Broken Symmetry of Stock Returns – a Modified Jones-Faddy Skew t-Distribution ArXiv ID: 2512.23640 “View on arXiv” Authors: Siqi Shao, Arshia Ghasemi, Hamed Farahani, R. A. Serota Abstract We argue that negative skew and positive mean of the distribution of stock returns are largely due to the broken symmetry of stochastic volatility governing gains and losses. Starting with stochastic differential equations for stock returns and for stochastic volatility we argue that the distribution of stock returns can be effectively split in two – for gains and losses – assuming difference in parameters of their respective stochastic volatilities. A modified Jones-Faddy skew t-distribution utilized here allows to reflect this in a single organic distribution which tends to meaningfully capture this asymmetry. We illustrate its application on distribution of daily S&P500 returns, including analysis of its tails. ...

Impact of Volatility on Time-Based Transaction Ordering Policies ArXiv ID: 2512.23386 “View on arXiv” Authors: Sunghun Ko, Jinsuk Park Abstract We study Arbitrum’s Express Lane Auction (ELA), an ahead-of-time second-price auction that grants the winner an exclusive latency advantage for one minute. Building on a single-round model with risk-averse bidders, we propose a hypothesis that the value of priority access is discounted relative to risk-neutral valuation due to the difficulty of forecasting short-horizon volatility and bidders’ risk aversion. We test these predictions using ELA bid records matched to high-frequency ETH prices and find that the result is consistent with the model. ...

Beyond Binary Screens: A Continuous Shariah Compliance Index for Asset Pricing and Portfolio Design ArXiv ID: 2512.22858 “View on arXiv” Authors: Abdulrahman Qadi, Akash Sharma, Francesca Medda Abstract Binary Shariah screens vary across standards and apply hard thresholds that create discontinuous classifications. We construct a Continuous Shariah Compliance Index (CSCI) in $[“0,1”]$ by mapping standard screening ratios to smooth scores between conservative ``comfort’’ bounds and permissive outer bounds, and aggregating them conservatively with a sectoral activity factor. Using CRSP/Compustat U.S. equities (1999-2024) with lagged accounting inputs and monthly rebalancing, we find that CSCI-based long-only portfolios have historical risk-adjusted performance similar to an emulated binary Islamic benchmark. Tightening the minimum compliance threshold reduces the investable universe and diversification and is associated with lower Sharpe ratios. The framework yields a practical compliance gradient that supports portfolio construction, constraint design, and cross-standard comparisons without reliance on pass/fail screening. ...

Squeezed Covariance Matrix Estimation: Analytic Eigenvalue Control ArXiv ID: 2512.23021 “View on arXiv” Authors: Layla Abu Khalaf, William Smyth Abstract We revisit Gerber’s Informational Quality (IQ) framework, a data-driven approach for constructing correlation matrices from co-movement evidence, and address two obstacles that limit its use in portfolio optimization: guaranteeing positive semidefinite ness (PSD) and controlling spectral conditioning. We introduce a squeezing identity that represents IQ estimators as a convex-like combination of structured channel matrices, and propose an atomic-IQ parameterization in which each channel-class matrix is built from PSD atoms with a single class-level normalization. This yields constructive PSD guarantees over an explicit feasibility region, avoiding reliance on ex-post projection. To regulate conditioning, we develop an analytic eigen floor that targets either a minimum eigenvalue or a desired condition number and, when necessary, repairs PSD violations in closed form while remaining compatible with the squeezing identity. In long-only tangency back tests with transaction costs, atomic-IQ improves out-of-sample Sharpe ratios and delivers a more stable risk profile relative to a broad set of standard covariance estimators. ...

