Pathwise analysis of log-optimal portfolios ArXiv ID: 2507.18232 “View on arXiv” Authors: Andrew L. Allan, Anna P. Kwossek, Chong Liu, David J. Prömel Abstract Based on the theory of càdlàg rough paths, we develop a pathwise approach to analyze stability and approximation properties of portfolios along individual price trajectories generated by standard models of financial markets. As a prototypical example from portfolio theory, we study the log-optimal portfolio in a classical investment-consumption optimization problem on a frictionless financial market modelled by an Itô diffusion process. We identify a fully deterministic framework that enables a pathwise construction of the log-optimal portfolio, for which we then establish pathwise stability estimates with respect to the underlying model parameters. We also derive pathwise error estimates arising from the time-discretization of the log-optimal portfolio and its associated capital process. ...

Analysing Models for Volatility Clustering with Subordinated Processes: VGSA and Beyond ArXiv ID: 2507.17431 “View on arXiv” Authors: Sourojyoti Barick, Sudip Ratan Chandra Abstract This paper explores a comprehensive class of time-changed stochastic processes constructed by subordinating Brownian motion with Levy processes, where the subordination is further governed by stochastic arrival mechanisms such as the Cox Ingersoll Ross (CIR) and Chan Karolyi Longstaff Sanders (CKLS) processes. These models extend classical jump frameworks like the Variance Gamma (VG) and CGMY processes, allowing for more flexible modeling of market features such as jump clustering, heavy tails, and volatility persistence. We first revisit the theory of Levy subordinators and establish strong consistency results for the VG process under Gamma subordination. Building on this, we prove asymptotic normality for both the VG and VGSA (VG with stochastic arrival) processes when the arrival process follows CIR or CKLS dynamics. The analysis is then extended to the more general CGMY process under stochastic arrival, for which we derive analogous consistency and limit theorems under positivity and regularity conditions on the arrival process. A simulation study accompanies the theoretical work, confirming our results through Monte Carlo experiments, with visualizations and normality testing (via Shapiro-Wilk statistics) that show approximate Gaussian behavior even for processes driven by heavy-tailed jumps. This work provides a rigorous and unified probabilistic framework for analyzing subordinated models with stochastic time changes, with applications to financial modeling and inference under uncertainty. ...

EFS: Evolutionary Factor Searching for Sparse Portfolio Optimization Using Large Language Models ArXiv ID: 2507.17211 “View on arXiv” Authors: Haochen Luo, Yuan Zhang, Chen Liu Abstract Sparse portfolio optimization is a fundamental yet challenging problem in quantitative finance, since traditional approaches heavily relying on historical return statistics and static objectives can hardly adapt to dynamic market regimes. To address this issue, we propose Evolutionary Factor Search (EFS), a novel framework that leverages large language models (LLMs) to automate the generation and evolution of alpha factors for sparse portfolio construction. By reformulating the asset selection problem as a top-m ranking task guided by LLM-generated factors, EFS incorporates an evolutionary feedback loop to iteratively refine the factor pool based on performance. Extensive experiments on five Fama-French benchmark datasets and three real-market datasets (US50, HSI45 and CSI300) demonstrate that EFS significantly outperforms both statistical-based and optimization-based baselines, especially in larger asset universes and volatile conditions. Comprehensive ablation studies validate the importance of prompt composition, factor diversity, and LLM backend choice. Our results highlight the promise of language-guided evolution as a robust and interpretable paradigm for portfolio optimization under structural constraints. ...

Optimal Trading under Instantaneous and Persistent Price Impact, Predictable Returns and Multiscale Stochastic Volatility ArXiv ID: 2507.17162 “View on arXiv” Authors: Patrick Chan, Ronnie Sircar, Iosif Zimbidis Abstract We consider a dynamic portfolio optimization problem that incorporates predictable returns, instantaneous transaction costs, price impact, and stochastic volatility, extending the classical results of Garleanu and Pedersen (2013), which assume constant volatility. Constructing the optimal portfolio strategy in this general setting is challenging due to the nonlinear nature of the resulting Hamilton-Jacobi-Bellman (HJB) equations. To address this, we propose a multi-scale volatility expansion that captures stochastic volatility dynamics across different time scales. Specifically, the analysis involves a singular perturbation for the fast mean-reverting volatility factor and a regular perturbation for the slow-moving factor. We also introduce an approximation for small price impact and demonstrate its numerical accuracy. We formally derive asymptotic approximations up to second order and use Monte Carlo simulations to show how incorporating these corrections improves the Profit and Loss (PnL) of the resulting portfolio strategy. ...

Statistical modeling of SOFR term structure ArXiv ID: 2508.02691 “View on arXiv” Authors: Teemu Pennanen, Waleed Taoum Abstract SOFR derivatives market remains illiquid and incomplete so it is not amenable to classical risk-neutral term structure models which are based on the assumption of perfect liquidity and completeness. This paper develops a statistical SOFR term structure model that is well-suited for risk management and derivatives pricing within the incomplete markets paradigm. The model incorporates relevant macroeconomic factors that drive central bank policy rates which, in turn, cause jumps often observed in the SOFR rates. The model is easy to calibrate to historical data, current market quotes, and the user’s views concerning the future development of the relevant macroeconomic factors. The model is well suited for large-scale simulations often required in risk management, portfolio optimization and indifference pricing of interest rate derivatives. ...

