Equities

Asset Pricing in Pre-trained Transformer ArXiv ID: 2505.01575 “View on arXiv” Authors: Shanyan Lai Abstract This paper proposes an innovative Transformer model, Single-directional representative from Transformer (SERT), for US large capital stock pricing. It also innovatively applies the pre-trained Transformer models under the stock pricing and factor investment context. They are compared with standard Transformer models and encoder-only Transformer models in three periods covering the entire COVID-19 pandemic to examine the model adaptivity and suitability during the extreme market fluctuations. Namely, pre-COVID-19 period (mild up-trend), COVID-19 period (sharp up-trend with deep down shock) and 1-year post-COVID-19 (high fluctuation sideways movement). The best proposed SERT model achieves the highest out-of-sample R2, 11.2% and 10.91% respectively, when extreme market fluctuation takes place followed by pre-trained Transformer models (10.38% and 9.15%). Their Trend-following-based strategy wise performance also proves their excellent capability for hedging downside risks during market shocks. The proposed SERT model achieves a Sortino ratio 47% higher than the buy-and-hold benchmark in the equal-weighted portfolio and 28% higher in the value-weighted portfolio when the pandemic period is attended. It proves that Transformer models have a great capability to capture patterns of temporal sparsity data in the asset pricing factor model, especially with considerable volatilities. We also find the softmax signal filter as the common configuration of Transformer models in alternative contexts, which only eliminates differences between models, but does not improve strategy-wise performance, while increasing attention heads improve the model performance insignificantly and applying the ’layer norm first’ method do not boost the model performance in our case. ...

Multiscale Causal Analysis of Market Efficiency via News Uncertainty Networks and the Financial Chaos Index ArXiv ID: 2505.01543 “View on arXiv” Authors: Masoud Ataei Abstract This study evaluates the scale-dependent informational efficiency of stock markets using the Financial Chaos Index, a tensor-eigenvalue-based measure of realized volatility. Incorporating Granger causality and network-theoretic analysis across a range of economic, policy, and news-based uncertainty indices, we assess whether public information is efficiently incorporated into asset price fluctuations. Based on a 34-year time period from 1990 to 2023, at the daily frequency, the semi-strong form of the Efficient Market Hypothesis is rejected at the 1% level of significance, indicating that asset price changes respond predictably to lagged news-based uncertainty. In contrast, at the monthly frequency, such predictive structure largely vanishes, supporting informational efficiency at coarser temporal resolutions. A structural analysis of the Granger causality network reveals that fiscal and monetary policy uncertainties act as core initiators of systemic volatility, while peripheral indices, such as those related to healthcare and consumer prices, serve as latent bridges that become activated under crisis conditions. These findings underscore the role of time-scale decomposition and structural asymmetries in diagnosing market inefficiencies and mapping the propagation of macro-financial uncertainty. ...

A new architecture of high-order deep neural networks that learn martingales ArXiv ID: 2505.03789 “View on arXiv” Authors: Syoiti Ninomiya, Yuming Ma Abstract A new deep-learning neural network architecture based on high-order weak approximation algorithms for stochastic differential equations (SDEs) is proposed. The architecture enables the efficient learning of martingales by deep learning models. The behaviour of deep neural networks based on this architecture, when applied to the problem of pricing financial derivatives, is also examined. The core of this new architecture lies in the high-order weak approximation algorithms of the explicit Runge–Kutta type, wherein the approximation is realised solely through iterative compositions and linear combinations of vector fields of the target SDEs. ...

