Causal Inference

Forward-Oriented Causal Observables for Non-Stationary Financial Markets ArXiv ID: 2512.24621 “View on arXiv” Authors: Lucas A. Souza Abstract We study short-horizon forecasting in financial time series under strict causal constraints, treating the market as a non-stationary stochastic system in which any predictive observable must be computable online from information available up to the decision time. Rather than proposing a machine-learning predictor or a direct price-forecast model, we focus on \emph{“constructing”} an interpretable causal signal from heterogeneous micro-features that encode complementary aspects of the dynamics (momentum, volume pressure, trend acceleration, and volatility-normalized price location). The construction combines (i) causal centering, (ii) linear aggregation into a composite observable, (iii) causal stabilization via a one-dimensional Kalman filter, and (iv) an adaptive ``forward-like’’ operator that mixes the composite signal with a smoothed causal derivative term. The resulting observable is mapped into a transparent decision functional and evaluated through realized cumulative returns and turnover. An application to high-frequency EURUSDT (1-minute) illustrates that causally constructed observables can exhibit substantial economic relevance in specific regimes, while degrading under subsequent regime shifts, highlighting both the potential and the limitations of causal signal design in non-stationary markets. ...

Towards Causal Market Simulators ArXiv ID: 2511.04469 “View on arXiv” Authors: Dennis Thumm, Luis Ontaneda Mijares Abstract Market generators using deep generative models have shown promise for synthetic financial data generation, but existing approaches lack causal reasoning capabilities essential for counterfactual analysis and risk assessment. We propose a Time-series Neural Causal Model VAE (TNCM-VAE) that combines variational autoencoders with structural causal models to generate counterfactual financial time series while preserving both temporal dependencies and causal relationships. Our approach enforces causal constraints through directed acyclic graphs in the decoder architecture and employs the causal Wasserstein distance for training. We validate our method on synthetic autoregressive models inspired by the Ornstein-Uhlenbeck process, demonstrating superior performance in counterfactual probability estimation with L1 distances as low as 0.03-0.10 compared to ground truth. The model enables financial stress testing, scenario analysis, and enhanced backtesting by generating plausible counterfactual market trajectories that respect underlying causal mechanisms. ...

Causal PDE-Control for Adaptive Portfolio Optimization under Partial Information ArXiv ID: 2509.09585 “View on arXiv” Authors: Alejandro Rodriguez Dominguez Abstract Classical portfolio models tend to degrade under structural breaks, whereas flexible machine-learning allocators often lack arbitrage consistency and interpretability. We propose Causal PDE-Control Models (CPCMs), a framework that links structural causal drivers, nonlinear filtering, and forward-backward PDE control to produce robust, transparent allocation rules under partial information. The main contributions are: (i) construction of scenario-conditional risk-neutral measures on the observable filtration via filtering, with an associated martingale representation; (ii) a projection-divergence duality that quantifies stability costs when deviating from the causal driver span; (iii) a causal completeness condition showing when a finite driver span captures systematic premia; and (iv) conformal transport and smooth subspace evolution guaranteeing time-consistent projections on a moving driver manifold. Markowitz, CAPM/APT, and Black-Litterman arise as limit or constrained cases; reinforcement learning and deep hedging appear as unconstrained approximations once embedded in the same pricing-control geometry. On a U.S. equity panel with 300+ candidate drivers, CPCM solvers achieve higher performance, lower turnover, and more persistent premia than econometric and ML benchmarks, offering a rigorous and interpretable basis for dynamic asset allocation in nonstationary markets. ...

