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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 study seeks to advance the understanding and prediction of stock market return uncertainty through the application of advanced deep learning techniques. We introduce a novel deep learning model that utilizes a Gaussian mixture…

Risk Management · Quantitative Finance 2025-03-11 Yanlong Wang , Jian Xu , Shao-Lun Huang , Danny Dongning Sun , Xiao-Ping Zhang

This paper provides an insight to the time-varying dynamics of the shape of the distribution of financial return series by proposing an exponential weighted moving average model that jointly estimates volatility, skewness and kurtosis over…

Risk Management · Quantitative Finance 2012-06-08 A. Gabrielsen , P. Zagaglia , A. Kirchner , Z. Liu

Appropriate risk management is crucial to ensure the competitiveness of financial institutions and the stability of the economy. One widely used financial risk measure is Value-at-Risk (VaR). VaR estimates based on linear and parametric…

Statistical Finance · Quantitative Finance 2020-09-16 Marius Lux , Wolfgang Karl Härdle , Stefan Lessmann

This study introduces a dynamic Bayesian network (DBN) framework for forecasting value at risk (VaR) and stressed VaR (SVaR) and compares its performance to several commonly applied models. Using daily S&P 500 index returns from 1991 to…

Risk Management · Quantitative Finance 2025-12-08 Eden Gross , Ryan Kruger , Francois Toerien

We develop an efficient sampling approach for handling complex missing data patterns and a large number of missing observations in conditionally Gaussian state space models. Two important examples are dynamic factor models with unbalanced…

Econometrics · Economics 2023-02-08 Joshua C. C. Chan , Aubrey Poon , Dan Zhu

Risk measure forecast and model have been developed in order to not only provide better forecast but also preserve its (empirical) property especially coherent property. Whilst the widely used risk measure of Value-at-Risk (VaR) has shown…

Risk Management · Quantitative Finance 2020-09-08 Bony Josaphat , Khreshna Syuhada

Accurate forecasting of the Volatility-Covariance Matrix (VCV) is central to regulatory capital adequacy processes such as the Internal Capital Adequacy Assessment Process (ICAAP) and the Comprehensive Capital Analysis and Review (CCAR).…

Risk Management · Quantitative Finance 2026-05-19 Ujjwala Vadrevu

This paper proposes a novel hybrid model, termed GARCH-FIS, for recursive rolling multi-step forecasting of financial time series. It integrates a Fuzzy Inference System (FIS) with a Generalized Autoregressive Conditional Heteroskedasticity…

Machine Learning · Computer Science 2026-03-17 Wen-Jing Li , Da-Qing Zhang

We identify a new variational inference scheme for dynamical systems whose transition function is modelled by a Gaussian process. Inference in this setting has either employed computationally intensive MCMC methods, or relied on…

Machine Learning · Statistics 2019-06-14 Alessandro Davide Ialongo , Mark van der Wilk , James Hensman , Carl Edward Rasmussen

Accurate forecasting of risk is the key to successful risk management techniques. Using the largest stock index futures from twelve European bourses, this paper presents VaR measures based on their unconditional and conditional…

Risk Management · Quantitative Finance 2011-03-30 John Cotter

We propose score dynamics (SD), a general framework for learning accelerated evolution operators with large timesteps from molecular-dynamics simulations. SD is centered around scores, or derivatives of the transition log-probability with…

Computational Physics · Physics 2024-03-08 Tim Hsu , Babak Sadigh , Vasily Bulatov , Fei Zhou

We propose a modeling framework for stochastic systems, termed Gaussian behaviors, that describes finite-length trajectories of a system as a Gaussian process. The proposed model naturally quantifies the uncertainty in the trajectories, yet…

Systems and Control · Electrical Eng. & Systems 2026-04-02 András Sasfi , Ivan Markovsky , Alberto Padoan , Florian Dörfler

We propose methods to improve the forecasts from generalized autoregressive score (GAS) models (Creal et. al, 2013; Harvey, 2013) by localizing their parameters using decision trees and random forests. These methods avoid the curse of…

Econometrics · Economics 2023-05-31 Andrew J. Patton , Yasin Simsek

Dynamic Uncertain Causality Graph(DUCG) is a recently proposed model for diagnoses of complex systems. It performs well for industry system such as nuclear power plants, chemical system and spacecrafts. However, the variable state…

Artificial Intelligence · Computer Science 2021-06-29 Hao Nie , Qin Zhang

This paper concerns sequential computation of risk measures for financial data and asks how, given a risk measurement procedure, we can tell whether the answers it produces are `correct'. We draw the distinction between `external' and…

Risk Management · Quantitative Finance 2015-11-20 Mark H. A. Davis

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

Value at Risk (VaR) and Conditional Value at Risk (CVaR) have become the most popular measures of market risk in Financial and Insurance fields. However, the estimation of both risk measures is challenging, because it requires the knowledge…

Methodology · Statistics 2024-10-17 Jacinto Martín , M. Isabel Parra , Eva L. Sanjuán , Mario M. Pizarro

The dynamic portfolio construction problem requires dynamic modeling of the joint distribution of multivariate stock returns. To achieve this, we propose a dynamic generative factor model which uses random variable transformation as an…

Portfolio Management · Quantitative Finance 2024-01-18 Chuting Sun , Qi Wu , Xing Yan

The conditional value-at-risk (CVaR) is a useful risk measure in fields such as machine learning, finance, insurance, energy, etc. When measuring very extreme risk, the commonly used CVaR estimation method of sample averaging does not work…

Methodology · Statistics 2021-03-10 Dylan Troop , Frédéric Godin , Jia Yuan Yu