Probabilistic Forecasting Cryptocurrencies Volatility: From Point to Quantile Forecasts ArXiv ID: 2508.15922 “View on arXiv” Authors: Grzegorz Dudek, Witold Orzeszko, Piotr Fiszeder Abstract Cryptocurrency markets are characterized by extreme volatility, making accurate forecasts essential for effective risk management and informed trading strategies. Traditional deterministic (point) forecasting methods are inadequate for capturing the full spectrum of potential volatility outcomes, underscoring the importance of probabilistic approaches. To address this limitation, this paper introduces probabilistic forecasting methods that leverage point forecasts from a wide range of base models, including statistical (HAR, GARCH, ARFIMA) and machine learning (e.g. LASSO, SVR, MLP, Random Forest, LSTM) algorithms, to estimate conditional quantiles of cryptocurrency realized variance. To the best of our knowledge, this is the first study in the literature to propose and systematically evaluate probabilistic forecasts of variance in cryptocurrency markets based on predictions derived from multiple base models. Our empirical results for Bitcoin demonstrate that the Quantile Estimation through Residual Simulation (QRS) method, particularly when applied to linear base models operating on log-transformed realized volatility data, consistently outperforms more sophisticated alternatives. Additionally, we highlight the robustness of the probabilistic stacking framework, providing comprehensive insights into uncertainty and risk inherent in cryptocurrency volatility forecasting. This research fills a significant gap in the literature, contributing practical probabilistic forecasting methodologies tailored specifically to cryptocurrency markets. ...

Deep Learning for Short Term Equity Trend Forecasting: A Behavior Driven Multi Factor Approach ArXiv ID: 2508.14656 “View on arXiv” Authors: Yuqi Luan Abstract This study proposes a behaviorally-informed multi-factor stock selection framework that integrates short-cycle technical alpha signals with deep learning. We design a dual-task multilayer perceptron (MLP) that jointly predicts five-day future returns and directional price movements, thereby capturing nonlinear market behaviors such as volume-price divergence, momentum-driven herding, and bottom reversals. The model is trained on 40 carefully constructed factors derived from price-volume patterns and behavioral finance insights. Empirical evaluation demonstrates that the dual-task MLP achieves superior and stable performance across both predictive accuracy and economic relevance, as measured by information coefficient (IC), information ratio (IR), and portfolio backtesting results. Comparative experiments further show that deep learning methods outperform linear baselines by effectively capturing structural interactions between factors. This work highlights the potential of structure-aware deep learning in enhancing multi-factor modeling and provides a practical framework for short-horizon quantitative investment strategies. ...

Directional Price Forecasting in the Continuous Intraday Market under Consideration of Neighboring Products and Limit Order Books ArXiv ID: 2509.04452 “View on arXiv” Authors: Timothée Hornek, Sergio Potenciano Menci, Ivan Pavić Abstract The increasing penetration of variable renewable energy and flexible demand technologies, such as electric vehicles and heat pumps, introduces significant uncertainty in power systems, resulting in greater imbalance; defined as the deviation between scheduled and actual supply or demand. Short-term power markets, such as the European continuous intraday market, play a critical role in mitigating these imbalances by enabling traders to adjust forecasts close to real time. Due to the high volatility of the continuous intraday market, traders increasingly rely on electricity price forecasting to guide trading decisions and mitigate price risk. However most electricity price forecasting approaches in the literature simplify the forecasting task. They focus on single benchmark prices, neglecting intra-product price dynamics and price signals from the limit order book. They also underuse high-frequency and cross-product price data. In turn, we propose a novel directional electricity price forecasting method for hourly products in the European continuous intraday market. Our method incorporates short-term features from both hourly and quarter-hourly products and is evaluated using German European Power Exchange data from 2024-2025. The results indicate that features derived from the limit order book are the most influential exogenous variables. In addition, features from neighboring products; especially those with delivery start times that overlap with the trading period of the target product; improve forecast accuracy. Finally, our evaluation of the value captured by our electricity price forecasting suggests that the proposed electricity price forecasting method has the potential to generate profit when applied in trading strategies. ...

