Multifractality and sample size influence on Bitcoin volatility patterns ArXiv ID: 2511.03314 “View on arXiv” Authors: Tetsuya Takaishi Abstract The finite sample effect on the Hurst exponent (HE) of realized volatility time series is examined using Bitcoin data. This study finds that the HE decreases as the sampling period $Δ$ increases and a simple finite sample ansatz closely fits the HE data. We obtain values of the HE as $Δ\rightarrow 0$, which are smaller than 1/2, indicating rough volatility. The relative error is found to be $1%$ for the widely used five-minute realized volatility. Performing a multifractal analysis, we find the multifractality in the realized volatility time series, smaller than that of the price-return time series. ...

When Reasoning Fails: Evaluating ‘Thinking’ LLMs for Stock Prediction ArXiv ID: 2511.08608 “View on arXiv” Authors: Rakeshkumar H Sodha Abstract Problem. “Thinking” LLMs (TLLMs) expose explicit or hidden reasoning traces and are widely believed to generalize better on complex tasks than direct LLMs. Whether this promise carries to noisy, heavy-tailed and regime-switching financial data remains unclear. Approach. Using Indian equities (NIFTY constituents), we run a rolling 48m/1m walk-forward evaluation at horizon k = 1 day and dial cross-sectional complexity via the universe size U in {“5, 11, 21, 36”} while keeping the reasoning budget fixed (B = 512 tokens) for the TLLM. We compare a direct LLM (gpt-4o-mini), a TLLM (gpt-5), and classical learners (ridge, random forest) on cross-sectional ranking loss 1 - IC, MSE, and long/short backtests with realistic costs. Statistical confidence is measured with Diebold-Mariano, Pesaran-Timmermann, and SPA tests. Main findings. (i) As U grows under a fixed budget B, the TLLM’s ranking quality deteriorates, whereas the direct LLM remains flat and classical baselines are stable. (ii) TLLM variance is higher, requiring ex-post calibration (winsorization and blending) for stability. (iii) Portfolio results under transaction costs do not support a net advantage for the TLLM. Hypotheses. Our results are consistent with the following testable hypotheses: H1 (Capacity-Complexity Mismatch): for fixed B, TLLM accuracy degrades superlinearly in cross-sectional complexity. H2 (Reasoning Variance): TLLM outputs exhibit higher dispersion date-by-date than direct LLMs, increasing error bars and turnover. H3 (Domain Misfit): next-token prediction objectives and token-budgeted inference are poorly aligned with heavy-tailed, weakly predictable stock returns. Implication. In our setting, “thinking” LLMs are not yet ready to replace classical or direct methods for short-horizon stock ranking; scaling the reasoning budget and/or re-aligning objectives appears necessary. ...

Modeling Hawkish-Dovish Latent Beliefs in Multi-Agent Debate-Based LLMs for Monetary Policy Decision Classification ArXiv ID: 2511.02469 “View on arXiv” Authors: Kaito Takano, Masanori Hirano, Kei Nakagawa Abstract Accurately forecasting central bank policy decisions, particularly those of the Federal Open Market Committee(FOMC) has become increasingly important amid heightened economic uncertainty. While prior studies have used monetary policy texts to predict rate changes, most rely on static classification models that overlook the deliberative nature of policymaking. This study proposes a novel framework that structurally imitates the FOMC’s collective decision-making process by modeling multiple large language models(LLMs) as interacting agents. Each agent begins with a distinct initial belief and produces a prediction based on both qualitative policy texts and quantitative macroeconomic indicators. Through iterative rounds, agents revise their predictions by observing the outputs of others, simulating deliberation and consensus formation. To enhance interpretability, we introduce a latent variable representing each agent’s underlying belief(e.g., hawkish or dovish), and we theoretically demonstrate how this belief mediates the perception of input information and interaction dynamics. Empirical results show that this debate-based approach significantly outperforms standard LLMs-based baselines in prediction accuracy. Furthermore, the explicit modeling of beliefs provides insights into how individual perspectives and social influence shape collective policy forecasts. ...