Numerical analysis on locally risk-minimizing strategies for Barndorff-Nielsen and Shephard models ArXiv ID: 2505.00255 “View on arXiv” Authors: Takuji Arai Abstract We develop a numerical method for locally risk-minimizing (LRM) strategies for Barndorff-Nielsen and Shephard (BNS) models. Arai et al. (2017) derived a mathematical expression for LRM strategies in BNS models using Malliavin calculus for Lévy processes and presented some numerical results only for the case where the asset price process is a martingale. Subsequently, Arai and Imai (2024) developed the first Monte Carlo (MC) method available for non-martingale BNS models with infinite active jumps. Here, we modify the expression obtained by Arai et al. (2017) into a numerically tractable form, and, using the MC method developed by Arai and Imai (2024), propose a numerical method of LRM strategies available for non-martingale BNS models with infinite active jumps. In the final part of this paper, we will conduct some numerical experiments. ...

Approximation and regularity results for the Heston model and related processes ArXiv ID: 2504.21658 “View on arXiv” Authors: Edoardo Lombardo Abstract This Ph.D. thesis explores approximations and regularity for the Heston stochastic volatility model through three interconnected works. The first work focuses on developing high-order weak approximations for the Cox-Ingersoll-Ross (CIR) process, essential for financial modelling but challenging due to the square root diffusion term preventing standard methods. By employing the random grid technique (Alfonsi & Bally, 2021) built upon Alfonsi’s (2010) second-order scheme, the work proves that weak approximations of any order can be achieved for smooth test functions. This holds under a condition that is less restrictive than the famous Feller’s one. Numerical results confirm convergence for both CIR and Heston models and show significant computational time improvements. The second work extends the random grid technique to the log-Heston process. Two second-order schemes are introduced (one using exact volatility simulation, another using Ninomiya-Victoir splitting under a the same restriction used above). Convergence to any desired order is rigorously proven. Numerical experiments validate the schemes’ effectiveness for pricing European and Asian options and suggest potential applicability to multifactor/rough Heston models. The third work investigates the partial differential equation (PDE) associated with the log-Heston model. It extends classical solution results and establishes the existence and uniqueness of viscosity solutions without relying on the Feller condition. Uniqueness is proven even for certain discontinuous initial data, relevant for pricing instruments like digital options. Furthermore, the convergence of a hybrid numerical scheme to the viscosity solution is shown under relaxed regularity (continuity) for the initial data. An appendix includes supplementary results for the CIR process. ...

ClusterLOB: Enhancing Trading Strategies by Clustering Orders in Limit Order Books ArXiv ID: 2504.20349 “View on arXiv” Authors: Yichi Zhang, Mihai Cucuringu, Alexander Y. Shestopaloff, Stefan Zohren Abstract In the rapidly evolving world of financial markets, understanding the dynamics of limit order book (LOB) is crucial for unraveling market microstructure and participant behavior. We introduce ClusterLOB as a method to cluster individual market events in a stream of market-by-order (MBO) data into different groups. To do so, each market event is augmented with six time-dependent features. By applying the K-means++ clustering algorithm to the resulting order features, we are then able to assign each new order to one of three distinct clusters, which we identify as directional, opportunistic, and market-making participants, each capturing unique trading behaviors. Our experimental results are performed on one year of MBO data containing small-tick, medium-tick, and large-tick stocks from NASDAQ. To validate the usefulness of our clustering, we compute order flow imbalances across each cluster within 30-minute buckets during the trading day. We treat each cluster’s imbalance as a signal that provides insights into trading strategies and participants’ responses to varying market conditions. To assess the effectiveness of these signals, we identify the trading strategy with the highest Sharpe ratio in the training dataset, and demonstrate that its performance in the test dataset is superior to benchmark trading strategies that do not incorporate clustering. We also evaluate trading strategies based on order flow imbalance decompositions across different market event types, including add, cancel, and trade events, to assess their robustness in various market conditions. This work establishes a robust framework for clustering market participant behavior, which helps us to better understand market microstructure, and inform the development of more effective predictive trading signals with practical applications in algorithmic trading and quantitative finance. ...

