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In this paper, we develop a hybrid approach to forecasting the volatility and risk of financial instruments by combining common econometric GARCH time series models with deep learning neural networks. For the latter, we employ Gated…

Risk Management · Quantitative Finance 2023-10-03 Jakub Michańków , Łukasz Kwiatkowski , Janusz Morajda

Despite the impressive success of deep neural networks in many application areas, neural network models have so far not been widely adopted in the context of volatility forecasting. In this work, we aim to bridge the conceptual gap between…

Econometrics · Economics 2022-05-17 Rafael Reisenhofer , Xandro Bayer , Nikolaus Hautsch

Several academics have studied the ability of hybrid models mixing univariate Generalized Autoregressive Conditional Heteroskedasticity (GARCH) models and neural networks to deliver better volatility predictions than purely econometric…

Statistical Finance · Quantitative Finance 2021-09-03 Lucien Boulet

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

This study aims to compare multiple deep learning-based forecasters for the task of predicting volatility using multivariate data. The paper evaluates a range of models, starting from simpler and shallower ones and progressing to deeper and…

Statistical Finance · Quantitative Finance 2023-06-26 Wenbo Ge , Pooia Lalbakhsh , Leigh Isai , Artem Lensky , Hanna Suominen

This paper examines the influence of low-frequency macroeconomic variables on the high-frequency returns of copper futures and the long-term correlation with the S&P 500 index, employing GARCH-MIDAS and DCC-MIDAS modeling frameworks. The…

Statistical Finance · Quantitative Finance 2024-09-16 Zian Wang , Xinshu Li

Volatility is a quantity of measurement for the price movements of stocks or options which indicates the uncertainty within financial markets. As an indicator of the level of risk or the degree of variation, volatility is important to…

Machine Learning · Computer Science 2018-11-12 Qiang Zhang , Rui Luo , Yaodong Yang , Yuanyuan Liu

We propose a new approach to volatility modeling by combining deep learning (LSTM) and realized volatility measures. This LSTM-enhanced realized GARCH framework incorporates and distills modeling advances from financial econometrics, high…

Econometrics · Economics 2023-10-18 Chen Liu , Chao Wang , Minh-Ngoc Tran , Robert Kohn

In this paper, we investigate the problem of predicting the future volatility of Forex currency pairs using the deep learning techniques. We show step-by-step how to construct the deep-learning network by the guidance of the empirical…

Statistical Finance · Quantitative Finance 2021-12-06 Shujian Liao , Jian Chen , Hao Ni

In an environment of increasingly volatile financial markets, the accurate estimation of risk remains a major challenge. Traditional econometric models, such as GARCH and its variants, are based on assumptions that are often too rigid to…

Artificial Intelligence · Computer Science 2025-08-19 Fredy Pokou , Jules Sadefo Kamdem , François Benhmad

This paper introduces a novel multivariate volatility modeling framework, named Long Short-Term Memory enhanced BEKK (LSTM-BEKK), that integrates deep learning into multivariate GARCH processes. By combining the flexibility of recurrent…

Computational Finance · Quantitative Finance 2025-06-04 Haoyuan Wang , Chen Liu , Minh-Ngoc Tran , Chao Wang

In this work we show that prediction uncertainty estimates gleaned from deep learning models can be useful inputs for influencing the relative allocation of risk capital across trades. In this way, consideration of uncertainty is important…

Statistical Finance · Quantitative Finance 2020-08-03 Trent Spears , Stefan Zohren , Stephen Roberts

Volatility, which indicates the dispersion of returns, is a crucial measure of risk and is hence used extensively for pricing and discriminating between different financial investments. As a result, accurate volatility prediction receives…

Computational Finance · Quantitative Finance 2024-10-02 Zeda Xu , John Liechty , Sebastian Benthall , Nicholas Skar-Gislinge , Christopher McComb

Accurate covariance forecasting is central to portfolio allocation, risk management, and asset pricing, yet many existing methods struggle at medium-term horizons, where shifting market regimes and slower dynamics predominate. We propose a…

Computational Engineering, Finance, and Science · Computer Science 2026-05-21 Pedro Reis , Ana Paula Serra , João Gama

There has been much interest in accurate cryptocurrency price forecast models by investors and researchers. Deep Learning models are prominent machine learning techniques that have transformed various fields and have shown potential for…

Machine Learning · Computer Science 2024-06-04 Jingyang Wu , Xinyi Zhang , Fangyixuan Huang , Haochen Zhou , Rohtiash Chandra

This paper proposes an enhanced approach to modeling and forecasting volatility using high frequency data. Using a forecasting model based on Realized GARCH with multiple time-frequency decomposed realized volatility measures, we study the…

Statistical Finance · Quantitative Finance 2015-02-04 Jozef Barunik , Tomas Krehlik , Lukas Vacha

Several studies have shown that deep learning models can provide more accurate volatility forecasts than the traditional methods used within this domain. This paper presents a composite model that merges a deep learning approach with…

Machine Learning · Computer Science 2022-11-18 V Ncume , T. L van Zyl , A Paskaramoorthy

This study addresses the computational challenges of forecasting volatility in high-dimensional commodity markets. Building on the Network log-ARCH framework, we introduce a novel class of network topologies from GARCH-informed correlation…

Econometrics · Economics 2026-02-23 Fayçal Djebari , Kahina Mehidi , Khelifa Mazouz , Philipp Otto

We have applied a Long Short-Term Memory neural network to model S&P 500 volatility, incorporating Google domestic trends as indicators of the public mood and macroeconomic factors. In a held-out test set, our Long Short-Term Memory model…

Computational Finance · Quantitative Finance 2016-02-17 Ruoxuan Xiong , Eric P. Nichols , Yuan Shen

This study aims to address the challenges of futures price prediction in high-frequency trading (HFT) by proposing a continuous learning factor predictor based on graph neural networks. The model integrates multi-factor pricing theories…

Machine Learning · Computer Science 2023-12-20 Min Hu , Zhizhong Tan , Bin Liu , Guosheng Yin
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