AutoQuant: An Auditable Expert-System Framework for Execution-Constrained Auto-Tuning in Cryptocurrency Perpetual Futures ArXiv ID: 2512.22476 “View on arXiv” Authors: Kaihong Deng Abstract Backtests of cryptocurrency perpetual futures are fragile when they ignore microstructure frictions and reuse evaluation windows during parameter search. We study four liquid perpetuals (BTC/USDT, ETH/USDT, SOL/USDT, AVAX/USDT) and quantify how execution delay, funding, fees, and slippage can inflate reported performance. We introduce AutoQuant, an execution-centric, alpha-agnostic framework for auditable strategy configuration selection. AutoQuant encodes strict T+1 execution semantics and no-look-ahead funding alignment, runs Bayesian optimization under realistic costs, and applies a two-stage double-screening protocol across held-out rolling windows and a cost-sensitivity grid. We show that fee-only and zero-cost backtests can materially overestimate annualized returns relative to a fully costed configuration, and that double screening tends to reduce drawdowns under the same strict semantics even when returns are not higher. A CSCV/PBO diagnostic indicates substantial residual overfitting risk, motivating AutoQuant as validation and governance infrastructure rather than a claim of persistent alpha. Returns are reported for small-account simulations with linear trading costs and without market impact or capacity modeling. ...

Index-Tracking Portfolio Construction and Rebalancing under Bayesian Sparse Modelling and Uncertainty Quantification ArXiv ID: 2512.22109 “View on arXiv” Authors: Dimitrios Roxanas Abstract We study the construction and rebalancing of sparse index-tracking portfolios from an operational research perspective, with explicit emphasis on uncertainty quantification and implementability. The decision variables are portfolio weights constrained to sum to one; the aims are to track a reference index closely while controlling the number of names and the turnover induced by rebalancing. We cast index tracking as a high-dimensional linear regression of index returns on constituent returns, and employ a sparsity-inducing Laplace prior on the weights. A single global shrinkage parameter controls the trade-off between tracking error and sparsity, and is calibrated by an empirical-Bayes stochastic approximation scheme. Conditional on this calibration, we approximate the posterior distribution of the portfolio weights using proximal Langevin-type Markov chain Monte Carlo algorithms tailored to the budget constraint. This yields posterior uncertainty on tracking error, portfolio composition and prospective rebalancing moves. Building on these posterior samples, we propose rules for rebalancing that gate trades through magnitude-based thresholds and posterior activation probabilities, thereby trading off expected tracking error against turnover and portfolio size. A case study on tracking the S&P~500 index is carried out to showcase how our tools shape the decision process from portfolio construction to rebalancing. ...

Investigating Conditional Restricted Boltzmann Machines in Regime Detection ArXiv ID: 2512.21823 “View on arXiv” Authors: Siddhartha Srinivas Rentala Abstract This study investigates the efficacy of Conditional Restricted Boltzmann Machines (CRBMs) for modeling high-dimensional financial time series and detecting systemic risk regimes. We extend the classical application of static Restricted Boltzmann Machines (RBMs) by incorporating autoregressive conditioning and utilizing Persistent Contrastive Divergence (PCD) to incorporate complex temporal dependency structures. Comparing a discrete Bernoulli-Bernoulli architecture against a continuous Gaussian-Bernoulli variant across a multi-asset dataset spanning 2013-2025, we observe a dichotomy between generative fidelity and regime detection. While the Gaussian CRBM successfully preserves static asset correlations, it exhibits limitations in generating long-range volatility clustering. Thus, we analyze the free energy as a relative negative log-likelihood (surprisal) under a fixed, trained model. We demonstrate that the model’s free energy serves as a robust, regime stability metric. By decomposing the free energy into quadratic (magnitude) and structural (correlation) components, we show that the model can distinguish between pure magnitude shocks and market regimes. Our findings suggest that the CRBM offers a valuable, interpretable diagnostic tool for monitoring systemic risk, providing a supplemental metric to implied volatility metrics like the VIX. ...

