On the potential of quantum walks for modeling financial return distributions ArXiv ID: 2403.19502 “View on arXiv” Authors: Unknown Abstract Accurate modeling of the temporal evolution of asset prices is crucial for understanding financial markets. We explore the potential of discrete-time quantum walks to model the evolution of asset prices. Return distributions obtained from a model based on the quantum walk algorithm are compared with those obtained from classical methodologies. We focus on specific limitations of the classical models, and illustrate that the quantum walk model possesses great flexibility in overcoming these. This includes the potential to generate asymmetric return distributions with complex market tendencies and higher probabilities for extreme events than in some of the classical models. Furthermore, the temporal evolution in the quantum walk possesses the potential to provide asset price dynamics. ...

Reinforcement Learning in Agent-Based Market Simulation: Unveiling Realistic Stylized Facts and Behavior ArXiv ID: 2403.19781 “View on arXiv” Authors: Unknown Abstract Investors and regulators can greatly benefit from a realistic market simulator that enables them to anticipate the consequences of their decisions in real markets. However, traditional rule-based market simulators often fall short in accurately capturing the dynamic behavior of market participants, particularly in response to external market impact events or changes in the behavior of other participants. In this study, we explore an agent-based simulation framework employing reinforcement learning (RL) agents. We present the implementation details of these RL agents and demonstrate that the simulated market exhibits realistic stylized facts observed in real-world markets. Furthermore, we investigate the behavior of RL agents when confronted with external market impacts, such as a flash crash. Our findings shed light on the effectiveness and adaptability of RL-based agents within the simulation, offering insights into their response to significant market events. ...

Growth rate of liquidity provider’s wealth in G3Ms ArXiv ID: 2403.18177 “View on arXiv” Authors: Unknown Abstract We study how trading fees and continuous-time arbitrage affect the profitability of liquidity providers (LPs) in Geometric Mean Market Makers (G3Ms). We use stochastic reflected diffusion processes to analyze the dynamics of a G3M model under the arbitrage-driven market. Our research focuses on calculating LP wealth and extends the findings of Tassy and White related to the constant product market maker (Uniswap v2) to a wider range of G3Ms, including Balancer. This allows us to calculate the long-term expected logarithmic growth of LP wealth, offering new insights into the complex dynamics of AMMs and their implications for LPs in decentralized finance. ...

Optimal Rebalancing in Dynamic AMMs ArXiv ID: 2403.18737 “View on arXiv” Authors: Unknown Abstract Dynamic AMM pools, as found in Temporal Function Market Making, rebalance their holdings to a new desired ratio (e.g. moving from being 50-50 between two assets to being 90-10 in favour of one of them) by introducing an arbitrage opportunity that disappears when their holdings are in line with their target. Structuring this arbitrage opportunity reduces to the problem of choosing the sequence of portfolio weights the pool exposes to the market via its trading function. Linear interpolation from start weights to end weights has been used to reduce the cost paid by pools to arbitrageurs to rebalance. Here we obtain the $\textit{“optimal”}$ interpolation in the limit of small weight changes (which has the downside of requiring a call to a transcendental function) and then obtain a cheap-to-compute approximation to that optimal approach that gives almost the same performance improvement. We then demonstrate this method on a range of market backtests, including simulating pool performance when trading fees are present, finding that the new approximately-optimal method of changing weights gives robust increases in pool performance. For a BTC-ETH-DAI pool from July 2022 to June 2023, the increases of pool P&L from approximately-optimal weight changes is $\sim25%$ for a range of different strategies and trading fees. ...

Stock Recommendations for Individual Investors: A Temporal Graph Network Approach with Mean-Variance Efficient Sampling ArXiv ID: 2404.07223 “View on arXiv” Authors: Unknown Abstract Recommender systems can be helpful for individuals to make well-informed decisions in complex financial markets. While many studies have focused on predicting stock prices, even advanced models fall short of accurately forecasting them. Additionally, previous studies indicate that individual investors often disregard established investment theories, favoring their personal preferences instead. This presents a challenge for stock recommendation systems, which must not only provide strong investment performance but also respect these individual preferences. To create effective stock recommender systems, three critical elements must be incorporated: 1) individual preferences, 2) portfolio diversification, and 3) the temporal dynamics of the first two. In response, we propose a new model, Portfolio Temporal Graph Network Recommender PfoTGNRec, which can handle time-varying collaborative signals and incorporates diversification-enhancing sampling. On real-world individual trading data, our approach demonstrates superior performance compared to state-of-the-art baselines, including cutting-edge dynamic embedding models and existing stock recommendation models. Indeed, we show that PfoTGNRec is an effective solution that can balance customer preferences with the need to suggest portfolios with high Return-on-Investment. The source code and data are available at https://github.com/youngandbin/PfoTGNRec. ...

