Financial Data Analysis with Robust Federated Logistic Regression ArXiv ID: 2504.20250 “View on arXiv” Authors: Kun Yang, Nikhil Krishnan, Sanjeev R. Kulkarni Abstract In this study, we focus on the analysis of financial data in a federated setting, wherein data is distributed across multiple clients or locations, and the raw data never leaves the local devices. Our primary focus is not only on the development of efficient learning frameworks (for protecting user data privacy) in the field of federated learning but also on the importance of designing models that are easier to interpret. In addition, we care about the robustness of the framework to outliers. To achieve these goals, we propose a robust federated logistic regression-based framework that strives to strike a balance between these goals. To verify the feasibility of our proposed framework, we carefully evaluate its performance not only on independently identically distributed (IID) data but also on non-IID data, especially in scenarios involving outliers. Extensive numerical results collected from multiple public datasets demonstrate that our proposed method can achieve comparable performance to those of classical centralized algorithms, such as Logistical Regression, Decision Tree, and K-Nearest Neighbors, in both binary and multi-class classification tasks. ...

Mechanisms of information communication and market price movements. The case of SP 500 market ArXiv ID: 2505.09625 “View on arXiv” Authors: Inga Ivanova, Grzegorz Rzadkowski Abstract In this paper we analyze how market prices change in response to information processing among the market participants and how non-linear information dynamics drive market price movement. We analyze historical data of the SP 500 market for the period 1950 -2025 using the logistic Continuous Wavelet Transformation method. This approach allows us to identify various patterns in market dynamics. These patterns are conceptualized using a new theory of reflexive communication of information in a market consisting of heterogeneous agents who assign meaning to information from different perspectives. This allows us to describe market dynamics and make forecasts of its development using the most general mechanisms of information circulation within the content-free approach. ...

Multi-Horizon Echo State Network Prediction of Intraday Stock Returns ArXiv ID: 2504.19623 “View on arXiv” Authors: Giovanni Ballarin, Jacopo Capra, Petros Dellaportas Abstract Stock return prediction is a problem that has received much attention in the finance literature. In recent years, sophisticated machine learning methods have been shown to perform significantly better than ‘‘classical’’ prediction techniques. One downside of these approaches is that they are often very expensive to implement, for both training and inference, because of their high complexity. We propose a return prediction framework for intraday returns at multiple horizons based on Echo State Network (ESN) models, wherein a large portion of parameters are drawn at random and never trained. We show that this approach enjoys the benefits of recurrent neural network expressivity, inherently efficient implementation, and strong forecasting performance. ...

Some PDE results in Heston model with applications ArXiv ID: 2504.19859 “View on arXiv” Authors: Edoardo Lombardo Abstract We present here some results for the PDE related to the logHeston model. We present different regularity results and prove a verification theorem that shows that the solution produced via the Feynman-Kac theorem is the unique viscosity solution for a wide choice of initial data (even discontinuous) and source data. In addition, our techniques do not use Feller’s condition at any time. In the end, we prove a convergence theorem to approximate this solution by means of a hybrid (finite differences/tree scheme) approach. ...

Impact of the COVID-19 pandemic on the financial market efficiency of price returns, absolute returns, and volatility increment: Evidence from stock and cryptocurrency markets ArXiv ID: 2504.18960 “View on arXiv” Authors: Tetsuya Takaishi Abstract This study examines the impact of the coronavirus disease 2019 (COVID-19) pandemic on market efficiency by analyzing three time series – price returns, absolute returns, and volatility increments – in stock (Deutscher Aktienindex, Nikkei 225, Shanghai Stock Exchange (SSE), and Volatility Index) and cryptocurrency (Bitcoin and Ethereum) markets. The effect is found to vary by asset class and market. In the stock market, while the pandemic did not influence the Hurst exponent of volatility increments, it affected that of returns and absolute returns (except in the SSE, where returns remained unaffected). In the cryptocurrency market, the pandemic did not alter the Hurst exponent for any time series but influenced the strength of multifractality in returns and absolute returns. Some Hurst exponent time series exhibited a gradual decline over time, complicating the assessment of pandemic-related effects. Consequently, segmented analyses by pandemic periods may erroneously suggest an impact, warranting caution in period-based studies. ...

