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We propose a novel class of multivariate GARCH models that incorporate realized measures of volatility and correlations. The key innovation is an unconstrained vector parametrization of the conditional correlation matrix, which enables the…

Econometrics · Economics 2025-02-07 Ilya Archakov , Peter Reinhard Hansen , Asger Lunde

Volatility asymmetry is a hot topic in high-frequency financial market. In this paper, we propose a new econometric model, which could describe volatility asymmetry based on high-frequency historical data and low-frequency historical data.…

Methodology · Statistics 2021-01-15 Huiling Yuan , Yong Zhou , Lu Xu , Yun Lei Sun , Xiang Yu Cui

We propose an adaptive algorithm for tracking of historical volatility. The algorithm is built under the assumption that the historical volatility function belongs to the Stone-Ibragimov-Khasminskii class of $k$ times differentiable…

Probability · Mathematics 2007-06-13 L. Goldentayer , F. Klebaner , R. Liptser

We develop a procedure for forecasting the volatility of a time series immediately following a news shock. Adapting the similarity-based framework of Lin and Eck (2020), we exploit series that have experienced similar shocks. We aggregate…

Methodology · Statistics 2024-08-08 David P. Lundquist , Daniel J. Eck

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

We review the recently introduced concept of variety of a financial portfolio and we sketch its importance for risk control purposes. The empirical behaviour of variety, correlation, exceedance correlation and asymmetry of the probability…

Statistical Mechanics · Physics 2008-12-10 Fabrizio Lillo , Rosario N. Mantegna , Jean-Philippe Bouchaud , Marc Potters

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

We introduce a new identification strategy for uncertainty shocks to explain macroeconomic volatility in financial markets. The Chicago Board Options Exchange Volatility Index (VIX) measures market expectations of future volatility, but…

Econometrics · Economics 2024-11-06 Ayush Jha , Abootaleb Shirvani , Svetlozar T. Rachev , Frank J. Fabozzi

Volatility is the canonical measure of financial risk, a role largely inherited from Modern Portfolio Theory. Yet, its universality rests on restrictive efficiency assumptions that render volatility, at best, an incomplete proxy for true…

Mathematical Finance · Quantitative Finance 2026-05-01 Sergio Bianchi , Daniele Angelini

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

In this chapter, we consider volatility swap, variance swap and VIX future pricing under different stochastic volatility models and jump diffusion models which are commonly used in financial market. We use convexity correction approximation…

Mathematical Finance · Quantitative Finance 2017-12-08 Anatoliy Swishchuk , Zijia Wang

This paper explores option portfolio optimization when the underlying returns are skew-elliptical t-distributed. We use the variance and value at risk (VaR) to measure portfolio risk. The novelty of our work is the departure from the…

Portfolio Management · Quantitative Finance 2026-05-01 Kyle Sung , Traian A. Pirvu

The popularity of modern portfolio theory has decreased among practitioners because of its unfavorable out-of-sample performance. Estimation errors tend to affect the optimal weight calculation noticeably, especially when a large number of…

Portfolio Management · Quantitative Finance 2019-10-28 Sven Husmann , Antoniya Shivarova , Rick Steinert

This paper studies a robust portfolio optimization problem under the multi-factor volatility model introduced by Christoffersen et al. (2009). The optimal strategy is derived analytically under the worst-case scenario with or without…

Mathematical Finance · Quantitative Finance 2020-06-16 Ben-Zhang Yang , Xiaoping Lu , Guiyuan Ma , Song-Ping Zhu

This paper aims to more effectively manage and mitigate stock market risks by accurately characterizing financial market returns and volatility. We enhance the Stochastic Volatility (SV) model by incorporating fat-tailed distributions and…

Applications · Statistics 2024-12-31 Minheng Xiao

Volatility for financial assets returns can be used to gauge the risk for financial market. We propose a deep stochastic volatility model (DSVM) based on the framework of deep latent variable models. It uses flexible deep learning models to…

Machine Learning · Computer Science 2021-02-26 Xiuqin Xu , Ying Chen

We provided proof here that coefficient of variation (CV) is a direct measure of risk using an equation that has been derived here for the first time. We also presented a method to generate a stock CV based on return that strongly…

Mathematical Finance · Quantitative Finance 2022-06-22 Julius O. Campeciño

We create a time series model for annual returns of three asset classes: the USA Standard & Poor (S&P) stock index, the international stock index, and the USA Bank of America investment-grade corporate bond index. Using this, we made an…

Risk Management · Quantitative Finance 2025-12-29 Andrey Sarantsev , Angel Piotrowski , Ian Anderson

We study tail risk dynamics in high-frequency financial markets and their connection with trading activity and market uncertainty. We introduce a dynamic extreme value regression model accommodating both stationary and local unit-root…

Econometrics · Economics 2023-01-05 Julien Hambuckers , Li Sun , Luca Trapin

We examine volatility of an Indian stock market in terms of aspects like participation, synchronization of stocks and quantification of volatility using the random matrix approach. Volatility pattern of the market is found using the BSE…

Physics and Society · Physics 2008-12-02 V. Kulkarni , N. Deo