Predicting Realized Variance Out of Sample: Can Anything Beat The Benchmark? ArXiv ID: 2506.07928 “View on arXiv” Authors: Austin Pollok Abstract The discrepancy between realized volatility and the market’s view of volatility has been known to predict individual equity options at the monthly horizon. It is not clear how this predictability depends on a forecast’s ability to predict firm-level volatility. We consider this phenomenon at the daily frequency using high-dimensional machine learning models, as well as low-dimensional factor models. We find that marginal improvements to standard forecast error measurements can lead to economically significant gains in portfolio performance. This makes a case for re-imagining the way we train models that are used to construct portfolios. ...

Supervised Similarity for Firm Linkages ArXiv ID: 2506.19856 “View on arXiv” Authors: Ryan Samson, Adrian Banner, Luca Candelori, Sebastien Cottrell, Tiziana Di Matteo, Paul Duchnowski, Vahagn Kirakosyan, Jose Marques, Kharen Musaelian, Stefano Pasquali, Ryan Stever, Dario Villani Abstract We introduce a novel proxy for firm linkages, Characteristic Vector Linkages (CVLs). We use this concept to estimate firm linkages, first through Euclidean similarity, and then by applying Quantum Cognition Machine Learning (QCML) to similarity learning. We demonstrate that both methods can be used to construct profitable momentum spillover trading strategies, but QCML similarity outperforms the simpler Euclidean similarity. ...

The Subtle Interplay between Square-root Impact, Order Imbalance & Volatility: A Unifying Framework ArXiv ID: 2506.07711 “View on arXiv” Authors: Guillaume Maitrier, Jean-Philippe Bouchaud Abstract In this work, we aim to reconcile several apparently contradictory observations in market microstructure: is the famous “square-root law” of metaorder impact, which decays with time, compatible with the random-walk nature of prices and the linear impact of order imbalances? Can one entirely explain the volatility of prices as resulting from the flow of uninformed metaorders that mechanically impact them? We introduce a new theoretical framework to describe metaorders with different signs, sizes and durations, which all impact prices as a square-root of volume but with a subsequent time decay. We show that, as in the original propagator model, price diffusion is ensured by the long memory of cross-correlations between metaorders. In order to account for the effect of strongly fluctuating volumes q of individual trades, we further introduce two q-dependent exponents, which allow us to describe how the moments of generalized volume imbalance and the correlation between price changes and generalized order flow imbalance scale with T. We predict in particular that the corresponding power-laws depend in a non-monotonic fashion on a parameter a, which allows one to put the same weight on all child orders or to overweight large ones, a behaviour that is clearly borne out by empirical data. We also predict that the correlation between price changes and volume imbalances should display a maximum as a function of a, which again matches observations. Such noteworthy agreement between theory and data suggests that our framework correctly captures the basic mechanism at the heart of price formation, namely the average impact of metaorders. We argue that our results support the “Order-Driven” theory of excess volatility, and are at odds with the idea that a “Fundamental” component accounts for a large share of the volatility of financial markets. ...

From Axioms to Algorithms: Mechanized Proofs of the vNM Utility Theorem ArXiv ID: 2506.07066 “View on arXiv” Authors: Li Jingyuan Abstract This paper presents a comprehensive formalization of the von Neumann-Morgenstern (vNM) expected utility theorem using the Lean 4 interactive theorem prover. We implement the classical axioms of preference-completeness, transitivity, continuity, and independence-enabling machine-verified proofs of both the existence and uniqueness of utility representations. Our formalization captures the mathematical structure of preference relations over lotteries, verifying that preferences satisfying the vNM axioms can be represented by expected utility maximization. Our contributions include a granular implementation of the independence axiom, formally verified proofs of fundamental claims about mixture lotteries, constructive demonstrations of utility existence, and computational experiments validating the results. We prove equivalence to classical presentations while offering greater precision at decision boundaries. This formalization provides a rigorous foundation for applications in economic modeling, AI alignment, and management decision systems, bridging the gap between theoretical decision theory and computational implementation. ...

Uncertainty-Aware Strategies: A Model-Agnostic Framework for Robust Financial Optimization through Subsampling ArXiv ID: 2506.07299 “View on arXiv” Authors: Hans Buehler, Blanka Horvath, Yannick Limmer, Thorsten Schmidt Abstract This paper addresses the challenge of model uncertainty in quantitative finance, where decisions in portfolio allocation, derivative pricing, and risk management rely on estimating stochastic models from limited data. In practice, the unavailability of the true probability measure forces reliance on an empirical approximation, and even small misestimations can lead to significant deviations in decision quality. Building on the framework of Klibanoff et al. (2005), we enhance the conventional objective - whether this is expected utility in an investing context or a hedging metric - by superimposing an outer “uncertainty measure”, motivated by traditional monetary risk measures, on the space of models. In scenarios where a natural model distribution is lacking or Bayesian methods are impractical, we propose an ad hoc subsampling strategy, analogous to bootstrapping in statistical finance and related to mini-batch sampling in deep learning, to approximate model uncertainty. To address the quadratic memory demands of naive implementations, we also present an adapted stochastic gradient descent algorithm that enables efficient parallelization. Through analytical, simulated, and empirical studies - including multi-period, real data and high-dimensional examples - we demonstrate that uncertainty measures outperform traditional mixture of measures strategies and our model-agnostic subsampling-based approach not only enhances robustness against model risk but also achieves performance comparable to more elaborate Bayesian methods. ...

