Deep Learning

Gradient Reduction Convolutional Neural Network Policy for Financial Deep Reinforcement Learning ArXiv ID: 2408.11859 “View on arXiv” Authors: Unknown Abstract Building on our prior explorations of convolutional neural networks (CNNs) for financial data processing, this paper introduces two significant enhancements to refine our CNN model’s predictive performance and robustness for financial tabular data. Firstly, we integrate a normalization layer at the input stage to ensure consistent feature scaling, addressing the issue of disparate feature magnitudes that can skew the learning process. This modification is hypothesized to aid in stabilizing the training dynamics and improving the model’s generalization across diverse financial datasets. Secondly, we employ a Gradient Reduction Architecture, where earlier layers are wider and subsequent layers are progressively narrower. This enhancement is designed to enable the model to capture more complex and subtle patterns within the data, a crucial factor in accurately predicting financial outcomes. These advancements directly respond to the limitations identified in previous studies, where simpler models struggled with the complexity and variability inherent in financial applications. Initial tests confirm that these changes improve accuracy and model stability, suggesting that deeper and more nuanced network architectures can significantly benefit financial predictive tasks. This paper details the implementation of these enhancements and evaluates their impact on the model’s performance in a controlled experimental setting. ...

A forward differential deep learning-based algorithm for solving high-dimensional nonlinear backward stochastic differential equations ArXiv ID: 2408.05620 “View on arXiv” Authors: Unknown Abstract In this work, we present a novel forward differential deep learning-based algorithm for solving high-dimensional nonlinear backward stochastic differential equations (BSDEs). Motivated by the fact that differential deep learning can efficiently approximate the labels and their derivatives with respect to inputs, we transform the BSDE problem into a differential deep learning problem. This is done by leveraging Malliavin calculus, resulting in a system of BSDEs. The unknown solution of the BSDE system is a triple of processes $(Y, Z, Γ)$, representing the solution, its gradient, and the Hessian matrix. The main idea of our algorithm is to discretize the integrals using the Euler-Maruyama method and approximate the unknown discrete solution triple using three deep neural networks. The parameters of these networks are then optimized by globally minimizing a differential learning loss function, which is novelty defined as a weighted sum of the dynamics of the discretized system of BSDEs. Through various high-dimensional examples, we demonstrate that our proposed scheme is more efficient in terms of accuracy and computation time compared to other contemporary forward deep learning-based methodologies. ...

Deep Learning for Options Trading: An End-To-End Approach ArXiv ID: 2407.21791 “View on arXiv” Authors: Unknown Abstract We introduce a novel approach to options trading strategies using a highly scalable and data-driven machine learning algorithm. In contrast to traditional approaches that often require specifications of underlying market dynamics or assumptions on an option pricing model, our models depart fundamentally from the need for these prerequisites, directly learning non-trivial mappings from market data to optimal trading signals. Backtesting on more than a decade of option contracts for equities listed on the S&P 100, we demonstrate that deep learning models trained according to our end-to-end approach exhibit significant improvements in risk-adjusted performance over existing rules-based trading strategies. We find that incorporating turnover regularization into the models leads to further performance enhancements at prohibitively high levels of transaction costs. ...

Enhancing Black-Scholes Delta Hedging via Deep Learning ArXiv ID: 2407.19367 “View on arXiv” Authors: Unknown Abstract This paper proposes a deep delta hedging framework for options, utilizing neural networks to learn the residuals between the hedging function and the implied Black-Scholes delta. This approach leverages the smoother properties of these residuals, enhancing deep learning performance. Utilizing ten years of daily S&P 500 index option data, our empirical analysis demonstrates that learning the residuals, using the mean squared one-step hedging error as the loss function, significantly improves hedging performance over directly learning the hedging function, often by more than 100%. Adding input features when learning the residuals enhances hedging performance more for puts than calls, with market sentiment being less crucial. Furthermore, learning the residuals with three years of data matches the hedging performance of directly learning with ten years of data, proving that our method demands less data. ...

Hopfield Networks for Asset Allocation ArXiv ID: 2407.17645 “View on arXiv” Authors: Unknown Abstract We present the first application of modern Hopfield networks to the problem of portfolio optimization. We performed an extensive study based on combinatorial purged cross-validation over several datasets and compared our results to both traditional and deep-learning-based methods for portfolio selection. Compared to state-of-the-art deep-learning methods such as Long-Short Term Memory networks and Transformers, we find that the proposed approach performs on par or better, while providing faster training times and better stability. Our results show that Modern Hopfield Networks represent a promising approach to portfolio optimization, allowing for an efficient, scalable, and robust solution for asset allocation, risk management, and dynamic rebalancing. ...