Fast reliable pricing and calibration of the rough Heston model ArXiv ID: 2508.15080 “View on arXiv” Authors: Svetlana Boyarchenko, Marco de Innocentis, Sergei Levendorskiĭ Abstract The paper is an extended and modified version of the preprint S.Boyarchenko and S.Levendorskiĭ Correct implied volatility shapes and reliable pricing in the rough Heston model". We combine a modification of the Adams method with the SINH-acceleration method S.Boyarchenko and S.Levendorskii (IJTAF 2019, v.22) of Fourier inversion (iFT) to price vanilla options under the rough Heston model. For moderate or long maturities and strikes near spot, thousands of prices are computed in several milliseconds (ms) in Matlab on a Mac with moderate specs, with relative errors $\lesssim 10^{"-4"}$. Even for options close to expiry and far-OTM, the pricing takes a few tens or hundreds of ms. We show that, for the calibrated parameters in El Euch and Rosenbaum (Math.Finance 2019, v.29), the model implied vol surface is much flatter and fits the market data poorly; thus the calibration in op.cit. is a case of ghost calibration’’ (M.Boyarchenko and S.Levendorskiĭ, Quant. Finance 2015, v.15): numerical error and model specification error offset each other, creating an apparently good fit that vanishes when a more accurate pricer is used. We explain how such errors arise in popular iFT implementations that use fixed numerical parameters, yielding spurious smiles/skews, and provide numerical evidence that SINH acceleration is faster and more accurate than competing methods. Robust error control is ensured by a general Conformal Bootstrap principle that we formulate; the principle is applicable to many Fourier-pricing methods. We outline how this principle and our method enable accurate calibration procedures that are hundreds of times faster than approaches commonly used in the industry. Disclaimer: The views expressed herein are those of the authors only. No other representation should be attributed. ...

Generative Neural Operators of Log-Complexity Can Simultaneously Solve Infinitely Many Convex Programs ArXiv ID: 2508.14995 “View on arXiv” Authors: Anastasis Kratsios, Ariel Neufeld, Philipp Schmocker Abstract Neural operators (NOs) are a class of deep learning models designed to simultaneously solve infinitely many related problems by casting them into an infinite-dimensional space, whereon these NOs operate. A significant gap remains between theory and practice: worst-case parameter bounds from universal approximation theorems suggest that NOs may require an unrealistically large number of parameters to solve most operator learning problems, which stands in direct opposition to a slew of experimental evidence. This paper closes that gap for a specific class of {“NOs”}, generative {“equilibrium operators”} (GEOs), using (realistic) finite-dimensional deep equilibrium layers, when solving families of convex optimization problems over a separable Hilbert space $X$. Here, the inputs are smooth, convex loss functions on $X$, and outputs are the associated (approximate) solutions to the optimization problem defined by each input loss. We show that when the input losses lie in suitable infinite-dimensional compact sets, our GEO can uniformly approximate the corresponding solutions to arbitrary precision, with rank, depth, and width growing only logarithmically in the reciprocal of the approximation error. We then validate both our theoretical results and the trainability of GEOs on three applications: (1) nonlinear PDEs, (2) stochastic optimal control problems, and (3) hedging problems in mathematical finance under liquidity constraints. ...

Graph Learning for Foreign Exchange Rate Prediction and Statistical Arbitrage ArXiv ID: 2508.14784 “View on arXiv” Authors: Yoonsik Hong, Diego Klabjan Abstract We propose a two-step graph learning approach for foreign exchange statistical arbitrages (FXSAs), addressing two key gaps in prior studies: the absence of graph-learning methods for foreign exchange rate prediction (FXRP) that leverage multi-currency and currency-interest rate relationships, and the disregard of the time lag between price observation and trade execution. In the first step, to capture complex multi-currency and currency-interest rate relationships, we formulate FXRP as an edge-level regression problem on a discrete-time spatiotemporal graph. This graph consists of currencies as nodes and exchanges as edges, with interest rates and foreign exchange rates serving as node and edge features, respectively. We then introduce a graph-learning method that leverages the spatiotemporal graph to address the FXRP problem. In the second step, we present a stochastic optimization problem to exploit FXSAs while accounting for the observation-execution time lag. To address this problem, we propose a graph-learning method that enforces constraints through projection and ReLU, maximizes risk-adjusted return by leveraging a graph with exchanges as nodes and influence relationships as edges, and utilizes the predictions from the FXRP method for the constraint parameters and node features. Moreover, we prove that our FXSA method satisfies empirical arbitrage constraints. The experimental results demonstrate that our FXRP method yields statistically significant improvements in mean squared error, and that the FXSA method achieves a 61.89% higher information ratio and a 45.51% higher Sortino ratio than a benchmark. Our approach provides a novel perspective on FXRP and FXSA within the context of graph learning. ...