Time Deep Gradient Flow Method for pricing American options ArXiv ID: 2507.17606 “View on arXiv” Authors: Jasper Rou Abstract In this research, we explore neural network-based methods for pricing multidimensional American put options under the BlackScholes and Heston model, extending up to five dimensions. We focus on two approaches: the Time Deep Gradient Flow (TDGF) method and the Deep Galerkin Method (DGM). We extend the TDGF method to handle the free-boundary partial differential equation inherent in American options. We carefully design the sampling strategy during training to enhance performance. Both TDGF and DGM achieve high accuracy while outperforming conventional Monte Carlo methods in terms of computational speed. In particular, TDGF tends to be faster during training than DGM. ...

Adaptive Market Intelligence: A Mixture of Experts Framework for Volatility-Sensitive Stock Forecasting ArXiv ID: 2508.02686 “View on arXiv” Authors: Diego Vallarino Abstract This study develops and empirically validates a Mixture of Experts (MoE) framework for stock price prediction across heterogeneous volatility regimes using real market data. The proposed model combines a Recurrent Neural Network (RNN) optimized for high-volatility stocks with a linear regression model tailored to stable equities. A volatility-aware gating mechanism dynamically weights the contributions of each expert based on asset classification. Using a dataset of 30 publicly traded U.S. stocks spanning diverse sectors, the MoE approach consistently outperforms both standalone models. Specifically, it achieves up to 33% improvement in MSE for volatile assets and 28% for stable assets relative to their respective baselines. Stratified evaluation across volatility classes demonstrates the model’s ability to adapt complexity to underlying market dynamics. These results confirm that no single model suffices across market regimes and highlight the advantage of adaptive architectures in financial prediction. Future work should explore real-time gate learning, dynamic volatility segmentation, and applications to portfolio optimization. ...

Alternative Loss Function in Evaluation of Transformer Models ArXiv ID: 2507.16548 “View on arXiv” Authors: Jakub Michańków, Paweł Sakowski, Robert Ślepaczuk Abstract The proper design and architecture of testing machine learning models, especially in their application to quantitative finance problems, is crucial. The most important aspect of this process is selecting an adequate loss function for training, validation, estimation purposes, and hyperparameter tuning. Therefore, in this research, through empirical experiments on equity and cryptocurrency assets, we apply the Mean Absolute Directional Loss (MADL) function, which is more adequate for optimizing forecast-generating models used in algorithmic investment strategies. The MADL function results are compared between Transformer and LSTM models, and we show that in almost every case, Transformer results are significantly better than those obtained with LSTM. ...

Benchmarking Classical and Quantum Models for DeFi Yield Prediction on Curve Finance ArXiv ID: 2508.02685 “View on arXiv” Authors: Chi-Sheng Chen, Aidan Hung-Wen Tsai Abstract The rise of decentralized finance (DeFi) has created a growing demand for accurate yield and performance forecasting to guide liquidity allocation strategies. In this study, we benchmark six models, XGBoost, Random Forest, LSTM, Transformer, quantum neural networks (QNN), and quantum support vector machines with quantum feature maps (QSVM-QNN), on one year of historical data from 28 Curve Finance pools. We evaluate model performance on test MAE, RMSE, and directional accuracy. Our results show that classical ensemble models, particularly XGBoost and Random Forest, consistently outperform both deep learning and quantum models. XGBoost achieves the highest directional accuracy (71.57%) with a test MAE of 1.80, while Random Forest attains the lowest test MAE of 1.77 and 71.36% accuracy. In contrast, quantum models underperform with directional accuracy below 50% and higher errors, highlighting current limitations in applying quantum machine learning to real-world DeFi time series data. This work offers a reproducible benchmark and practical insights into model suitability for DeFi applications, emphasizing the robustness of classical methods over emerging quantum approaches in this domain. ...

Binary Tree Option Pricing Under Market Microstructure Effects: A Random Forest Approach ArXiv ID: 2507.16701 “View on arXiv” Authors: Akash Deep, Chris Monico, W. Brent Lindquist, Svetlozar T. Rachev, Frank J. Fabozzi Abstract We propose a machine learning-based extension of the classical binomial option pricing model that incorporates key market microstructure effects. Traditional models assume frictionless markets, overlooking empirical features such as bid-ask spreads, discrete price movements, and serial return correlations. Our framework augments the binomial tree with path-dependent transition probabilities estimated via Random Forest classifiers trained on high-frequency market data. This approach preserves no-arbitrage conditions while embedding real-world trading dynamics into the pricing model. Using 46,655 minute-level observations of SPY from January to June 2025, we achieve an AUC of 88.25% in forecasting one-step price movements. Order flow imbalance is identified as the most influential predictor, contributing 43.2% to feature importance. After resolving time-scaling inconsistencies in tree construction, our model yields option prices that deviate by 13.79% from Black-Scholes benchmarks, highlighting the impact of microstructure on fair value estimation. While computational limitations restrict the model to short-term derivatives, our results offer a robust, data-driven alternative to classical pricing methods grounded in empirical market behavior. ...