DeepUnifiedMom: Unified Time-series Momentum Portfolio Construction via Multi-Task Learning with Multi-Gate Mixture of Experts ArXiv ID: 2406.08742 “View on arXiv” Authors: Unknown Abstract This paper introduces DeepUnifiedMom, a deep learning framework that enhances portfolio management through a multi-task learning approach and a multi-gate mixture of experts. The essence of DeepUnifiedMom lies in its ability to create unified momentum portfolios that incorporate the dynamics of time series momentum across a spectrum of time frames, a feature often missing in traditional momentum strategies. Our comprehensive backtesting, encompassing diverse asset classes such as equity indexes, fixed income, foreign exchange, and commodities, demonstrates that DeepUnifiedMom consistently outperforms benchmark models, even after factoring in transaction costs. This superior performance underscores DeepUnifiedMom’s capability to capture the full spectrum of momentum opportunities within financial markets. The findings highlight DeepUnifiedMom as an effective tool for practitioners looking to exploit the entire range of momentum opportunities. It offers a compelling solution for improving risk-adjusted returns and is a valuable strategy for navigating the complexities of portfolio management. ...

Financial Assets Dependency Prediction Utilizing Spatiotemporal Patterns ArXiv ID: 2406.11886 “View on arXiv” Authors: Unknown Abstract Financial assets exhibit complex dependency structures, which are crucial for investors to create diversified portfolios to mitigate risk in volatile financial markets. To explore the financial asset dependencies dynamics, we propose a novel approach that models the dependencies of assets as an Asset Dependency Matrix (ADM) and treats the ADM sequences as image sequences. This allows us to leverage deep learning-based video prediction methods to capture the spatiotemporal dependencies among assets. However, unlike images where neighboring pixels exhibit explicit spatiotemporal dependencies due to the natural continuity of object movements, assets in ADM do not have a natural order. This poses challenges to organizing the relational assets to reveal better the spatiotemporal dependencies among neighboring assets for ADM forecasting. To tackle the challenges, we propose the Asset Dependency Neural Network (ADNN), which employs the Convolutional Long Short-Term Memory (ConvLSTM) network, a highly successful method for video prediction. ADNN can employ static and dynamic transformation functions to optimize the representations of the ADM. Through extensive experiments, we demonstrate that our proposed framework consistently outperforms the baselines in the ADM prediction and downstream application tasks. This research contributes to understanding and predicting asset dependencies, offering valuable insights for financial market participants. ...

Deep learning for quadratic hedging in incomplete jump market ArXiv ID: 2407.13688 “View on arXiv” Authors: Unknown Abstract We propose a deep learning approach to study the minimal variance pricing and hedging problem in an incomplete jump diffusion market. It is based upon a rigorous stochastic calculus derivation of the optimal hedging portfolio, optimal option price, and the corresponding equivalent martingale measure through the means of the Stackelberg game approach. A deep learning algorithm based on the combination of the feedforward and LSTM neural networks is tested on three different market models, two of which are incomplete. In contrast, the complete market Black-Scholes model serves as a benchmark for the algorithm’s performance. The results that indicate the algorithm’s good performance are presented and discussed. In particular, we apply our results to the special incomplete market model studied by Merton and give a detailed comparison between our results based on the minimal variance principle and the results obtained by Merton based on a different pricing principle. Using deep learning, we find that the minimal variance principle leads to typically higher option prices than those deduced from the Merton principle. On the other hand, the minimal variance principle leads to lower losses than the Merton principle. ...

Low-dimensional approximations of the conditional law of Volterra processes: a non-positive curvature approach ArXiv ID: 2405.20094 “View on arXiv” Authors: Unknown Abstract Predicting the conditional evolution of Volterra processes with stochastic volatility is a crucial challenge in mathematical finance. While deep neural network models offer promise in approximating the conditional law of such processes, their effectiveness is hindered by the curse of dimensionality caused by the infinite dimensionality and non-smooth nature of these problems. To address this, we propose a two-step solution. Firstly, we develop a stable dimension reduction technique, projecting the law of a reasonably broad class of Volterra process onto a low-dimensional statistical manifold of non-positive sectional curvature. Next, we introduce a sequentially deep learning model tailored to the manifold’s geometry, which we show can approximate the projected conditional law of the Volterra process. Our model leverages an auxiliary hypernetwork to dynamically update its internal parameters, allowing it to encode non-stationary dynamics of the Volterra process, and it can be interpreted as a gating mechanism in a mixture of expert models where each expert is specialized at a specific point in time. Our hypernetwork further allows us to achieve approximation rates that would seemingly only be possible with very large networks. ...

HLOB – Information Persistence and Structure in Limit Order Books ArXiv ID: 2405.18938 “View on arXiv” Authors: Unknown Abstract We introduce a novel large-scale deep learning model for Limit Order Book mid-price changes forecasting, and we name it `HLOB’. This architecture (i) exploits the information encoded by an Information Filtering Network, namely the Triangulated Maximally Filtered Graph, to unveil deeper and non-trivial dependency structures among volume levels; and (ii) guarantees deterministic design choices to handle the complexity of the underlying system by drawing inspiration from the groundbreaking class of Homological Convolutional Neural Networks. We test our model against 9 state-of-the-art deep learning alternatives on 3 real-world Limit Order Book datasets, each including 15 stocks traded on the NASDAQ exchange, and we systematically characterize the scenarios where HLOB outperforms state-of-the-art architectures. Our approach sheds new light on the spatial distribution of information in Limit Order Books and on its degradation over increasing prediction horizons, narrowing the gap between microstructural modeling and deep learning-based forecasting in high-frequency financial markets. ...