Scaling and shape of financial returns distributions modeled as conditionally independent random variables ArXiv ID: 2504.20488 “View on arXiv” Authors: Hernán Larralde, Roberto Mota Navarro Abstract We show that assuming that the returns are independent when conditioned on the value of their variance (volatility), which itself varies in time randomly, then the distribution of returns is well described by the statistics of the sum of conditionally independent random variables. In particular, we show that the distribution of returns can be cast in a simple scaling form, and that its functional form is directly related to the distribution of the volatilities. This approach explains the presence of power-law tails in the returns as a direct consequence of the presence of a power law tail in the distribution of volatilities. It also provides the form of the distribution of Bitcoin returns, which behaves as a stretched exponential, as a consequence of the fact that the Bitcoin volatilities distribution is also closely described by a stretched exponential. We test our predictions with data from the S&P 500 index, Apple and Paramount stocks; and Bitcoin. ...

Compounding Effects in Leveraged ETFs: Beyond the Volatility Drag Paradigm ArXiv ID: 2504.20116 “View on arXiv” Authors: Chung-Han Hsieh, Jow-Ran Chang, Hui Hsiang Chen Abstract A common belief is that leveraged ETFs (LETFs) suffer long-term performance decay due to \emph{“volatility drag”}. We show that this view is incomplete: LETF performance depends fundamentally on return autocorrelation and return dynamics. In markets with independent returns, LETFs exhibit positive expected compounding effects on their target multiples. In serially correlated markets, trends enhance returns, while mean reversion induces underperformance. With a unified framework incorporating AR(1) and AR-GARCH models, continuous-time regime switching, and flexible rebalancing frequencies, we demonstrate that return dynamics – including return autocorrelation, volatility clustering, and regime persistence – determine whether LETFs outperform or underperform their targets. Empirically, using about 20 years of SPDR S&P~500 ETF and Nasdaq-100 ETF data, we confirm these theoretical predictions. Daily-rebalanced LETFs enhance returns in momentum-driven markets, whereas infrequent rebalancing mitigates losses in mean-reverting regimes. ...

Multi-Horizon Echo State Network Prediction of Intraday Stock Returns ArXiv ID: 2504.19623 “View on arXiv” Authors: Giovanni Ballarin, Jacopo Capra, Petros Dellaportas Abstract Stock return prediction is a problem that has received much attention in the finance literature. In recent years, sophisticated machine learning methods have been shown to perform significantly better than ‘‘classical’’ prediction techniques. One downside of these approaches is that they are often very expensive to implement, for both training and inference, because of their high complexity. We propose a return prediction framework for intraday returns at multiple horizons based on Echo State Network (ESN) models, wherein a large portion of parameters are drawn at random and never trained. We show that this approach enjoys the benefits of recurrent neural network expressivity, inherently efficient implementation, and strong forecasting performance. ...

Modeling Regime Structure and Informational Drivers of Stock Market Volatility via the Financial Chaos Index ArXiv ID: 2504.18958 “View on arXiv” Authors: Masoud Ataei Abstract This paper investigates the structural dynamics of stock market volatility through the Financial Chaos Index, a tensor- and eigenvalue-based measure designed to capture realized volatility via mutual fluctuations among asset prices. Motivated by empirical evidence of regime-dependent volatility behavior and perceptual time dilation during financial crises, we develop a regime-switching framework based on the Modified Lognormal Power-Law distribution. Analysis of the FCIX from January 1990 to December 2023 identifies three distinct market regimes, low-chaos, intermediate-chaos, and high-chaos, each characterized by differing levels of systemic stress, statistical dispersion and persistence characteristics. Building upon the segmented regime structure, we further examine the informational forces that shape forward-looking market expectations. Using sentiment-based predictors derived from the Equity Market Volatility tracker, we employ an elastic net regression model to forecast implied volatility, as proxied by the VIX index. Our findings indicate that shifts in macroeconomic, financial, policy, and geopolitical uncertainty exhibit strong predictive power for volatility dynamics across regimes. Together, these results offer a unified empirical perspective on how systemic uncertainty governs both the realized evolution of financial markets and the anticipatory behavior embedded in implied volatility measures. ...