Alessandra Amendola , Vincenzo Candila , Antonio Naimoli , Giuseppe Storti

We propose a new approach, termed Realized Risk Measures (RRM), to estimate Value-at-Risk (VaR) and Expected Shortfall (ES) using high-frequency financial data. It extends the Realized Quantile (RQ) approach proposed by Dimitriadis and…

Risk Management · Quantitative Finance 2025-10-21 Federico Gatta , Fabrizio Lillo , Piero Mazzarisi

The debate of what quantitative risk measure to choose in practice has mainly focused on the dichotomy between Value at Risk (VaR) -- a quantile -- and Expected Shortfall (ES) -- a tail expectation. Range Value at Risk (RVaR) is a natural…

Statistics Theory · Mathematics 2022-06-27 Tobias Fissler , Johanna F. Ziegel

This thesis evaluates most of the extreme mixture models and methods that have appended in the literature and implements them in the context of finance and insurance. The paper also reviews and studies extreme value theory, time series,…

General Economics · Economics 2024-07-09 Yujuan Qiu

Systemic risk measures quantify the potential risk to an individual financial constituent arising from the distress of entire financial system. As a generalization of two widely applied risk measures, Value-at-Risk and Expected Shortfall,…

Methodology · Statistics 2025-11-24 Qingzhao Zhong , Yanxi Hou

Extreme Value Theory (EVT) is one of the most commonly used approaches in finance for measuring the downside risk of investment portfolios, especially during financial crises. In this paper, we propose a novel approach based on EVT called…

General Economics · Economics 2020-11-16 Hamidreza Arian , Hossein Poorvasei , Azin Sharifi , Shiva Zamani

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 applies the Extreme-Value (EV) Generalised Pareto distribution to the extreme tails of the return distributions for the S&P500, FT100, DAX, Hang Seng, and Nikkei225 futures contracts. It then uses tail estimators from these…

Risk Management · Quantitative Finance 2011-03-30 John Cotter , Kevin Dowd

This paper presents non-parametric estimates of spectral risk measures applied to long and short positions in 5 prominent equity futures contracts. It also compares these to estimates of two popular alternative measures, the Value-at-Risk…

Risk Management · Quantitative Finance 2011-03-30 john cotter , kevin dowd

Value at Risk (VaR) is a quantitative measure used to evaluate the risk linked to the potential loss of investment or capital. Estimation of the VaR entails the quantification of prospective losses in a portfolio of investments, using a…

Mathematical Finance · Quantitative Finance 2024-10-01 Minglian Lin , Indranil SenGupta , William Wilson

The joint Value at Risk (VaR) and expected shortfall (ES) quantile regression model of Taylor (2017) is extended via incorporating a realized measure, to drive the tail risk dynamics, as a potentially more efficient driver than daily…

Risk Management · Quantitative Finance 2018-05-23 Richard Gerlach , Chao 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

Extreme values and the tail behavior of probability distributions are essential for quantifying and mitigating risk in complex systems of all kinds. In multivariate settings, accounting for correlations is crucial. Although extreme value…

Statistical Finance · Quantitative Finance 2026-03-06 Benjamin Köhler , Anton J. Heckens , Thomas Guhr

A method for quantile-based, semi-parametric historical simulation estimation of multiple step ahead Value-at-Risk (VaR) and Expected Shortfall (ES) models is developed. It uses the quantile loss function, analogous to how the…

Statistical Finance · Quantitative Finance 2025-03-06 Richard Gerlach , Antonio Naimoli , Giuseppe Storti

Value-at-risk (VaR) and expected shortfall (ES) are two commonly utilized metrics for quantifying financial risk. In this study, we review the widely employed Generalized Autoregressive Conditional Heteroskedasticity (GARCH) models. These…

Computation · Statistics 2024-05-14 Kanon Kamronnaher , Andrew Bellucco , Whitney K. Huang , Colin M. Gallagher

This paper investigates how two important sources of risk -- market tail risk and extreme market volatility risk -- are priced into the cross-section of asset returns across various investment horizons. To identify such risks, we propose a…

Pricing of Securities · Quantitative Finance 2021-12-13 Jozef Baruník , Matěj Nevrla

This paper presents analytical solutions to the problem of how to calculate sensible VaR (Value-at-Risk) and ES (Expected Shortfall) contributions in the CreditRisk+ methodology. Via the ES contributions, ES itself can be exactly computed…

Condensed Matter · Physics 2011-08-09 Alexandre Kurth , Dirk Tasche

We introduce a method to estimate simultaneously the tail and the threshold parameters of an extreme value regression model. This standard model finds its use in finance to assess the effect of market variables on extreme loss distributions…

Methodology · Statistics 2023-04-17 Julien Hambuckers , Marie Kratz , Antoine Usseglio-Carleve
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