Deep Learning

Deep Limit Order Book Forecasting ArXiv ID: 2403.09267 “View on arXiv” Authors: Unknown Abstract We exploit cutting-edge deep learning methodologies to explore the predictability of high-frequency Limit Order Book mid-price changes for a heterogeneous set of stocks traded on the NASDAQ exchange. In so doing, we release `LOBFrame’, an open-source code base to efficiently process large-scale Limit Order Book data and quantitatively assess state-of-the-art deep learning models’ forecasting capabilities. Our results are twofold. We demonstrate that the stocks’ microstructural characteristics influence the efficacy of deep learning methods and that their high forecasting power does not necessarily correspond to actionable trading signals. We argue that traditional machine learning metrics fail to adequately assess the quality of forecasts in the Limit Order Book context. As an alternative, we propose an innovative operational framework that evaluates predictions’ practicality by focusing on the probability of accurately forecasting complete transactions. This work offers academics and practitioners an avenue to make informed and robust decisions on the application of deep learning techniques, their scope and limitations, effectively exploiting emergent statistical properties of the Limit Order Book. ...

A time-stepping deep gradient flow method for option pricing in (rough) diffusion models ArXiv ID: 2403.00746 “View on arXiv” Authors: Unknown Abstract We develop a novel deep learning approach for pricing European options in diffusion models, that can efficiently handle high-dimensional problems resulting from Markovian approximations of rough volatility models. The option pricing partial differential equation is reformulated as an energy minimization problem, which is approximated in a time-stepping fashion by deep artificial neural networks. The proposed scheme respects the asymptotic behavior of option prices for large levels of moneyness, and adheres to a priori known bounds for option prices. The accuracy and efficiency of the proposed method is assessed in a series of numerical examples, with particular focus in the lifted Heston model. ...

A Study on Stock Forecasting Using Deep Learning and Statistical Models ArXiv ID: 2402.06689 “View on arXiv” Authors: Unknown Abstract Predicting a fast and accurate model for stock price forecasting is been a challenging task and this is an active area of research where it is yet to be found which is the best way to forecast the stock price. Machine learning, deep learning and statistical analysis techniques are used here to get the accurate result so the investors can see the future trend and maximize the return of investment in stock trading. This paper will review many deep learning algorithms for stock price forecasting. We use a record of s&p 500 index data for training and testing. The survey motive is to check various deep learning and statistical model techniques for stock price forecasting that are Moving Averages, ARIMA which are statistical techniques and LSTM, RNN, CNN, and FULL CNN which are deep learning models. It will discuss various models, including the Auto regression integration moving average model, the Recurrent neural network model, the long short-term model which is the type of RNN used for long dependency for data, the convolutional neural network model, and the full convolutional neural network model, in terms of error calculation or percentage of accuracy that how much it is accurate which measures by the function like Root mean square error, mean absolute error, mean squared error. The model can be used to predict the stock price by checking the low MAE value as lower the MAE value the difference between the predicting and the actual value will be less and this model will predict the price more accurately than other models. ...

DeepTraderX: Challenging Conventional Trading Strategies with Deep Learning in Multi-Threaded Market Simulations ArXiv ID: 2403.18831 “View on arXiv” Authors: Unknown Abstract In this paper, we introduce DeepTraderX (DTX), a simple Deep Learning-based trader, and present results that demonstrate its performance in a multi-threaded market simulation. In a total of about 500 simulated market days, DTX has learned solely by watching the prices that other strategies produce. By doing this, it has successfully created a mapping from market data to quotes, either bid or ask orders, to place for an asset. Trained on historical Level-2 market data, i.e., the Limit Order Book (LOB) for specific tradable assets, DTX processes the market state $S$ at each timestep $T$ to determine a price $P$ for market orders. The market data used in both training and testing was generated from unique market schedules based on real historic stock market data. DTX was tested extensively against the best strategies in the literature, with its results validated by statistical analysis. Our findings underscore DTX’s capability to rival, and in many instances, surpass, the performance of public-domain traders, including those that outclass human traders, emphasising the efficiency of simple models, as this is required to succeed in intricate multi-threaded simulations. This highlights the potential of leveraging “black-box” Deep Learning systems to create more efficient financial markets. ...

Option pricing for Barndorff-Nielsen and Shephard model by supervised deep learning ArXiv ID: 2402.00445 “View on arXiv” Authors: Unknown Abstract This paper aims to develop a supervised deep-learning scheme to compute call option prices for the Barndorff-Nielsen and Shephard model with a non-martingale asset price process having infinite active jumps. In our deep learning scheme, teaching data is generated through the Monte Carlo method developed by Arai and Imai (2024). Moreover, the BNS model includes many variables, which makes the deep learning accuracy worse. Therefore, we will create another input variable using the Black-Scholes formula. As a result, the accuracy is improved dramatically. ...

