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In the recent Basel Accords, the Expected Shortfall (ES) replaces the Value-at-Risk (VaR) as the standard risk measure for market risk in the banking sector, making it the most important risk measure in financial regulation. One of the most…

Risk Management · Quantitative Finance 2026-04-16 Qiuqi Wang , Ruodu Wang , Johanna Ziegel

Risk is an inherent feature of agricultural production and marketing and accurate measurement of it helps inform more efficient use of resources. This paper examines three tail quantile-based risk measures applied to the estimation of…

Risk Management · Quantitative Finance 2011-03-31 John Cotter , Kevin Dowd , Wyn Morgan

In this paper, we generalize the parametric delta-VaR method from portfolios with normally distributed risk factors to portfolios with elliptically distributed ones. We treat both the expected shortfall and the Value-at-Risk of such…

Classical Analysis and ODEs · Mathematics 2008-12-02 Jules Sadefo Kamdem

Semiparametric regression offers a flexible framework for modeling non-linear relationships between a response and covariates. A prime example are generalized additive models where splines (say) are used to approximate non-linear functional…

Statistics Theory · Mathematics 2018-10-05 Francis K. C. Hui , Chong You , Han Lin Shang , Samuel Müller

We consider calculation of capital requirements when the underlying economic scenarios are determined by simulatable risk factors. In the respective nested simulation framework, the goal is to estimate portfolio tail risk, quantified via…

Risk Management · Quantitative Finance 2018-05-18 Michael Ludkovski , James Risk

Estimating conditional quantiles of financial time series is essential for risk management and many other applications in finance. It is well-known that financial time series display conditional heteroscedasticity. Among the large number of…

Methodology · Statistics 2016-10-25 Yao Zheng , Qianqian Zhu , Guodong Li , Zhijie Xiao

The contour maps of the error of historical resp. parametric estimates for large random portfolios optimized under the risk measure Expected Shortfall (ES) are constructed. Similar maps for the sensitivity of the portfolio weights to small…

Risk Management · Quantitative Finance 2015-10-19 Fabio Caccioli , Imre Kondor , Gábor Papp

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

Modeling the time-varying covariance structures of high-dimensional variables is critical across diverse scientific and industrial applications; however, existing approaches exhibit notable limitations in either modeling flexibility or…

Methodology · Statistics 2026-01-21 Taehee Lee , Jun S. Liu

We study the properties of Expected Shortfall from the point of view of financial risk management. This measure --- which emerges as a natural remedy in some cases where Value at Risk (VaR) is not able to distinguish portfolios which bear…

Statistical Mechanics · Physics 2008-12-02 Carlo Acerbi , Claudio Nordio , Carlo Sirtori

We introduce a novel GARCH model that integrates two sources of uncertainty to better capture the rich, multi-component dynamics often observed in the volatility of financial assets. This model provides a quasi closed-form representation of…

Econometrics · Economics 2024-10-21 Luca Vincenzo Ballestra , Enzo D'Innocenzo , Christian Tezza

This project introduces the GNAR-HARX model, which combines Generalised Network Autoregressive (GNAR) structure with Heterogeneous Autoregressive (HAR) dynamics and exogenous predictors such as implied volatility. The model is designed for…

Applications · Statistics 2025-10-29 Tom Ó Nualláin

For a given time horizon DT, this article explores the relationship between the realized volatility (the volatility that will occur between t and t+DT), the implied volatility (corresponding to at-the-money option with expiry at t+DT), and…

Pricing of Securities · Quantitative Finance 2009-01-16 Gilles Zumbach

Expected Shortfall (ES) is a coherent measure of tail risk that captures the average loss beyond a quantile threshold. Despite the growing literature on ES regression conditional on covariates, no existing work considers ES modeling in…

Methodology · Statistics 2026-04-15 Yujie Hou , Xinbing Kong , Yalin Wang , Bin Wu

Recent financial disasters emphasised the need to investigate the consequence associated with the tail co-movements among institutions; episodes of contagion are frequently observed and increase the probability of large losses affecting…

Methodology · Statistics 2013-11-05 Mauro Bernardi , Ghislaine Gayraud , Lea Petrella

In this work we provide a simple estimation procedure for a general frailty model for analysis of prospective correlated failure times. Rigorous large-sample theory for the proposed estimators of both the regression coefficient vector and…

Statistics Theory · Mathematics 2007-06-13 Malka Gorfine , David M. Zucker , Li Hsu

We develop a continuous-time penalized regression framework for the estimation of time-varying coefficients and variable selection when both the response and covariates are It\^o semimartingales with jumps. The coefficient paths are…

Econometrics · Economics 2026-04-28 Aleksey Kolokolov , Shifan Yu

Optimizing risk measures such as Value-at-Risk (VaR) and Conditional Value-at-Risk (CVaR) of a general loss distribution is usually difficult, because 1) the loss function might lack structural properties such as convexity or…

Optimization and Control · Mathematics 2016-08-03 Helin Zhu , Joshua Hale , Enlu Zhou

Basel II and Solvency 2 both use the Value-at-Risk (VaR) as the risk measure to compute the Capital Requirements. In practice, to calibrate the VaR, a normal approximation is often chosen for the unknown distribution of the yearly log…

Methodology · Statistics 2013-11-04 Marie Kratz

Accurate forecasting of volatility and return quantiles is essential for evaluating financial tail risks such as value-at-risk and expected shortfall. This study proposes an extension of the traditional stochastic volatility model, termed…

Econometrics · Economics 2026-02-02 Makoto Takahashi , Yuta Yamauchi , Toshiaki Watanabe , Yasuhiro Omori
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