Variational Quantum Eigensolver for Real-World Finance: Scalable Solutions for Dynamic Portfolio Optimization Problems ArXiv ID: 2512.22001 “View on arXiv” Authors: Irene De León, Danel Arias, Manuel Martín-Cordero, María Esperanza Molina, Pablo Serrano, Senaida Hernández-Santana, Miguel Ángel Jiménez Herrera, Joana Fraxanet, Ginés Carrascal, Escolástico Sánchez, Inmaculada Posadillo, Álvaro Nodar Abstract We present a scalable, hardware-aware methodology for extending the Variational Quantum Eigensolver (VQE) to large, realistic Dynamic Portfolio Optimization (DPO) problems. Building on the scaling strategy from our previous work, where we tailored a VQE workflow to both the DPO formulation and the target QPU, we now put forward two significant advances. The first is the implementation of the Ising Sample-based Quantum Configuration Recovery (ISQR) routine, which improves solution quality in Quadratic Unconstrained Binary Optimization problems. The second is the use of the VQE Constrained method to decompose the optimization task, enabling us to handle DPO instances with more variables than the available qubits on current hardware. These advances, which are broadly applicable to other optimization problems, allow us to address a portfolio with a size relevant to the financial industry, consisting of up to 38 assets and covering the full Spanish stock index (IBEX 35). Our results, obtained on a real Quantum Processing Unit (IBM Fez), show that this tailored workflow achieves financial performance on par with classical methods while delivering a broader set of high-quality investment strategies, demonstrating a viable path towards obtaining practical advantage from quantum optimization in real financial applications. ...

Chaos, Ito-Stratonovich dilemma, and topological supersymmetry ArXiv ID: 2512.21539 “View on arXiv” Authors: Igor V. Ovchinnikov Abstract It was recently established that the formalism of the generalized transfer operator (GTO) of dynamical systems (DS) theory, applied to stochastic differential equations (SDEs) of arbitrary form, belongs to the family of cohomological topological field theories (TFT) – a class of models at the intersection of algebraic topology and high-energy physics. This interdisciplinary approach, which can be called the supersymmetric theory of stochastic dynamics (STS), can be seen as an algebraic dual to the traditional set-theoretic framework of the DS theory, with its algebraic structure enabling the extension of some DS theory concepts to stochastic dynamics. Moreover, it reveals the presence of a topological supersymmetry (TS) in the GTOs of all SDEs. It also shows that among the various definitions of chaos, positive “pressure”, defined as the logarithm of the GTO spectral radius, stands out as particularly meaningful from a physical perspective, as it corresponds to the spontaneous breakdown of TS on the TFT side. Via the Goldstone theorem, this definition has a potential to provide the long-sought explanation for the experimental signature of chaotic dynamics known as 1/f noise. Additionally, STS clarifies that among the various existing interpretations of SDEs, only the Stratonovich interpretation yields evolution operators that match the corresponding GTOs and, consequently, have a clear-cut mathematical meaning. Here, we discuss these and other aspects of STS from both the DS theory and TFT perspectives, focusing on links between these two fields and providing mathematical concepts with physical interpretations that may be useful in some contexts. ...

Deep Generative Models for Synthetic Financial Data: Applications to Portfolio and Risk Modeling ArXiv ID: 2512.21798 “View on arXiv” Authors: Christophe D. Hounwanou, Yae Ulrich Gaba Abstract Synthetic financial data provides a practical solution to the privacy, accessibility, and reproducibility challenges that often constrain empirical research in quantitative finance. This paper investigates the use of deep generative models, specifically Time-series Generative Adversarial Networks (TimeGAN) and Variational Autoencoders (VAEs) to generate realistic synthetic financial return series for portfolio construction and risk modeling applications. Using historical daily returns from the S and P 500 as a benchmark, we generate synthetic datasets under comparable market conditions and evaluate them using statistical similarity metrics, temporal structure tests, and downstream financial tasks. The study shows that TimeGAN produces synthetic data with distributional shapes, volatility patterns, and autocorrelation behaviour that are close to those observed in real returns. When applied to mean–variance portfolio optimization, the resulting synthetic datasets lead to portfolio weights, Sharpe ratios, and risk levels that remain close to those obtained from real data. The VAE provides more stable training but tends to smooth extreme market movements, which affects risk estimation. Finally, the analysis supports the use of synthetic datasets as substitutes for real financial data in portfolio analysis and risk simulation, particularly when models are able to capture temporal dynamics. Synthetic data therefore provides a privacy-preserving, cost-effective, and reproducible tool for financial experimentation and model development. ...