Numerical valuation of European options under two-asset infinite-activity exponential Lévy models ArXiv ID: 2511.02700 “View on arXiv” Authors: Massimiliano Moda, Karel J. in ’t Hout, Michèle Vanmaele, Fred Espen Benth Abstract We propose a numerical method for the valuation of European-style options under two-asset infinite-activity exponential Lévy models. Our method extends the effective approach developed by Wang, Wan & Forsyth (2007) for the 1-dimensional case to the 2-dimensional setting and is applicable for general Lévy measures under mild assumptions. A tailored discretization of the non-local integral term is developed, which can be efficiently evaluated by means of the fast Fourier transform. For the temporal discretization, the semi-Lagrangian theta-method is employed in a convenient splitting fashion, where the diffusion term is treated implicitly and the integral term is handled explicitly by a fixed-point iteration. Numerical experiments for put-on-the-average options under Normal Tempered Stable dynamics reveal favourable second-order convergence of our method whenever the exponential Lévy process has finite-variation. ...

Option market making with hedging-induced market impact ArXiv ID: 2511.02518 “View on arXiv” Authors: Paulin Aubert, Etienne Chevalier, Vathana Ly Vath Abstract This paper develops a model for option market making in which the hedging activity of the market maker generates price impact on the underlying asset. The option order flow is modeled by Cox processes, with intensities depending on the state of the underlying and on the market maker’s quoted prices. The resulting dynamics combine stochastic option demand with both permanent and transient impact on the underlying, leading to a coupled evolution of inventory and price. We first study market manipulation and arbitrage phenomena that may arise from the feedback between option trading and underlying impact. We then establish the well-posedness of the mixed control problem, which involves continuous quoting decisions and impulsive hedging actions. Finally, we implement a numerical method based on policy optimization to approximate optimal strategies and illustrate the interplay between option market liquidity, inventory risk, and underlying impact. ...

ABIDES-MARL: A Multi-Agent Reinforcement Learning Environment for Endogenous Price Formation and Execution in a Limit Order Book ArXiv ID: 2511.02016 “View on arXiv” Authors: Patrick Cheridito, Jean-Loup Dupret, Zhexin Wu Abstract We present ABIDES-MARL, a framework that combines a new multi-agent reinforcement learning (MARL) methodology with a new realistic limit-order-book (LOB) simulation system to study equilibrium behavior in complex financial market games. The system extends ABIDES-Gym by decoupling state collection from kernel interruption, enabling synchronized learning and decision-making for multiple adaptive agents while maintaining compatibility with standard RL libraries. It preserves key market features such as price-time priority and discrete tick sizes. Methodologically, we use MARL to approximate equilibrium-like behavior in multi-period trading games with a finite number of heterogeneous agents-an informed trader, a liquidity trader, noise traders, and competing market makers-all with individual price impacts. This setting bridges optimal execution and market microstructure by embedding the liquidity trader’s optimization problem within a strategic trading environment. We validate the approach by solving an extended Kyle model within the simulation system, recovering the gradual price discovery phenomenon. We then extend the analysis to a liquidity trader’s problem where market liquidity arises endogenously and show that, at equilibrium, execution strategies shape market-maker behavior and price dynamics. ABIDES-MARL provides a reproducible foundation for analyzing equilibrium and strategic adaptation in realistic markets and contributes toward building economically interpretable agentic AI systems for finance. ...

High-Dimensional Spatial Arbitrage Pricing Theory with Heterogeneous Interactions ArXiv ID: 2511.01271 “View on arXiv” Authors: Zhaoxing Gao, Sihan Tu, Ruey S. Tsay Abstract This paper investigates estimation and inference of a Spatial Arbitrage Pricing Theory (SAPT) model that integrates spatial interactions with multi-factor analysis, accommodating both observable and latent factors. Building on the classical mean-variance analysis, we introduce a class of Spatial Capital Asset Pricing Models (SCAPM) that account for spatial effects in high-dimensional assets, where we define {"\it spatial rho"} as a counterpart to market beta in CAPM. We then extend SCAPM to a general SAPT framework under a {"\it complete"} market setting by incorporating multiple factors. For SAPT with observable factors, we propose a generalized shrinkage Yule-Walker (SYW) estimation method that integrates ridge regression to estimate spatial and factor coefficients. When factors are latent, we first apply an autocovariance-based eigenanalysis to extract factors, then employ the SYW method using the estimated factors. We establish asymptotic properties for these estimators under high-dimensional settings where both the dimension and sample size diverge. Finally, we use simulated and real data examples to demonstrate the efficacy and usefulness of the proposed model and method. ...