Rethinking Beta: A Causal Take on CAPM ArXiv ID: 2509.05760 “View on arXiv” Authors: Naftali Cohen Abstract The CAPM regression is typically interpreted as if the market return contemporaneously \emph{“causes”} individual returns, motivating beta-neutral portfolios and factor attribution. For realized equity returns, however, this interpretation is inconsistent: a same-period arrow $R_{“m,t”} \to R_{“i,t”}$ conflicts with the fact that $R_m$ is itself a value-weighted aggregate of its constituents, unless $R_m$ is lagged or leave-one-out – the aggregator contradiction.'' We formalize CAPM as a structural causal model and analyze the admissible three-node graphs linking an external driver $Z$, the market $R_m$, and an asset $R_i$. The empirically plausible baseline is a \emph{"fork"}, $Z \to \{"R_m, R_i\"}$, not $R_m \to R_i$. In this setting, OLS beta reflects not a causal transmission, but an attenuated proxy for how well $R_m$ captures the underlying driver $Z$. Consequently, beta-neutral’’ portfolios can remain exposed to macro or sectoral shocks, and hedging on $R_m$ can import index-specific noise. Using stylized models and large-cap U.S.\ equity data, we show that contemporaneous betas act like proxies rather than mechanisms; any genuine market-to-stock channel, if at all, appears only at a lag and with modest economic significance. The practical message is clear: CAPM should be read as associational. Risk management and attribution should shift from fixed factor menus to explicitly declared causal paths, with ``alpha’’ reserved for what remains invariant once those causal paths are explicitly blocked. ...

Non-parametric Causal Discovery for EU Allowances Returns Through the Information Imbalance ArXiv ID: 2508.15667 “View on arXiv” Authors: Cristiano Salvagnin, Vittorio del Tatto, Maria Elena De Giuli, Antonietta Mira, Aldo Glielmo Abstract We propose to use a recently introduced non-parametric tool named Differentiable Information Imbalance (DII) to identify variables that are causally related – potentially through non-linear relationships – to the financial returns of the European Union Allowances (EUAs) within the EU Emissions Trading System (EU ETS). We examine data from January 2013 to April 2024 and compare the DII approach with multivariate Granger causality, a well-known linear approach based on VAR models. We find significant overlap among the causal variables identified by linear and non-linear methods, such as the coal futures prices and the IBEX35 index. We also find important differences between the two causal sets identified. On two synthetic datasets, we show how these differences could originate from limitations of the linear methodology. ...

A Framework for Predictive Directional Trading Based on Volatility and Causal Inference ArXiv ID: 2507.09347 “View on arXiv” Authors: Ivan Letteri Abstract Purpose: This study introduces a novel framework for identifying and exploiting predictive lead-lag relationships in financial markets. We propose an integrated approach that combines advanced statistical methodologies with machine learning models to enhance the identification and exploitation of predictive relationships between equities. Methods: We employed a Gaussian Mixture Model (GMM) to cluster nine prominent stocks based on their mid-range historical volatility profiles over a three-year period. From the resulting clusters, we constructed a multi-stage causal inference pipeline, incorporating the Granger Causality Test (GCT), a customised Peter-Clark Momentary Conditional Independence (PCMCI) test, and Effective Transfer Entropy (ETE) to identify robust, predictive linkages. Subsequently, Dynamic Time Warping (DTW) and a K-Nearest Neighbours (KNN) classifier were utilised to determine the optimal time lag for trade execution. The resulting strategy was rigorously backtested. Results: The proposed volatility-based trading strategy, tested from 8 June 2023 to 12 August 2023, demonstrated substantial efficacy. The portfolio yielded a total return of 15.38%, significantly outperforming the 10.39% return of a comparative Buy-and-Hold strategy. Key performance metrics, including a Sharpe Ratio up to 2.17 and a win rate up to 100% for certain pairs, confirmed the strategy’s viability. Conclusion: This research contributes a systematic and robust methodology for identifying profitable trading opportunities derived from volatility-based causal relationships. The findings have significant implications for both academic research in financial modelling and the practical application of algorithmic trading, offering a structured approach to developing resilient, data-driven strategies. ...

