An Empirical Analysis on Financial Markets: Insights from the Application of Statistical Physics ArXiv ID: 2308.14235 “View on arXiv” Authors: Unknown Abstract In this study, we introduce a physical model inspired by statistical physics for predicting price volatility and expected returns by leveraging Level 3 order book data. By drawing parallels between orders in the limit order book and particles in a physical system, we establish unique measures for the system’s kinetic energy and momentum as a way to comprehend and evaluate the state of limit order book. Our model goes beyond examining merely the top layers of the order book by introducing the concept of ‘active depth’, a computationally-efficient approach for identifying order book levels that have impact on price dynamics. We empirically demonstrate that our model outperforms the benchmarks of traditional approaches and machine learning algorithm. Our model provides a nuanced comprehension of market microstructure and produces more accurate forecasts on volatility and expected returns. By incorporating principles of statistical physics, this research offers valuable insights on understanding the behaviours of market participants and order book dynamics. ...

Breaking the Bank with ChatGPT: Few-Shot Text Classification for Finance ArXiv ID: 2308.14634 “View on arXiv” Authors: Unknown Abstract We propose the use of conversational GPT models for easy and quick few-shot text classification in the financial domain using the Banking77 dataset. Our approach involves in-context learning with GPT-3.5 and GPT-4, which minimizes the technical expertise required and eliminates the need for expensive GPU computing while yielding quick and accurate results. Additionally, we fine-tune other pre-trained, masked language models with SetFit, a recent contrastive learning technique, to achieve state-of-the-art results both in full-data and few-shot settings. Our findings show that querying GPT-3.5 and GPT-4 can outperform fine-tuned, non-generative models even with fewer examples. However, subscription fees associated with these solutions may be considered costly for small organizations. Lastly, we find that generative models perform better on the given task when shown representative samples selected by a human expert rather than when shown random ones. We conclude that a) our proposed methods offer a practical solution for few-shot tasks in datasets with limited label availability, and b) our state-of-the-art results can inspire future work in the area. ...

Deep multi-step mixed algorithm for high dimensional non-linear PDEs and associated BSDEs ArXiv ID: 2308.14487 “View on arXiv” Authors: Unknown Abstract We propose a new multistep deep learning-based algorithm for the resolution of moderate to high dimensional nonlinear backward stochastic differential equations (BSDEs) and their corresponding parabolic partial differential equations (PDE). Our algorithm relies on the iterated time discretisation of the BSDE and approximates its solution and gradient using deep neural networks and automatic differentiation at each time step. The approximations are obtained by sequential minimisation of local quadratic loss functions at each time step through stochastic gradient descent. We provide an analysis of approximation error in the case of a network architecture with weight constraints requiring only low regularity conditions on the generator of the BSDE. The algorithm increases accuracy from its single step parent model and has reduced complexity when compared to similar models in the literature. ...

Joint Calibration of Local Volatility Models with Stochastic Interest Rates using Semimartingale Optimal Transport ArXiv ID: 2308.14473 “View on arXiv” Authors: Unknown Abstract We develop and implement a non-parametric method for joint exact calibration of a local volatility model and a correlated stochastic short rate model using semimartingale optimal transport. The method relies on the duality results established in Joseph, Loeper, and Obloj, 2023 and jointly calibrates the whole equity-rate dynamics. It uses an iterative approach which starts with a parametric model and tries to stay close to it, until a perfect calibration is obtained. We demonstrate the performance of our approach on market data using European SPX options and European cap interest rate options. Finally, we compare the joint calibration approach with the sequential calibration, in which the short rate model is calibrated first and frozen. ...

TimeTrail: Unveiling Financial Fraud Patterns through Temporal Correlation Analysis ArXiv ID: 2308.14215 “View on arXiv” Authors: Unknown Abstract In the field of financial fraud detection, understanding the underlying patterns and dynamics is important to ensure effective and reliable systems. This research introduces a new technique, “TimeTrail,” which employs advanced temporal correlation analysis to explain complex financial fraud patterns. The technique leverages time-related insights to provide transparent and interpretable explanations for fraud detection decisions, enhancing accountability and trust. The “TimeTrail” methodology consists of three key phases: temporal data enrichment, dynamic correlation analysis, and interpretable pattern visualization. Initially, raw financial transaction data is enriched with temporal attributes. Dynamic correlations between these attributes are then quantified using innovative statistical measures. Finally, a unified visualization framework presents these correlations in an interpretable manner. To validate the effectiveness of “TimeTrail,” a study is conducted on a diverse financial dataset, surrounding various fraud scenarios. Results demonstrate the technique’s capability to uncover hidden temporal correlations and patterns, performing better than conventional methods in both accuracy and interpretability. Moreover, a case study showcasing the application of “TimeTrail” in real-world scenarios highlights its utility for fraud detection. ...

