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We compare systematically several classes of stochastic volatility models of stock market fluctuations. We show that the long-time return distribution is either Gaussian or develops a power-law tail, while the short-time return distribution…

Statistical Finance · Quantitative Finance 2010-09-15 Frantisek Slanina

In this study, we develop a unified volatility modeling framework that embeds GARCH dynamics directly within recurrent neural networks. We propose two interpretable hybrid architectures, GARCH-GRU and GARCH-LSTM, that integrate the…

Statistical Finance · Quantitative Finance 2025-11-25 Jingyi Wei , Steve Yang , Zhenyu Cui

In this paper, we show that the recent integration of statistical models with deep recurrent neural networks provides a new way of formulating volatility (the degree of variation of time series) models that have been widely used in time…

Machine Learning · Computer Science 2018-12-06 Rui Luo , Weinan Zhang , Xiaojun Xu , Jun Wang

The aim of this paper is to analyse the Bitcoin in order to shed some light on its nature and behaviour. We select 9 cryptocurrencies that account for almost 75\% of total market capitalisation and compare their evolution with that of a…

Statistical Finance · Quantitative Finance 2023-09-08 Esther Cabezas-Rivas , Felipe Sánchez-Coll , Isaac Tormo-Xaixo

We suggest two classes of multivariate GARCH--models which are both easy to estimate and perform well in forecasting the covariance matrix of more than one hundred stocks. We apply methods from random matrix theory (RMT) to determine the…

Condensed Matter · Physics 2007-05-23 C. Reese , B. Rosenow

In order to obtain a reasonable and reliable forecast method for crude oil price volatility, this paper evaluates the forecast performance of single-regime GARCH models (including the standard linear GARCH model and the nonlinear GJR-GARCH…

Economics · Quantitative Finance 2015-12-08 Yue-Jun Zhang , Ting Yao , Ling-Yun He

This is the first paper that estimates the price determinants of BitCoin in a Generalised Autoregressive Conditional Heteroscedasticity framework using high frequency data. Derived from a theoretical model, we estimate BitCoin transaction…

Statistical Finance · Quantitative Finance 2018-12-27 Pavel Ciaian , d'Artis Kancs , Miroslava Rajcaniova

This paper uses simulation-based portfolio optimization to mitigate the left tail risk of the portfolio. The contribution is twofold. (i) We propose the Markov regime-switching GARCH model with multivariate normal tempered stable innovation…

Risk Management · Quantitative Finance 2023-02-03 Cheng Peng , Young Shin Kim , Stefan Mittnik

Financial studies require volatility based models which provides useful insights on risks related to investments. Stochastic volatility models are one of the most popular approaches to model volatility in such studies. The asset returns…

Methodology · Statistics 2021-10-26 Soham Mukherjee

This paper develops a Bayesian framework for the realized exponential generalized autoregressive conditional heteroskedasticity (realized EGARCH) model, which can incorporate multiple realized volatility measures for the modelling of a…

Risk Management · Quantitative Finance 2020-08-25 Vica Tendenan , Richard Gerlach , Chao Wang

We show Bitcoin implied volatility on a 5 minute time horizon is modestly predictable from price, volatility momentum and alternative data including sentiment and engagement. Lagged Bitcoin index price and volatility movements contribute to…

Statistical Finance · Quantitative Finance 2020-10-30 Faizaan Pervaiz , Christopher Goh , Ashley Pennington , Samuel Holt , James West , Shaun Ng

The cryptocurrency market presents both significant investment opportunities and higher risks relative to traditional financial assets. This study examines the tail behavior of daily returns for two leading cryptocurrencies, Bitcoin and…

Statistical Finance · Quantitative Finance 2025-07-04 A. H. Nzokem

Generalized autoregressive conditional heteroscedasticity (GARCH) models have long been considered as one of the most successful families of approaches for volatility modeling in financial return series. In this paper, we propose an…

Machine Learning · Computer Science 2013-01-29 Emmanouil A. Platanios , Sotirios P. Chatzis

This paper introduces an extension of the Markov switching GARCH model where the volatility in each state is a convex combination of two different GARCH components with time varying weights. This model has the dynamic behavior to capture…

Methodology · Statistics 2014-02-20 N. Alemohammad , S. Rezakhah , S. H. Alizadeh

We employ single-qubit quantum circuit learning (QCL) to model the dynamics of volatility time series. To assess its effectiveness, we generate synthetic data using the Rational GARCH model, which is specifically designed to capture…

Computational Finance · Quantitative Finance 2026-04-29 Tetsuya Takaishi

A Bayesian estimation of a GARCH model is performed for US Dollar/Japanese Yen exchange rate by the Metropolis-Hastings algorithm with a proposal density given by the adaptive construction scheme. In the adaptive construction scheme the…

Statistical Finance · Quantitative Finance 2013-04-23 Tetsuya Takaishi

This paper examines volatility in REITs using a multivariate GARCH based model. The Multivariate VAR-GARCH technique documents the return and volatility linkages between REIT sub-sectors and also examines the influence of other US equity…

Statistical Finance · Quantitative Finance 2011-03-30 John Cotter , Simon Stevenson

We construct liquidity-adjusted return and volatility using purposely designed liquidity metrics (liquidity jump and liquidity diffusion) that incorporate additional liquidity information. Based on these measures, we introduce a…

Statistical Finance · Quantitative Finance 2025-03-13 Qi Deng , Zhong-guo Zhou

Range-measured return contains more information than the traditional scalar-valued return. In this paper, we propose to model the [low, high] price range as a random interval and suggest an interval-valued GARCH (Int-GARCH) model for the…

Methodology · Statistics 2019-01-11 Yan Sun , Guanghua Lian , Zudi Lu , Jennifer Loveland , Isaac Blackhurst

The family of location and scale mixtures of Gaussians has the ability to generate a number of flexible distributional forms. It nests as particular cases several important asymmetric distributions like the Generalised Hyperbolic…

Methodology · Statistics 2014-08-05 Darren Wraith , Florence Forbes