Causal Interventions in Bond Multi-Dealer-to-Client Platforms ArXiv ID: 2506.18147 “View on arXiv” Authors: Paloma Marín, Sergio Ardanza-Trevijano, Javier Sabio Abstract The digitalization of financial markets has shifted trading from voice to electronic channels, with Multi-Dealer-to-Client (MD2C) platforms now enabling clients to request quotes (RfQs) for financial instruments like bonds from multiple dealers simultaneously. In this competitive landscape, dealers cannot see each other’s prices, making a rigorous analysis of the negotiation process crucial to ensure their profitability. This article introduces a novel general framework for analyzing the RfQ process using probabilistic graphical models and causal inference. Within this framework, we explore different inferential questions that are relevant for dealers participating in MD2C platforms, such as the computation of optimal prices, estimating potential revenues and the identification of clients that might be interested in trading the dealer’s axes. We then move into analyzing two different approaches for model specification: a generative model built on the work of (Fermanian, Guéant, & Pu, 2017); and discriminative models utilizing machine learning techniques. Our results show that generative models can match the predictive accuracy of leading discriminative algorithms such as LightGBM (ROC-AUC: 0.742 vs. 0.743) while simultaneously enforcing critical business requirements, notably spread monotonicity. ...

Causal Portfolio Optimization: Principles and Sensitivity-Based Solutions ArXiv ID: 2504.05743 “View on arXiv” Authors: Unknown Abstract Fundamental and necessary principles for achieving efficient portfolio optimization based on asset and diversification dynamics are presented. The Commonality Principle is a necessary and sufficient condition for identifying optimal drivers of a portfolio in terms of its diversification dynamics. The proof relies on the Reichenbach Common Cause Principle, along with the fact that the sensitivities of portfolio constituents with respect to the common causal drivers are themselves causal. A conformal map preserves idiosyncratic diversification from the unconditional setting while optimizing systematic diversification on an embedded space of these sensitivities. Causal methodologies for combinatorial driver selection are presented, such as the use of Bayesian networks and correlation-based algorithms from Reichenbach’s principle. Limitations of linear models in capturing causality are discussed, and included for completeness alongside more advanced models such as neural networks. Portfolio optimization methods are presented that map risk from the sensitivity space to other risk measures of interest. Finally, the work introduces a novel risk management framework based on Common Causal Manifolds, including both theoretical development and experimental validation. The sensitivity space is predicted along the common causal manifold, which is modeled as a causal time system. Sensitivities are forecasted using SDEs calibrated to data previously extracted from neural networks to move along the manifold via its tangent bundles. An optimization method is then proposed that accumulates information across future predicted tangent bundles on the common causal time system manifold. It aggregates sensitivity-based distance metrics along the trajectory to build a comprehensive sensitivity distance matrix. This matrix enables trajectory-wide optimal diversification, taking into account future dynamics. ...

Time-Causal VAE: Robust Financial Time Series Generator ArXiv ID: 2411.02947 “View on arXiv” Authors: Unknown Abstract We build a time-causal variational autoencoder (TC-VAE) for robust generation of financial time series data. Our approach imposes a causality constraint on the encoder and decoder networks, ensuring a causal transport from the real market time series to the fake generated time series. Specifically, we prove that the TC-VAE loss provides an upper bound on the causal Wasserstein distance between market distributions and generated distributions. Consequently, the TC-VAE loss controls the discrepancy between optimal values of various dynamic stochastic optimization problems under real and generated distributions. To further enhance the model’s ability to approximate the latent representation of the real market distribution, we integrate a RealNVP prior into the TC-VAE framework. Finally, extensive numerical experiments show that TC-VAE achieves promising results on both synthetic and real market data. This is done by comparing real and generated distributions according to various statistical distances, demonstrating the effectiveness of the generated data for downstream financial optimization tasks, as well as showcasing that the generated data reproduces stylized facts of real financial market data. ...

Trading with Time Series Causal Discovery: An Empirical Study ArXiv ID: 2408.15846 “View on arXiv” Authors: Unknown Abstract This study investigates the application of causal discovery algorithms in equity markets, with a focus on their potential to build investment strategies. An investment strategy was developed based on the causal structures identified by these algorithms. The performance of the strategy is evaluated based on the profitability and effectiveness in stock markets. The results indicate that causal discovery algorithms can successfully uncover actionable causal relationships in large markets, leading to profitable investment outcomes. However, the research also identifies a critical challenge: the computational complexity and scalability of these algorithms when dealing with large datasets. This challenge presents practical limitations for their application in real-world market analysis. ...