JAX-LOB: A GPU-Accelerated limit order book simulator to unlock large scale reinforcement learning for trading ArXiv ID: 2308.13289 “View on arXiv” Authors: Unknown Abstract Financial exchanges across the world use limit order books (LOBs) to process orders and match trades. For research purposes it is important to have large scale efficient simulators of LOB dynamics. LOB simulators have previously been implemented in the context of agent-based models (ABMs), reinforcement learning (RL) environments, and generative models, processing order flows from historical data sets and hand-crafted agents alike. For many applications, there is a requirement for processing multiple books, either for the calibration of ABMs or for the training of RL agents. We showcase the first GPU-enabled LOB simulator designed to process thousands of books in parallel, with a notably reduced per-message processing time. The implementation of our simulator - JAX-LOB - is based on design choices that aim to best exploit the powers of JAX without compromising on the realism of LOB-related mechanisms. We integrate JAX-LOB with other JAX packages, to provide an example of how one may address an optimal execution problem with reinforcement learning, and to share some preliminary results from end-to-end RL training on GPUs. ...

The Potential of Quantum Techniques for Stock Price Prediction ArXiv ID: 2308.13642 “View on arXiv” Authors: Unknown Abstract We explored the potential applications of various Quantum Algorithms for stock price prediction by conducting a series of experimental simulations using both Classical as well as Quantum Hardware. Firstly, we extracted various stock price indicators, such as Moving Averages (MA), Average True Range (ATR), and Aroon, to gain insights into market trends and stock price movements. Next, we employed Quantum Annealing (QA) for feature selection and Principal Component Analysis (PCA) for dimensionality reduction. Further, we transformed the stock price prediction task essentially into a classification problem. We trained the Quantum Support Vector Machine (QSVM) to predict price movements (whether up or down) contrasted their performance with classical models and analyzed their accuracy on a dataset formulated using Quantum Annealing and PCA individually. We focused on the stock price prediction and binary classification of stock prices for four different companies, namely Apple, Visa, Johnson and Jonson, and Honeywell. We primarily used the real-time stock data of the raw stock prices of these companies. We compared various Quantum Computing techniques with their classical counterparts in terms of accuracy and F-score of the prediction model. Through these experimental simulations, we shed light on the potential advantages and limitations of Quantum Algorithms in stock price prediction and contribute to the growing body of knowledge at the intersection of Quantum Computing and Finance. ...

Grover Search for Portfolio Selection ArXiv ID: 2308.13063 “View on arXiv” Authors: Unknown Abstract We present explicit oracles designed to be used in Grover’s algorithm to match investor preferences. Specifically, the oracles select portfolios with returns and standard deviations exceeding and falling below certain thresholds, respectively. One potential use case for the oracles is selecting portfolios with the best Sharpe ratios. We have implemented these algorithms using quantum simulators. Keywords: Grover’s Algorithm, Portfolio Selection, Quantum Oracles, Sharpe Ratio, Quantum Computing ...

Spatial and Spatiotemporal Volatility Models: A Review ArXiv ID: 2308.13061 “View on arXiv” Authors: Unknown Abstract Spatial and spatiotemporal volatility models are a class of models designed to capture spatial dependence in the volatility of spatial and spatiotemporal data. Spatial dependence in the volatility may arise due to spatial spillovers among locations; that is, if two locations are in close proximity, they can exhibit similar volatilities. In this paper, we aim to provide a comprehensive review of the recent literature on spatial and spatiotemporal volatility models. We first briefly review time series volatility models and their multivariate extensions to motivate their spatial and spatiotemporal counterparts. We then review various spatial and spatiotemporal volatility specifications proposed in the literature along with their underlying motivations and estimation strategies. Through this analysis, we effectively compare all models and provide practical recommendations for their appropriate usage. We highlight possible extensions and conclude by outlining directions for future research. ...

Generative AI for End-to-End Limit Order Book Modelling: A Token-Level Autoregressive Generative Model of Message Flow Using a Deep State Space Network ArXiv ID: 2309.00638 “View on arXiv” Authors: Unknown Abstract Developing a generative model of realistic order flow in financial markets is a challenging open problem, with numerous applications for market participants. Addressing this, we propose the first end-to-end autoregressive generative model that generates tokenized limit order book (LOB) messages. These messages are interpreted by a Jax-LOB simulator, which updates the LOB state. To handle long sequences efficiently, the model employs simplified structured state-space layers to process sequences of order book states and tokenized messages. Using LOBSTER data of NASDAQ equity LOBs, we develop a custom tokenizer for message data, converting groups of successive digits to tokens, similar to tokenization in large language models. Out-of-sample results show promising performance in approximating the data distribution, as evidenced by low model perplexity. Furthermore, the mid-price returns calculated from the generated order flow exhibit a significant correlation with the data, indicating impressive conditional forecast performance. Due to the granularity of generated data, and the accuracy of the model, it offers new application areas for future work beyond forecasting, e.g. acting as a world model in high-frequency financial reinforcement learning applications. Overall, our results invite the use and extension of the model in the direction of autoregressive large financial models for the generation of high-frequency financial data and we commit to open-sourcing our code to facilitate future research. ...