Temporal Graph Networks for Graph Anomaly Detection in Financial Networks ArXiv ID: 2404.00060 “View on arXiv” Authors: Unknown Abstract This paper explores the utilization of Temporal Graph Networks (TGN) for financial anomaly detection, a pressing need in the era of fintech and digitized financial transactions. We present a comprehensive framework that leverages TGN, capable of capturing dynamic changes in edges within financial networks, for fraud detection. Our study compares TGN’s performance against static Graph Neural Network (GNN) baselines, as well as cutting-edge hypergraph neural network baselines using DGraph dataset for a realistic financial context. Our results demonstrate that TGN significantly outperforms other models in terms of AUC metrics. This superior performance underlines TGN’s potential as an effective tool for detecting financial fraud, showcasing its ability to adapt to the dynamic and complex nature of modern financial systems. We also experimented with various graph embedding modules within the TGN framework and compared the effectiveness of each module. In conclusion, we demonstrated that, even with variations within TGN, it is possible to achieve good performance in the anomaly detection task. ...

Revisiting Elastic String Models of Forward Interest Rates ArXiv ID: 2403.18126 “View on arXiv” Authors: Unknown Abstract Twenty five years ago, several authors proposed to describe the forward interest rate curve (FRC) as an elastic string along which idiosyncratic shocks propagate, accounting for the peculiar structure of the return correlation across different maturities. In this paper, we revisit the specific “stiff’’ elastic string field theory of Baaquie and Bouchaud (2004) in a way that makes its micro-foundation more transparent. Our model can be interpreted as capturing the effect of market forces that set the rates of nearby tenors in a self-referential fashion. The model is parsimonious and accurately reproduces the whole correlation structure of the FRC over the time period 1994-2023, with an error around 1% and with only one adjustable parameter, the value of which being very stable across the last three decades. The dependence of correlation on time resolution (also called the Epps effect) is also faithfully reproduced within the model and leads to a cross-tenor information propagation time on the order of 30 minutes. Finally, we confirm that the perceived time in interest rate markets is a strongly sub-linear function of real time, as surmised by Baaquie and Bouchaud (2004). In fact, our results are fully compatible with hyperbolic discounting, in line with the recent behavioral Finance literature (Farmer and Geanakoplos, 2009). ...

An End-to-End Structure with Novel Position Mechanism and Improved EMD for Stock Forecasting ArXiv ID: 2404.07969 “View on arXiv” Authors: Unknown Abstract As a branch of time series forecasting, stock movement forecasting is one of the challenging problems for investors and researchers. Since Transformer was introduced to analyze financial data, many researchers have dedicated themselves to forecasting stock movement using Transformer or attention mechanisms. However, existing research mostly focuses on individual stock information but ignores stock market information and high noise in stock data. In this paper, we propose a novel method using the attention mechanism in which both stock market information and individual stock information are considered. Meanwhile, we propose a novel EMD-based algorithm for reducing short-term noise in stock data. Two randomly selected exchange-traded funds (ETFs) spanning over ten years from US stock markets are used to demonstrate the superior performance of the proposed attention-based method. The experimental analysis demonstrates that the proposed attention-based method significantly outperforms other state-of-the-art baselines. Code is available at https://github.com/DurandalLee/ACEFormer. ...

High-Dimensional Mean-Variance Spanning Tests ArXiv ID: 2403.17127 “View on arXiv” Authors: Unknown Abstract We introduce a new framework for the mean-variance spanning (MVS) hypothesis testing. The procedure can be applied to any test-asset dimension and only requires stationary asset returns and the number of benchmark assets to be smaller than the number of time periods. It involves individually testing moment conditions using a robust Student-t statistic based on the batch-mean method and combining the p-values using the Cauchy combination test. Simulations demonstrate the superior performance of the test compared to state-of-the-art approaches. For the empirical application, we look at the problem of domestic versus international diversification in equities. We find that the advantages of diversification are influenced by economic conditions and exhibit cross-country variation. We also highlight that the rejection of the MVS hypothesis originates from the potential to reduce variance within the domestic global minimum-variance portfolio. ...

Revisiting Boehmer et al. (2021): Recent Period, Alternative Method, Different Conclusions ArXiv ID: 2403.17095 “View on arXiv” Authors: Unknown Abstract We reassess Boehmer et al. (2021, BJZZ)’s seminal work on the predictive power of retail order imbalance (ROI) for future stock returns. First, we replicate their 2010-2015 analysis in the more recent 2016-2021 period. We find that the ROI’s predictive power weakens significantly. Specifically, past ROI can no longer predict weekly returns on large-cap stocks, and the long-short strategy based on past ROI is no longer profitable. Second, we analyze the effect of using the alternative quote midpoint (QMP) method to identify and sign retail trades on their main conclusions. While the results based on the QMP method align with BJZZ’s findings in 2010-2015, the two methods provide different conclusions in 2016-2021. Our study shows that BJZZ’s original findings are sensitive to the sample period and the approach to identify ROIs. ...