Convergence of the deep BSDE method for stochastic control problems formulated through the stochastic maximum principle ArXiv ID: 2401.17472 “View on arXiv” Authors: Unknown Abstract It is well-known that decision-making problems from stochastic control can be formulated by means of a forward-backward stochastic differential equation (FBSDE). Recently, the authors of Ji et al. 2022 proposed an efficient deep learning algorithm based on the stochastic maximum principle (SMP). In this paper, we provide a convergence result for this deep SMP-BSDE algorithm and compare its performance with other existing methods. In particular, by adopting a strategy as in Han and Long 2020, we derive a-posteriori estimate, and show that the total approximation error can be bounded by the value of the loss functional and the discretization error. We present numerical examples for high-dimensional stochastic control problems, both in case of drift- and diffusion control, which showcase superior performance compared to existing algorithms. ...

Deep Learning for Dynamic NFT Valuation ArXiv ID: 2312.05346 “View on arXiv” Authors: Unknown Abstract I study the price dynamics of non-fungible tokens (NFTs) and propose a deep learning framework for dynamic valuation of NFTs. I use data from the Ethereum blockchain and OpenSea to train a deep learning model on historical trades, market trends, and traits/rarity features of Bored Ape Yacht Club NFTs. After hyperparameter tuning, the model is able to predict the price of NFTs with high accuracy. I propose an application framework for this model using zero-knowledge machine learning (zkML) and discuss its potential use cases in the context of decentralized finance (DeFi) applications. ...

Deep Calibration of Market Simulations using Neural Density Estimators and Embedding Networks ArXiv ID: 2311.11913 “View on arXiv” Authors: Unknown Abstract The ability to construct a realistic simulator of financial exchanges, including reproducing the dynamics of the limit order book, can give insight into many counterfactual scenarios, such as a flash crash, a margin call, or changes in macroeconomic outlook. In recent years, agent-based models have been developed that reproduce many features of an exchange, as summarised by a set of stylised facts and statistics. However, the ability to calibrate simulators to a specific period of trading remains an open challenge. In this work, we develop a novel approach to the calibration of market simulators by leveraging recent advances in deep learning, specifically using neural density estimators and embedding networks. We demonstrate that our approach is able to correctly identify high probability parameter sets, both when applied to synthetic and historical data, and without reliance on manually selected or weighted ensembles of stylised facts. ...

Error Analysis of Option Pricing via Deep PDE Solvers: Empirical Study ArXiv ID: 2311.07231 “View on arXiv” Authors: Unknown Abstract Option pricing, a fundamental problem in finance, often requires solving non-linear partial differential equations (PDEs). When dealing with multi-asset options, such as rainbow options, these PDEs become high-dimensional, leading to challenges posed by the curse of dimensionality. While deep learning-based PDE solvers have recently emerged as scalable solutions to this high-dimensional problem, their empirical and quantitative accuracy remains not well-understood, hindering their real-world applicability. In this study, we aimed to offer actionable insights into the utility of Deep PDE solvers for practical option pricing implementation. Through comparative experiments, we assessed the empirical performance of these solvers in high-dimensional contexts. Our investigation identified three primary sources of errors in Deep PDE solvers: (i) errors inherent in the specifications of the target option and underlying assets, (ii) errors originating from the asset model simulation methods, and (iii) errors stemming from the neural network training. Through ablation studies, we evaluated the individual impact of each error source. Our results indicate that the Deep BSDE method (DBSDE) is superior in performance and exhibits robustness against variations in option specifications. In contrast, some other methods are overly sensitive to option specifications, such as time to expiration. We also find that the performance of these methods improves inversely proportional to the square root of batch size and the number of time steps. This observation can aid in estimating computational resources for achieving desired accuracies with Deep PDE solvers. ...

Portfolio Construction using Black-Litterman Model and Factors ArXiv ID: 2311.04475 “View on arXiv” Authors: Unknown Abstract This paper presents a portfolio construction process, including mainly two parts, Factors Selection and Weight Allocations. For the factors selection part, We have chosen 20 factors by considering three aspects, the global market, different assets class, and stock idiosyncratic characteristics. Each factor is proxied by a corresponding ETF. Then, we would apply several weight allocation methods to those factors, including two fixed weight allocation methods, three optimisation methods, and a Black-Litterman model. In addition, we would also fit a Deep Learning model for generating views periodically and incorporating views with the prior to achieve dynamically updated weights by using the Black-Litterman model. In the end, the robustness checking shows how weights change with respect to time evolving and variance increasing. Results using shrinkage variance are provided to alleviate the impacts of representativeness of historical data, but there sadly has little impact. Overall, the model by using the Deep Learning plus Black-Litterman model results outperform the portfolio by other weight allocation schemes, even though further improvement and robustness checking should be performed. ...