Recent advancements in time-series forecasting have highlighted the importance of frequency-domain modeling. However, deep learning models primarily operate in the time domain, limiting their ability to capture frequency-based patterns. Existing approaches normally introduce novel neural network architectures tailored to task-specific frequency properties, yet they often lack generalization and require extensive domain-specific adaptations. In this paper, we propose FAT, a novel pretraining framework that learns generalizable Frequency-Aware Time-series representations through self-supervised learning. The key idea of FAT is to pretrain any backbone model to directly extract generalizable frequency patterns from time-domain signals and encode them into robust representations-eliminating the need for architectural modifications or additional modules during inference. This is achieved via a frequency reformer that amplifies critical frequency components learned through self-supervision and enforces similarity between the original and frequency-reformed time-series representations produced by the encoder. In addition, recognizing that semantically equivalent time-series can exhibit different frequency expressions-analogous to how the same phrase is pronounced differently by different speakers-FAT introduces a Knowledge-Guided Frequency Reformer that unifies the expression of frequency patterns with the same underlying semantics and extends similarity constraints to frequency-invariant augmented samples to enhance robustness of learned representation. Experiments on 14 benchmark datasets across regression and classification tasks show that FAT consistently achieves state-of-the-art performance while maintaining robustness across diverse backbone models, significantly outperforming existing pretraining methods. Our code is available at https://github.com/JiaXiangfei/FAT.

In this paper we develop a novel neural network model for predicting implied volatility surface. Prior financial domain knowledge is taken into account. A new activation function that incorporates volatility smile is proposed, which is used for the hidden nodes that process the underlying asset price. In addition, financial conditions, such as the absence of arbitrage, the boundaries and the asymptotic slope, are embedded into the loss function. This is one of the very first studies which discuss a methodological framework that incorporates prior financial domain knowledge into neural network architecture design and model training. The proposed model outperforms the benchmarked models with the option data on the S&P 500 index over 20 years. More importantly, the domain knowledge is satisfied empirically, showing the model is consistent with the existing financial theories and conditions related to implied volatility surface.

We address the problem of partial index tracking, replicating a benchmark index using a small number of assets. Accurate tracking with a sparse portfolio is extensively studied as a classic finance problem. However in practice, a tracking portfolio must also be diverse in order to minimise risk-a requirement which has only been dealt with by ad-hoc methods before. We introduce the first index tracking method that explicitly optimises both diversity and sparsity in a single joint framework. Diversity is realised by a regulariser based on pairwise similarity of assets, and we demonstrate that learning similarity from data can outperform some existing heuristics. Finally, we show that the way we model diversity leads to an easy solution for sparsity, allowing both constraints to be optimised easily and efficiently. we run out-of-sample back-testing for a long interval of 15 years (2003-2018), and the results demonstrate the superiority of the proposed algorithm.

We propose a neural network approach to price EU call options that significantly outperforms some existing pricing models and comes with guarantees that its predictions are economically reasonable. To achieve this, we introduce a class of gated neural networks that automatically learn to divide-and-conquer the problem space for robust and accurate pricing. We then derive instantiations of these networks that are 'rational by design' in terms of naturally encoding a valid call option surface that enforces no arbitrage principles. This integration of human insight within data-driven learning provides significantly better generalisation in pricing performance due to the encoded inductive bias in the learning, guarantees sanity in the model's predictions, and provides econometrically useful byproduct such as risk neutral density.