Modeling Regime Structure and Informational Drivers of Stock Market Volatility via the Financial Chaos Index ArXiv ID: 2504.18958 “View on arXiv” Authors: Masoud Ataei Abstract This paper investigates the structural dynamics of stock market volatility through the Financial Chaos Index, a tensor- and eigenvalue-based measure designed to capture realized volatility via mutual fluctuations among asset prices. Motivated by empirical evidence of regime-dependent volatility behavior and perceptual time dilation during financial crises, we develop a regime-switching framework based on the Modified Lognormal Power-Law distribution. Analysis of the FCIX from January 1990 to December 2023 identifies three distinct market regimes, low-chaos, intermediate-chaos, and high-chaos, each characterized by differing levels of systemic stress, statistical dispersion and persistence characteristics. Building upon the segmented regime structure, we further examine the informational forces that shape forward-looking market expectations. Using sentiment-based predictors derived from the Equity Market Volatility tracker, we employ an elastic net regression model to forecast implied volatility, as proxied by the VIX index. Our findings indicate that shifts in macroeconomic, financial, policy, and geopolitical uncertainty exhibit strong predictive power for volatility dynamics across regimes. Together, these results offer a unified empirical perspective on how systemic uncertainty governs both the realized evolution of financial markets and the anticipatory behavior embedded in implied volatility measures. ...

On Bitcoin Price Prediction ArXiv ID: 2504.18982 “View on arXiv” Authors: Grégory Bournassenko Abstract In recent years, cryptocurrencies have attracted growing attention from both private investors and institutions. Among them, Bitcoin stands out for its impressive volatility and widespread influence. This paper explores the predictability of Bitcoin’s price movements, drawing a parallel with traditional financial markets. We examine whether the cryptocurrency market operates under the efficient market hypothesis (EMH) or if inefficiencies still allow opportunities for arbitrage. Our methodology combines theoretical reviews, empirical analyses, machine learning approaches, and time series modeling to assess the extent to which Bitcoin’s price can be predicted. We find that while, in general, the Bitcoin market tends toward efficiency, specific conditions, including information asymmetries and behavioral anomalies, occasionally create exploitable inefficiencies. However, these opportunities remain difficult to systematically identify and leverage. Our findings have implications for both investors and policymakers, particularly regarding the regulation of cryptocurrency brokers and derivatives markets. ...

Phase Transitions in Financial Markets Using the Ising Model: A Statistical Mechanics Perspective ArXiv ID: 2504.19050 “View on arXiv” Authors: Bruno Giorgio Abstract This dissertation investigates the ability of the Ising model to replicate statistical characteristics, or stylized facts, commonly observed in financial assets. The study specifically examines in the S&P500 index the following features: volatility clustering, negative skewness, heavy tails, the absence of autocorrelation in returns, and the presence of autocorrelation in absolute returns. A significant portion of the dissertation is dedicated to Ising model-based simulations. Due to the lack of an analytical or deterministic solution, the Monte Carlo method was employed to explore the model’s statistical properties. The results demonstrate that the Ising model is capable of replicating the majority of the statistical features analyzed. ...

Deep Learning vs. Black-Scholes: Option Pricing Performance on Brazilian Petrobras Stocks ArXiv ID: 2504.20088 “View on arXiv” Authors: Joao Felipe Gueiros, Hemanth Chandravamsi, Steven H. Frankel Abstract This paper explores the use of deep residual networks for pricing European options on Petrobras, one of the world’s largest oil and gas producers, and compares its performance with the Black-Scholes (BS) model. Using eight years of historical data from B3 (Brazilian Stock Exchange) collected via web scraping, a deep learning model was trained using a custom built hybrid loss function that incorporates market data and analytical pricing. The data for training and testing were drawn between the period spanning November 2016 to January 2025, using an 80-20 train-test split. The test set consisted of data from the final three months: November, December, and January 2025. The deep residual network model achieved a 64.3% reduction in the mean absolute error for the 3-19 BRL (Brazilian Real) range when compared to the Black-Scholes model on the test set. Furthermore, unlike the Black-Scholes solution, which tends to decrease its accuracy for longer periods of time, the deep learning model performed accurately for longer expiration periods. These findings highlight the potential of deep learning in financial modeling, with future work focusing on specialized models for different price ranges. ...

QuantBench: Benchmarking AI Methods for Quantitative Investment ArXiv ID: 2504.18600 “View on arXiv” Authors: Saizhuo Wang, Hao Kong, Jiadong Guo, Fengrui Hua, Yiyan Qi, Wanyun Zhou, Jiahao Zheng, Xinyu Wang, Lionel M. Ni, Jian Guo Abstract The field of artificial intelligence (AI) in quantitative investment has seen significant advancements, yet it lacks a standardized benchmark aligned with industry practices. This gap hinders research progress and limits the practical application of academic innovations. We present QuantBench, an industrial-grade benchmark platform designed to address this critical need. QuantBench offers three key strengths: (1) standardization that aligns with quantitative investment industry practices, (2) flexibility to integrate various AI algorithms, and (3) full-pipeline coverage of the entire quantitative investment process. Our empirical studies using QuantBench reveal some critical research directions, including the need for continual learning to address distribution shifts, improved methods for modeling relational financial data, and more robust approaches to mitigate overfitting in low signal-to-noise environments. By providing a common ground for evaluation and fostering collaboration between researchers and practitioners, QuantBench aims to accelerate progress in AI for quantitative investment, similar to the impact of benchmark platforms in computer vision and natural language processing. ...