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This paper introduces a novel process for both factor and idiosyncratic volatility matrices whose eigenvalues follow the vector auto-regressive (VAR) model. We call it the factor and idiosyncratic VAR (FIVAR) model. The FIVAR model accounts…

Methodology · Statistics 2025-09-25 Minseok Shin , Donggyu Kim , Yazhen Wang , Jianqing Fan

In financial trading, factor models are widely used to price assets and capture excess returns from mispricing. Recently, we have witnessed the rise of variational autoencoder-based latent factor models, which learn latent factors…

Machine Learning · Computer Science 2026-01-15 Yilei Zhao , Wentao Zhang , Tingran Yang , Yong Jiang , Fei Huang , Wei Yang Bryan Lim

Agents' heterogeneity is recognized as a driver mechanism for the persistence of financial volatility. We focus on the multiplicity of investment strategies' horizons, we embed this concept in a continuous time stochastic volatility…

Statistical Finance · Quantitative Finance 2013-04-04 Danilo Delpini , Giacomo Bormetti

We study the problem of optimal long term portfolio selection with a view to beat a benchmark. Two kinds of objectives are considered. One concerns the probability of outperforming the benchmark and seeks either to minimise the decay rate…

Probability · Mathematics 2017-12-04 Anatolii A. Puhalskii

Estimating large covariance and precision matrices are fundamental in modern multivariate analysis. The problems arise from statistical analysis of large panel economics and finance data. The covariance matrix reveals marginal correlations…

Methodology · Statistics 2015-04-17 Jianqing Fan , Yuan Liao , Han Liu

The local volatility model is a widely used for pricing and hedging financial derivatives. While its main appeal is its capability of reproducing any given surface of observed option prices---it provides a perfect fit---the essential…

Computational Finance · Quantitative Finance 2019-01-24 Martin Tegnér , Stephen Roberts

While large language models (LLMs) are driving the rapid advancement of artificial intelligence, effectively and reliably training these large models remains one of the field's most significant challenges. To address this challenge, we…

Machine Learning · Computer Science 2025-12-12 Zeju Qiu , Simon Buchholz , Tim Z. Xiao , Maximilian Dax , Bernhard Schölkopf , Weiyang Liu

Matrix-variate data of high dimensions are frequently observed in finance and economics, spanning extended time periods, such as the long-term data on international trade flows among numerous countries. To address potential structural…

Methodology · Statistics 2024-04-03 Bin Chen , Elynn Y. Chen , Stevenson Bolivar , Rong Chen

Ecess-over-Threshold method is a crucial technique in extreme value analysis, which approximately models larger observations over a threshold using a Generalized Pareto Distribution. This paper presents a comprehensive framework for…

Methodology · Statistics 2025-06-03 Yifan Hu , Yanxi Hou

We study a two-dimensional McKean-Vlasov stochastic differential equation, whose volatility coefficient depends on the conditional distribution of the second component with respect to the first component. We prove the strong existence and…

Probability · Mathematics 2024-06-21 Scander Mustapha

In this study, MLP models with dynamic structure are applied to factor models for asset pricing tasks. Concretely, the MLP pyramid model structure was employed on firm-characteristic-sorted portfolio factors for modelling the large-capital…

Pricing of Securities · Quantitative Finance 2025-05-07 Shanyan Lai

As the Chinese stock market continues to evolve and its market structure grows increasingly complex, traditional quantitative trading methods are facing escalating challenges. Particularly, due to policy uncertainty and the frequent market…

Trading and Market Microstructure · Quantitative Finance 2024-06-18 Bohan Ma , Yushan Xue , Yuan Lu , Jing Chen

Efficient and stable training of large language models (LLMs) remains a core challenge in modern machine learning systems. To address this challenge, Reparameterized Orthogonal Equivalence Training (POET), a spectrum-preserving framework…

Machine Learning · Computer Science 2026-03-06 Zeju Qiu , Lixin Liu , Adrian Weller , Han Shi , Weiyang Liu

This paper addresses the fundamental task of estimating covariance matrix functions for high-dimensional functional data/functional time series. We consider two functional factor structures encompassing either functional factors with scalar…

Methodology · Statistics 2025-10-28 Dong Li , Xinghao Qiao , Zihan Wang

This paper presents how the most recent improvements made on covariance matrix estimation and model order selection can be applied to the portfolio optimisation problem. The particular case of the Maximum Variety Portfolio is treated but…

Applications · Statistics 2018-04-03 Emmanuelle Jay , Eugénie Terreaux , Jean-Philippe Ovarlez , Frédéric Pascal

This paper investigates whether large language models (LLMs) can generate reliable stock market predictions. We evaluate four state-of-the-art models - ChatGPT, Gemini, DeepSeek, and Perplexity - across three prompting strategies: a naive…

Trading and Market Microstructure · Quantitative Finance 2026-04-21 Ricardo Crisostomo , Diana Mykhalyuk

Volatilities, in high-dimensional panels of economic time series with a dynamic factor structure on the levels or returns, typically also admit a dynamic factor decomposition. We consider a two-stage dynamic factor model method recovering…

Econometrics · Economics 2022-02-03 Matteo Barigozzi , Marc Hallin

We propose a fast and flexible method to scale multivariate return volatility predictions up to high-dimensions using a dynamic risk factor model. Our approach increases parsimony via time-varying sparsity on factor loadings and is able to…

Statistical Finance · Quantitative Finance 2021-11-15 Bruno P. C. Levy , Hedibert F. Lopes

We propose a confirmatory dynamic factor model for a large number of stocks whose returns are observed daily across multiple time zones. The model has a global factor and a continental factor that both drive the individual stock return…

Statistics Theory · Mathematics 2025-02-25 Oliver B. Linton , Haihan Tang , Jianbin Wu

In the stochastic volatility models for multivariate daily stock returns, it has been found that the estimates of parameters become unstable as the dimension of returns increases. To solve this problem, we focus on the factor structure of…

Econometrics · Economics 2021-09-16 Yuta Yamauchi , Yasuhiro Omori