DeepSupp: Attention-Driven Correlation Pattern Analysis for Dynamic Time Series Support and Resistance Levels Identification ArXiv ID: 2507.01971 “View on arXiv” Authors: Boris Kriuk, Logic Ng, Zarif Al Hossain Abstract Support and resistance (SR) levels are central to technical analysis, guiding traders in entry, exit, and risk management. Despite widespread use, traditional SR identification methods often fail to adapt to the complexities of modern, volatile markets. Recent research has introduced machine learning techniques to address the following challenges, yet most focus on price prediction rather than structural level identification. This paper presents DeepSupp, a new deep learning approach for detecting financial support levels using multi-head attention mechanisms to analyze spatial correlations and market microstructure relationships. DeepSupp integrates advanced feature engineering, constructing dynamic correlation matrices that capture evolving market relationships, and employs an attention-based autoencoder for robust representation learning. The final support levels are extracted through unsupervised clustering, leveraging DBSCAN to identify significant price thresholds. Comprehensive evaluations on S&P 500 tickers demonstrate that DeepSupp outperforms six baseline methods, achieving state-of-the-art performance across six financial metrics, including essential support accuracy and market regime sensitivity. With consistent results across diverse market conditions, DeepSupp addresses critical gaps in SR level detection, offering a scalable and reliable solution for modern financial analysis. Our approach highlights the potential of attention-based architectures to uncover nuanced market patterns and improve technical trading strategies. ...

Predicting Stock Market Crash with Bayesian Generalised Pareto Regression ArXiv ID: 2506.17549 “View on arXiv” Authors: Sourish Das Abstract This paper develops a Bayesian Generalised Pareto Regression (GPR) model to forecast extreme losses in Indian equity markets, with a focus on the Nifty 50 index. Extreme negative returns, though rare, can cause significant financial disruption, and accurate modelling of such events is essential for effective risk management. Traditional Generalised Pareto Distribution (GPD) models often ignore market conditions; in contrast, our framework links the scale parameter to covariates using a log-linear function, allowing tail risk to respond dynamically to market volatility. We examine four prior choices for Bayesian regularisation of regression coefficients: Cauchy, Lasso (Laplace), Ridge (Gaussian), and Zellner’s g-prior. Simulation results suggest that the Cauchy prior delivers the best trade-off between predictive accuracy and model simplicity, achieving the lowest RMSE, AIC, and BIC values. Empirically, we apply the model to large negative returns (exceeding 5%) in the Nifty 50 index. Volatility measures from the Nifty 50, S&P 500, and gold are used as covariates to capture both domestic and global risk drivers. Our findings show that tail risk increases significantly with higher market volatility. In particular, both S&P 500 and gold volatilities contribute meaningfully to crash prediction, highlighting global spillover and flight-to-safety effects. The proposed GPR model offers a robust and interpretable approach for tail risk forecasting in emerging markets. It improves upon traditional EVT-based models by incorporating real-time financial indicators, making it useful for practitioners, policymakers, and financial regulators concerned with systemic risk and stress testing. ...

Wealth Thermalization Hypothesis and Social Networks ArXiv ID: 2506.17720 “View on arXiv” Authors: Klaus M. Frahm, Dima L. Shepelyansky Abstract In 1955 Fermi, Pasta, Ulam and Tsingou performed first numerical studies with the aim to obtain the thermalization in a chain of nonlinear oscillators from dynamical equations of motion. This model happend to have several specific features and the dynamical thermalization was established only later in other studies. In this work we study more generic models based on Random Matrix Theory and social networks with a nonlinear perturbation leading to dynamical thermalization above a certain chaos border. These systems have two integrals of motion being total energy and norm so that the theoretical Rayleigh-Jeans thermal distribution depends on temperature and chemical potential. We introduce the wealth thermalization hypothesis according to which the society wealth is associated with energy in the Rayleigh-Jeans distribution. At relatively small values of total wealth or energy there is a formation of the Rayleigh-Jeans condensate, well studied in physical systems such as multimode optical fibers. This condensation leads to a huge fraction of poor households at low wealth and a small oligarchic fraction which monopolizes a dominant fraction of total wealth thus generating a strong inequality in human society. We show that this thermalization gives a good description of real data of Lorenz curves of US, UK, the whole world and capitalization of companies at Stock Exchange of New York SE (NYSE), London and Hong Kong. It is also shown that above a chaos border the dynamical Rayleigh-Jeans thermalization takes place also in social networks with the Lorenz curves being similar to those of wealth distribution in world countries. Possible actions for inequality reduction are briefly discussed. ...

Empirical Models of the Time Evolution of SPX Option Prices ArXiv ID: 2506.17511 “View on arXiv” Authors: Alessio Brini, David A. Hsieh, Patrick Kuiper, Sean Moushegian, David Ye Abstract The key objective of this paper is to develop an empirical model for pricing SPX options that can be simulated over future paths of the SPX. To accomplish this, we formulate and rigorously evaluate several statistical models, including neural network, random forest, and linear regression. These models use the observed characteristics of the options as inputs – their price, moneyness and time-to-maturity, as well as a small set of external inputs, such as the SPX and its past history, dividend yield, and the risk-free rate. Model evaluation is performed on historical options data, spanning 30 years of daily observations. Significant effort is given to understanding the data and ensuring explainability for the neural network. A neural network model with two hidden layers and four neurons per layer, trained with minimal hyperparameter tuning, performs well against the theoretical Black-Scholes-Merton model for European options, as well as two other empirical models based on the random forest and the linear regression. It delivers arbitrage-free option prices without requiring these conditions to be imposed. ...