Investment Portfolio Optimization Based on Modern Portfolio Theory and Deep Learning Models ArXiv ID: 2508.14999 “View on arXiv” Authors: Maciej Wysocki, Paweł Sakowski Abstract This paper investigates an important problem of an appropriate variance-covariance matrix estimation in the Modern Portfolio Theory. We propose a novel framework for variancecovariance matrix estimation for purposes of the portfolio optimization, which is based on deep learning models. We employ the long short-term memory (LSTM) recurrent neural networks (RNN) along with two probabilistic deep learning models: DeepVAR and GPVAR to the task of one-day ahead multivariate forecasting. We then use these forecasts to optimize portfolios of stocks and cryptocurrencies. Our analysis presents results across different combinations of observation windows and rebalancing periods to compare performances of classical and deep learning variance-covariance estimation methods. The conclusions of the study are that although the strategies (portfolios) performance differed significantly between different combinations of parameters, generally the best results in terms of the information ratio and annualized returns are obtained using the LSTM-RNN models. Moreover, longer observation windows translate into better performance of the deep learning models indicating that these methods require longer windows to be able to efficiently capture the long-term dependencies of the variance-covariance matrix structure. Strategies with less frequent rebalancing typically perform better than these with the shortest rebalancing windows across all considered methods. ...

Pricing Options on Forwards in Function-Valued Affine Stochastic Volatility Models ArXiv ID: 2508.14813 “View on arXiv” Authors: Jian He, Sven Karbach, Asma Khedher Abstract We study the pricing of European-style options written on forward contracts within function-valued infinite-dimensional affine stochastic volatility models. The dynamics of the underlying forward price curves are modeled within the Heath-Jarrow-Morton-Musiela framework as solution to a stochastic partial differential equation modulated by a stochastic volatility process. We analyze two classes of affine stochastic volatility models: (i) a Gaussian model governed by a finite-rank Wishart process, and (ii) a pure-jump affine model extending the Barndorff–Nielsen–Shephard framework with state-dependent jumps in the covariance component. For both models, we derive conditions for the existence of exponential moments and develop semi-closed Fourier-based pricing formulas for vanilla call and put options written on forward price curves. Our approach allows for tractable pricing in models with infinitely many risk factors, thereby capturing maturity-specific and term structure risk essential in forward markets. ...

Variable selection for minimum-variance portfolios ArXiv ID: 2508.14986 “View on arXiv” Authors: Guilherme V. Moura, André P. Santos, Hudson S. Torrent Abstract Machine learning (ML) methods have been successfully employed in identifying variables that can predict the equity premium of individual stocks. In this paper, we investigate if ML can also be helpful in selecting variables relevant for optimal portfolio choice. To address this question, we parameterize minimum-variance portfolio weights as a function of a large pool of firm-level characteristics as well as their second-order and cross-product transformations, yielding a total of 4,610 predictors. We find that the gains from employing ML to select relevant predictors are substantial: minimum-variance portfolios achieve lower risk relative to sparse specifications commonly considered in the literature, especially when non-linear terms are added to the predictor space. Moreover, some of the selected predictors that help decreasing portfolio risk also increase returns, leading to minimum-variance portfolios with good performance in terms of Shape ratios in some situations. Our evidence suggests that ad-hoc sparsity can be detrimental to the performance of minimum-variance characteristics-based portfolios. ...

AlphaX: An AI-Based Value Investing Strategy for the Brazilian Stock Market ArXiv ID: 2508.13429 “View on arXiv” Authors: Paulo André Lima de Castro Abstract Autonomous trading strategies have been a subject of research within the field of artificial intelligence (AI) for aconsiderable period. Various AI techniques have been explored to develop autonomous agents capable of trading financial assets. These approaches encompass traditional methods such as neural networks, fuzzy logic, and reinforcement learning, as well as more recent advancements, including deep neural networks and deep reinforcement learning. Many developers report success in creating strategies that exhibit strong performance during simulations using historical price data, a process commonly referred to as backtesting. However, when these strategies are deployed in real markets, their performance often deteriorates, particularly in terms of risk-adjusted returns. In this study, we propose an AI-based strategy inspired by a classical investment paradigm: Value Investing. Financial AI models are highly susceptible to lookahead bias and other forms of bias that can significantly inflate performance in backtesting compared to live trading conditions. To address this issue, we conducted a series of computational simulations while controlling for these biases, thereby reducing the risk of overfitting. Our results indicate that the proposed approach outperforms major Brazilian market benchmarks. Moreover, the strategy, named AlphaX, demonstrated superior performance relative to widely used technical indicators such as the Relative Strength Index (RSI) and Money Flow Index (MFI), with statistically significant results. Finally, we discuss several open challenges and highlight emerging technologies in qualitative analysis that may contribute to the development of a comprehensive AI-based Value Investing framework in the future ...