When is cross impact relevant? ArXiv ID: 2305.16915 “View on arXiv” Authors: Unknown Abstract Trading pressure from one asset can move the price of another, a phenomenon referred to as cross impact. Using tick-by-tick data spanning 5 years for 500 assets listed in the United States, we identify the features that make cross-impact relevant to explain the variance of price returns. We show that price formation occurs endogenously within highly liquid assets. Then, trades in these assets influence the prices of less liquid correlated products, with an impact velocity constrained by their minimum trading frequency. We investigate the implications of such a multidimensional price formation mechanism on interest rate markets. We find that the 10-year bond future serves as the primary liquidity reservoir, influencing the prices of cash bonds and futures contracts within the interest rate curve. Such behaviour challenges the validity of the theory in Financial Economics that regards long-term rates as agents anticipations of future short term rates. ...

Abnormal Trading Detection in the NFT Market ArXiv ID: 2306.04643 “View on arXiv” Authors: Unknown Abstract The Non-Fungible-Token (NFT) market has experienced explosive growth in recent years. According to DappRadar, the total transaction volume on OpenSea, the largest NFT marketplace, reached 34.7 billion dollars in February 2023. However, the NFT market is mostly unregulated and there are significant concerns about money laundering, fraud and wash trading. The lack of industry-wide regulations, and the fact that amateur traders and retail investors comprise a significant fraction of the NFT market, make this market particularly vulnerable to fraudulent activities. Therefore it is essential to investigate and highlight the relevant risks involved in NFT trading. In this paper, we attempted to uncover common fraudulent behaviors such as wash trading that could mislead other traders. Using market data, we designed quantitative features from the network, monetary, and temporal perspectives that were fed into K-means clustering unsupervised learning algorithm to sort traders into groups. Lastly, we discussed the clustering results’ significance and how regulations can reduce undesired behaviors. Our work can potentially help regulators narrow down their search space for bad actors in the market as well as provide insights for amateur traders to protect themselves from unforeseen frauds. ...

E2EAI: End-to-End Deep Learning Framework for Active Investing ArXiv ID: 2305.16364 “View on arXiv” Authors: Unknown Abstract Active investing aims to construct a portfolio of assets that are believed to be relatively profitable in the markets, with one popular method being to construct a portfolio via factor-based strategies. In recent years, there have been increasing efforts to apply deep learning to pursue “deep factors’’ with more active returns or promising pipelines for asset trends prediction. However, the question of how to construct an active investment portfolio via an end-to-end deep learning framework (E2E) is still open and rarely addressed in existing works. In this paper, we are the first to propose an E2E that covers almost the entire process of factor investing through factor selection, factor combination, stock selection, and portfolio construction. Extensive experiments on real stock market data demonstrate the effectiveness of our end-to-end deep leaning framework in active investing. ...

Generating Synergistic Formulaic Alpha Collections via Reinforcement Learning ArXiv ID: 2306.12964 “View on arXiv” Authors: Unknown Abstract In the field of quantitative trading, it is common practice to transform raw historical stock data into indicative signals for the market trend. Such signals are called alpha factors. Alphas in formula forms are more interpretable and thus favored by practitioners concerned with risk. In practice, a set of formulaic alphas is often used together for better modeling precision, so we need to find synergistic formulaic alpha sets that work well together. However, most traditional alpha generators mine alphas one by one separately, overlooking the fact that the alphas would be combined later. In this paper, we propose a new alpha-mining framework that prioritizes mining a synergistic set of alphas, i.e., it directly uses the performance of the downstream combination model to optimize the alpha generator. Our framework also leverages the strong exploratory capabilities of reinforcement learning~(RL) to better explore the vast search space of formulaic alphas. The contribution to the combination models’ performance is assigned to be the return used in the RL process, driving the alpha generator to find better alphas that improve upon the current set. Experimental evaluations on real-world stock market data demonstrate both the effectiveness and the efficiency of our framework for stock trend forecasting. The investment simulation results show that our framework is able to achieve higher returns compared to previous approaches. ...

Hierarchical forecasting for aggregated curves with an application to day-ahead electricity price auctions ArXiv ID: 2305.16255 “View on arXiv” Authors: Unknown Abstract Aggregated curves are common structures in economics and finance, and the most prominent examples are supply and demand curves. In this study, we exploit the fact that all aggregated curves have an intrinsic hierarchical structure, and thus hierarchical reconciliation methods can be used to improve the forecast accuracy. We provide an in-depth theory on how aggregated curves can be constructed or deconstructed, and conclude that these methods are equivalent under weak assumptions. We consider multiple reconciliation methods for aggregated curves, including previously established bottom-up, top-down, and linear optimal reconciliation approaches. We also present a new benchmark reconciliation method called ‘aggregated-down’ with similar complexity to bottom-up and top-down approaches, but it tends to provide better accuracy in this setup. We conducted an empirical forecasting study on the German day-ahead power auction market by predicting the demand and supply curves, where their equilibrium determines the electricity price for the next day. Our results demonstrate that hierarchical reconciliation methods can be used to improve the forecasting accuracy of aggregated curves. ...