News Sentiment Embeddings for Stock Price Forecasting ArXiv ID: 2507.01970 “View on arXiv” Authors: Ayaan Qayyum Abstract This paper will discuss how headline data can be used to predict stock prices. The stock price in question is the SPDR S&P 500 ETF Trust, also known as SPY that tracks the performance of the largest 500 publicly traded corporations in the United States. A key focus is to use news headlines from the Wall Street Journal (WSJ) to predict the movement of stock prices on a daily timescale with OpenAI-based text embedding models used to create vector encodings of each headline with principal component analysis (PCA) to exact the key features. The challenge of this work is to capture the time-dependent and time-independent, nuanced impacts of news on stock prices while handling potential lag effects and market noise. Financial and economic data were collected to improve model performance; such sources include the U.S. Dollar Index (DXY) and Treasury Interest Yields. Over 390 machine-learning inference models were trained. The preliminary results show that headline data embeddings greatly benefit stock price prediction by at least 40% compared to training and optimizing a machine learning system without headline data embeddings. ...

On Quantum BSDE Solver for High-Dimensional Parabolic PDEs ArXiv ID: 2506.14612 “View on arXiv” Authors: Howard Su, Huan-Hsin Tseng Abstract We propose a quantum machine learning framework for approximating solutions to high-dimensional parabolic partial differential equations (PDEs) that can be reformulated as backward stochastic differential equations (BSDEs). In contrast to popular quantum-classical network hybrid approaches, this study employs the pure Variational Quantum Circuit (VQC) as the core solver without trainable classical neural networks. The quantum BSDE solver performs pathwise approximation via temporal discretization and Monte Carlo simulation, framed as model-based reinforcement learning. We benchmark VQCbased and classical deep neural network (DNN) solvers on two canonical PDEs as representatives: the Black-Scholes and nonlinear Hamilton-Jacobi-Bellman (HJB) equations. The VQC achieves lower variance and improved accuracy in most cases, particularly in highly nonlinear regimes and for out-of-themoney options, demonstrating greater robustness than DNNs. These results, obtained via quantum circuit simulation, highlight the potential of VQCs as scalable and stable solvers for highdimensional stochastic control problems. ...

Implied Probabilities and Volatility in Credit Risk: A Merton-Based Approach with Binomial Trees ArXiv ID: 2506.12694 “View on arXiv” Authors: Jagdish Gnawali, Abootaleb Shirvani, Svetlozar T. Rachev Abstract We explore credit risk pricing by modeling equity as a call option and debt as the difference between the firm’s asset value and a put option, following the structural framework of the Merton model. Our approach proceeds in two stages: first, we calibrate the asset volatility using the Black-Scholes-Merton (BSM) formula; second, we recover implied mean return and probability surfaces under the physical measure. To achieve this, we construct a recombining binomial tree under the real-world (natural) measure, assuming a fixed initial asset value. The volatility input is taken from a specific region of the implied volatility surface - based on moneyness and maturity - which then informs the calibration of drift and probability. A novel mapping is established between risk-neutral and physical parameters, enabling construction of implied surfaces that reflect the market’s credit expectations and offer practical tools for stress testing and credit risk analysis. ...

A New Approach for the Continuous Time Kyle-Back Strategic Insider Equilibrium Problem ArXiv ID: 2506.12281 “View on arXiv” Authors: Bixing Qiao, Jianfeng Zhang Abstract This paper considers a continuous time Kyle-Back model which is a game problem between an insider and a market marker. The existing literature typically focuses on the existence of equilibrium by using the PDE approach, which requires certain Markovian structure and the equilibrium is in the bridge form. We shall provide a new approach which is used widely for stochastic controls and stochastic differential games. We characterize all equilibria through a coupled system of forward backward SDEs, where the forward one is the conditional law of the inside information and the backward one is the insider’s optimal value. In particular, when the time duration is small, we show that the FBSDE is wellposed and thus the game has a unique equilibrium. This is the first uniqueness result in the literature, without restricting the equilibria to certain special structure. Moreover, this unique equilibrium may not be Markovian, indicating that the PDE approach cannot work in this case. We next study the set value of the game, which roughly speaking is the set of insider’s values over all equilibria and thus is by nature unique. We show that, although the bridge type of equilibria in the literature does not satisfy the required integrability for our equilibria, its truncation serves as a desired approximate equilibrium and its value belongs to our set value. Finally, we characterize our set value through a level set of certain standard HJB equation. ...

Dynamic allocation: extremes, tail dependence, and regime Shifts ArXiv ID: 2506.12587 “View on arXiv” Authors: Yin Luo, Sheng Wang, Javed Jussa Abstract By capturing outliers, volatility clustering, and tail dependence in the asset return distribution, we build a sophisticated model to predict the downside risk of the global financial market. We further develop a dynamic regime switching model that can forecast real-time risk regime of the market. Our GARCH-DCC-Copula risk model can significantly improve both risk- and alpha-based global tactical asset allocation strategies. Our risk regime has strong predictive power of quantitative equity factor performance, which can help equity investors to build better factor models and asset allocation managers to construct more efficient risk premia portfolios. ...

Small Volatility Approximation and Multi-Factor HJM Models ArXiv ID: 2506.12584 “View on arXiv” Authors: V. M. Belyaev Abstract Here we demonstrate how we can use Small Volatility Approximation in calibration of Multi-Factor HJM model with deterministic correlations, factor volatilities and mean reversals. It is noticed that quality of this calibration is very good and it does not depend on number of factors. Keywords: Heath-Jarrow-Morton (HJM) Model, Small Volatility Approximation, Calibration, Deterministic Volatility, Term Structure, Fixed Income ...