Machine learning techniques have gained considerable attention in the field of empirical asset pricing. Conditioning on a broad set of firm characteristics, one of the most popular no-arbitrage workhorses is a nonlinear conditional asset pricing model that consists of two modules within a neural network structure, i.e., factor and beta estimates, for which we propose a novel contrastive adversarial variational Bayes (CAVB) framework. To exploit the factor structure, we employ adversarial variational Bayes that transforms the maximum-likelihood problem into a zero-sum game between a variational autoencoder (VAE) and a generative adversarial network (GAN), where an auxiliary discriminative network brings in arbitrary expressiveness to the inference model. To tackle the problem of learning indistinguishable feature representations in the beta network, we introduce a contrastive loss to learn distinctive hidden features of the factor loadings in correspondence to conditional quantiles of return distributions. CAVB establishes a robust relation between the cross-section of asset returns and the common latent factors with nonlinear factor loadings. Extensive experiments show that CAVB not only significantly outperforms prominent models in the existing literature in terms of total and predictive R-squares, but also delivers superior Sharpe ratios after transaction costs for both long-only and long-short portfolios.

Implied Volatility Surface (IVS) prediction is critical for options hedging, portfolio management, and risk control. These applications encounter significant challenges, including imbalanced data distributions and inherent uncertainties in forecasting. Recent advances relying on deep learning have led to significant progress in addressing these issues. However, several key problems have not yet been solved: (i) Moneyness and maturities of traded options change over time. Therefore, proper spatio-temporal alignment is an essential prerequisite for the downstream forecasting exercise. (ii) Different regions of the IVS are unevenly informed because of liquidity constraints and therefore should not be modeled uniformly. (iii) The complex interconnections among data points in the IVS from various perspectives-such as the well-known 'smirk' patterns across dimensions-are neither explicitly addressed nor effectively captured by existing models. To address these issues, we propose a novel end-to-end heterogeneous cross(x)-view aligned graph attention network (Hexagon-Net), which aligns historical IVS data, learns distinctive IVS patterns, propagates predictive information, and forecasts future IVS movements simultaneously. Extensive experiments on stock index options datasets demonstrate that Hexagon-Net significantly and consistently outperforms the previous approaches in IVS modeling and deep learning. Additionally, we present further experiments-such as ablation studies, sensitivity analyses, and alternative configurations-to explore the reasons behind its superior performance.

Recent developments in the applications of deep reinforcement learning methods to portfolio selection have achieved superior performance to conventional methods. However, two major challenges remain unaddressed in these models and inevitably lead to the deterioration of model performance. First, asset characteristics often suffer from low and unstable signal-to-noise ratios, leading to poor learning robustness of the predictive feature representations. Second, existing literature fails to consider the complexity and diversity in long-term and short-term spatio-temporal predictive relations between the feature sequences and portfolio objectives. To tackle these problems, we propose a novel Context-Aware Frequency-Embedding Graph Convolution Network (Cafe-GCN) for spatio-temporal portfolio selection. It contains three important modules: (1) frequency-embedding block that explicitly captures the short-term and long-term predictive information embedded in asset characteristics meanwhile filtering out noise; (2) context-aware block that learns multiscale temporal dependencies in the feature space; and (3) multi-relation graph convolutional block that exploits both static and dynamic spatial relations among assets. Extensive experiments on two real-world datasets demonstrate that Cafe-GCN consistently outperforms proposed techniques in the literature.