Explaining Risks: Axiomatic Risk Attributions for Financial Models ArXiv ID: 2506.06653 “View on arXiv” Authors: Dangxing Chen Abstract In recent years, machine learning models have achieved great success at the expense of highly complex black-box structures. By using axiomatic attribution methods, we can fairly allocate the contributions of each feature, thus allowing us to interpret the model predictions. In high-risk sectors such as finance, risk is just as important as mean predictions. Throughout this work, we address the following risk attribution problem: how to fairly allocate the risk given a model with data? We demonstrate with analysis and empirical examples that risk can be well allocated by extending the Shapley value framework. ...

Goal-based portfolio selection with mental accounting ArXiv ID: 2506.06654 “View on arXiv” Authors: Erhan Bayraktar, Bingyan Han Abstract We present a continuous-time portfolio selection framework that reflects goal-based investment principles and mental accounting behavior. In this framework, an investor with multiple investment goals constructs separate portfolios, each corresponding to a specific goal, with penalties imposed on fund transfers between these goals, referred to as mental costs. By applying the stochastic Perron’s method, we demonstrate that the value function is the unique constrained viscosity solution of a Hamilton-Jacobi-Bellman equation system. Numerical analysis reveals several key features: the free boundaries exhibit complex shapes with bulges and notches; the optimal strategy for one portfolio depends on the wealth level of another; investors must diversify both among stocks and across portfolios; and they may postpone reallocating surplus from an important goal to a less important one until the former’s deadline approaches. ...

Exploring Microstructural Dynamics in Cryptocurrency Limit Order Books: Better Inputs Matter More Than Stacking Another Hidden Layer ArXiv ID: 2506.05764 “View on arXiv” Authors: Haochuan Wang Abstract Cryptocurrency price dynamics are driven largely by microstructural supply demand imbalances in the limit order book (LOB), yet the highly noisy nature of LOB data complicates the signal extraction process. Prior research has demonstrated that deep-learning architectures can yield promising predictive performance on pre-processed equity and futures LOB data, but they often treat model complexity as an unqualified virtue. In this paper, we aim to examine whether adding extra hidden layers or parameters to “blackbox ish” neural networks genuinely enhances short term price forecasting, or if gains are primarily attributable to data preprocessing and feature engineering. We benchmark a spectrum of models from interpretable baselines, logistic regression, XGBoost to deep architectures (DeepLOB, Conv1D+LSTM) on BTC/USDT LOB snapshots sampled at 100 ms to multi second intervals using publicly available Bybit data. We introduce two data filtering pipelines (Kalman, Savitzky Golay) and evaluate both binary (up/down) and ternary (up/flat/down) labeling schemes. Our analysis compares models on out of sample accuracy, latency, and robustness to noise. Results reveal that, with data preprocessing and hyperparameter tuning, simpler models can match and even exceed the performance of more complex networks, offering faster inference and greater interpretability. ...

FlowOE: Imitation Learning with Flow Policy from Ensemble RL Experts for Optimal Execution under Heston Volatility and Concave Market Impacts ArXiv ID: 2506.05755 “View on arXiv” Authors: Yang Li, Zhi Chen Abstract Optimal execution in financial markets refers to the process of strategically transacting a large volume of assets over a period to achieve the best possible outcome by balancing the trade-off between market impact costs and timing or volatility risks. Traditional optimal execution strategies, such as static Almgren-Chriss models, often prove suboptimal in dynamic financial markets. This paper propose flowOE, a novel imitation learning framework based on flow matching models, to address these limitations. FlowOE learns from a diverse set of expert traditional strategies and adaptively selects the most suitable expert behavior for prevailing market conditions. A key innovation is the incorporation of a refining loss function during the imitation process, enabling flowOE not only to mimic but also to improve upon the learned expert actions. To the best of our knowledge, this work is the first to apply flow matching models in a stochastic optimal execution problem. Empirical evaluations across various market conditions demonstrate that flowOE significantly outperforms both the specifically calibrated expert models and other traditional benchmarks, achieving higher profits with reduced risk. These results underscore the practical applicability and potential of flowOE to enhance adaptive optimal execution. ...

Transformers Beyond Order: A Chaos-Markov-Gaussian Framework for Short-Term Sentiment Forecasting of Any Financial OHLC timeseries Data ArXiv ID: 2506.17244 “View on arXiv” Authors: Arif Pathan Abstract Short-term sentiment forecasting in financial markets (e.g., stocks, indices) is challenging due to volatility, non-linearity, and noise in OHLC (Open, High, Low, Close) data. This paper introduces a novel CMG (Chaos-Markov-Gaussian) framework that integrates chaos theory, Markov property, and Gaussian processes to improve prediction accuracy. Chaos theory captures nonlinear dynamics; the Markov chain models regime shifts; Gaussian processes add probabilistic reasoning. We enhance the framework with transformer-based deep learning models to capture temporal patterns efficiently. The CMG Framework is designed for fast, resource-efficient, and accurate forecasting of any financial instrument’s OHLC time series. Unlike traditional models that require heavy infrastructure and instrument-specific tuning, CMG reduces overhead and generalizes well. We evaluate the framework on market indices, forecasting sentiment for the next trading day’s first quarter. A comparative study against statistical, ML, and DL baselines trained on the same dataset with no feature engineering shows CMG consistently outperforms in accuracy and efficiency, making it valuable for analysts and financial institutions. ...