Market Making with Deep Reinforcement Learning from Limit Order Books ArXiv ID: 2305.15821 “View on arXiv” Authors: Unknown Abstract Market making (MM) is an important research topic in quantitative finance, the agent needs to continuously optimize ask and bid quotes to provide liquidity and make profits. The limit order book (LOB) contains information on all active limit orders, which is an essential basis for decision-making. The modeling of evolving, high-dimensional and low signal-to-noise ratio LOB data is a critical challenge. Traditional MM strategy relied on strong assumptions such as price process, order arrival process, etc. Previous reinforcement learning (RL) works handcrafted market features, which is insufficient to represent the market. This paper proposes a RL agent for market making with LOB data. We leverage a neural network with convolutional filters and attention mechanism (Attn-LOB) for feature extraction from LOB. We design a new continuous action space and a hybrid reward function for the MM task. Finally, we conduct comprehensive experiments on latency and interpretability, showing that our agent has good applicability. ...

Non-adversarial training of Neural SDEs with signature kernel scores ArXiv ID: 2305.16274 “View on arXiv” Authors: Unknown Abstract Neural SDEs are continuous-time generative models for sequential data. State-of-the-art performance for irregular time series generation has been previously obtained by training these models adversarially as GANs. However, as typical for GAN architectures, training is notoriously unstable, often suffers from mode collapse, and requires specialised techniques such as weight clipping and gradient penalty to mitigate these issues. In this paper, we introduce a novel class of scoring rules on pathspace based on signature kernels and use them as objective for training Neural SDEs non-adversarially. By showing strict properness of such kernel scores and consistency of the corresponding estimators, we provide existence and uniqueness guarantees for the minimiser. With this formulation, evaluating the generator-discriminator pair amounts to solving a system of linear path-dependent PDEs which allows for memory-efficient adjoint-based backpropagation. Moreover, because the proposed kernel scores are well-defined for paths with values in infinite dimensional spaces of functions, our framework can be easily extended to generate spatiotemporal data. Our procedure permits conditioning on a rich variety of market conditions and significantly outperforms alternative ways of training Neural SDEs on a variety of tasks including the simulation of rough volatility models, the conditional probabilistic forecasts of real-world forex pairs where the conditioning variable is an observed past trajectory, and the mesh-free generation of limit order book dynamics. ...

Automated Market Making and Arbitrage Profits in the Presence of Fees ArXiv ID: 2305.14604 “View on arXiv” Authors: Unknown Abstract We consider the impact of trading fees on the profits of arbitrageurs trading against an automated market maker (AMM) or, equivalently, on the adverse selection incurred by liquidity providers (LPs) due to arbitrage. We extend the model of Milionis et al. [“2022”] for a general class of two asset AMMs to introduce both fees and discrete Poisson block generation times. In our setting, we are able to compute the expected instantaneous rate of arbitrage profit in closed form. When the fees are low, in the fast block asymptotic regime, the impact of fees takes a particularly simple form: fees simply scale down arbitrage profits by the fraction of blocks which present profitable trading opportunities to arbitrageurs. This fraction decreases with an increasing block rate, hence our model yields an important practical insight: faster blockchains will result in reduced LP losses. Further introducing gas fees (fixed costs) in our model, we show that, in the fast block asymptotic regime, lower gas fees lead to smaller losses for LPs. ...

The Quadratic Local Variance Gamma Model: an arbitrage-free interpolation of class C3 for option prices ArXiv ID: 2305.13791 “View on arXiv” Authors: Unknown Abstract This paper generalizes the local variance gamma model of Carr and Nadtochiy, to a piecewise quadratic local variance function. The formulation encompasses the piecewise linear Bachelier and piecewise linear Black local variance gamma models. The quadratic local variance function results in an arbitrage-free interpolation of class C3. The increased smoothness over the piecewise-constant and piecewise-linear representation allows to reduce the number of knots when interpolating raw market quotes, thus providing an interesting alternative to regularization while reducing the computational cost. ...

A Simulation Package in VBA to Support Finance Students for Constructing Optimal Portfolios ArXiv ID: 2305.12826 “View on arXiv” Authors: Unknown Abstract This paper introduces a software component created in Visual Basic for Applications (VBA) that can be applied for creating an optimal portfolio using two different methods. The first method is the seminal approach of Markowitz that is based on finding budget shares via the minimization of the variance of the underlying portfolio. The second method is developed by El-Khatib and Hatemi-J, which combines risk and return directly in the optimization problem and yields budget shares that lead to maximizing the risk adjusted return of the portfolio. This approach is consistent with the expectation of rational investors since these investors consider both risk and return as the fundamental basis for selection of the investment assets. Our package offers another advantage that is usually neglected in the literature, which is the number of assets that should be included in the portfolio. The common practice is to assume that the number of assets is given exogenously when the portfolio is constructed. However, the current software component constructs all possible combinations and thus the investor can figure out empirically which portfolio is the best one among all portfolios considered. The software is consumer friendly via a graphical user interface. An application is also provided to demonstrate how the software can be used using real-time series data for several assets. ...