JaxMARL-HFT: GPU-Accelerated Large-Scale Multi-Agent Reinforcement Learning for High-Frequency Trading ArXiv ID: 2511.02136 “View on arXiv” Authors: Valentin Mohl, Sascha Frey, Reuben Leyland, Kang Li, George Nigmatulin, Mihai Cucuringu, Stefan Zohren, Jakob Foerster, Anisoara Calinescu Abstract Agent-based modelling (ABM) approaches for high-frequency financial markets are difficult to calibrate and validate, partly due to the large parameter space created by defining fixed agent policies. Multi-agent reinforcement learning (MARL) enables more realistic agent behaviour and reduces the number of free parameters, but the heavy computational cost has so far limited research efforts. To address this, we introduce JaxMARL-HFT (JAX-based Multi-Agent Reinforcement Learning for High-Frequency Trading), the first GPU-accelerated open-source multi-agent reinforcement learning environment for high-frequency trading (HFT) on market-by-order (MBO) data. Extending the JaxMARL framework and building on the JAX-LOB implementation, JaxMARL-HFT is designed to handle a heterogeneous set of agents, enabling diverse observation/action spaces and reward functions. It is designed flexibly, so it can also be used for single-agent RL, or extended to act as an ABM with fixed-policy agents. Leveraging JAX enables up to a 240x reduction in end-to-end training time, compared with state-of-the-art reference implementations on the same hardware. This significant speed-up makes it feasible to exploit the large, granular datasets available in high-frequency trading, and to perform the extensive hyperparameter sweeps required for robust and efficient MARL research in trading. We demonstrate the use of JaxMARL-HFT with independent Proximal Policy Optimization (IPPO) for a two-player environment, with an order execution and a market making agent, using one year of LOB data (400 million orders), and show that these agents learn to outperform standard benchmarks. The code for the JaxMARL-HFT framework is available on GitHub. ...

Numerical methods for solving PIDEs arising in swing option pricing under a two-factor mean-reverting model with jumps ArXiv ID: 2511.01587 “View on arXiv” Authors: Mustapha Regragui, Karel J. in ’t Hout, Michèle Vanmaele, Fred Espen Benth Abstract This paper concerns the numerical valuation of swing options with discrete action times under a linear two-factor mean-reverting model with jumps. The resulting sequence of two-dimensional partial integro-differential equations (PIDEs) are convection-dominated and possess a nonlocal integral term due to the presence of jumps. Further, the initial function is nonsmooth. We propose various second-order numerical methods that can adequately handle these challenging features. The stability and convergence of these numerical methods are analysed theoretically. By ample numerical experiments, we confirm their second-order convergence behaviour. ...

One model to solve them all: 2BSDE families via neural operators ArXiv ID: 2511.01125 “View on arXiv” Authors: Takashi Furuya, Anastasis Kratsios, Dylan Possamaï, Bogdan Raonić Abstract We introduce a mild generative variant of the classical neural operator model, which leverages Kolmogorov–Arnold networks to solve infinite families of second-order backward stochastic differential equations ($2$BSDEs) on regular bounded Euclidean domains with random terminal time. Our first main result shows that the solution operator associated with a broad range of $2$BSDE families is approximable by appropriate neural operator models. We then identify a structured subclass of (infinite) families of $2$BSDEs whose neural operator approximation requires only a polynomial number of parameters in the reciprocal approximation rate, as opposed to the exponential requirement in general worst-case neural operator guarantees. ...