Diffusion Variational Autoencoder for Tackling Stochasticity in Multi-Step Regression Stock Price Prediction ArXiv ID: 2309.00073 “View on arXiv” Authors: Unknown Abstract Multi-step stock price prediction over a long-term horizon is crucial for forecasting its volatility, allowing financial institutions to price and hedge derivatives, and banks to quantify the risk in their trading books. Additionally, most financial regulators also require a liquidity horizon of several days for institutional investors to exit their risky assets, in order to not materially affect market prices. However, the task of multi-step stock price prediction is challenging, given the highly stochastic nature of stock data. Current solutions to tackle this problem are mostly designed for single-step, classification-based predictions, and are limited to low representation expressiveness. The problem also gets progressively harder with the introduction of the target price sequence, which also contains stochastic noise and reduces generalizability at test-time. To tackle these issues, we combine a deep hierarchical variational-autoencoder (VAE) and diffusion probabilistic techniques to do seq2seq stock prediction through a stochastic generative process. The hierarchical VAE allows us to learn the complex and low-level latent variables for stock prediction, while the diffusion probabilistic model trains the predictor to handle stock price stochasticity by progressively adding random noise to the stock data. Our Diffusion-VAE (D-Va) model is shown to outperform state-of-the-art solutions in terms of its prediction accuracy and variance. More importantly, the multi-step outputs can also allow us to form a stock portfolio over the prediction length. We demonstrate the effectiveness of our model outputs in the portfolio investment task through the Sharpe ratio metric and highlight the importance of dealing with different types of prediction uncertainties. ...

IMM: An Imitative Reinforcement Learning Approach with Predictive Representation Learning for Automatic Market Making ArXiv ID: 2308.08918 “View on arXiv” Authors: Unknown Abstract Market making (MM) has attracted significant attention in financial trading owing to its essential function in ensuring market liquidity. With strong capabilities in sequential decision-making, Reinforcement Learning (RL) technology has achieved remarkable success in quantitative trading. Nonetheless, most existing RL-based MM methods focus on optimizing single-price level strategies which fail at frequent order cancellations and loss of queue priority. Strategies involving multiple price levels align better with actual trading scenarios. However, given the complexity that multi-price level strategies involves a comprehensive trading action space, the challenge of effectively training profitable RL agents for MM persists. Inspired by the efficient workflow of professional human market makers, we propose Imitative Market Maker (IMM), a novel RL framework leveraging both knowledge from suboptimal signal-based experts and direct policy interactions to develop multi-price level MM strategies efficiently. The framework start with introducing effective state and action representations adept at encoding information about multi-price level orders. Furthermore, IMM integrates a representation learning unit capable of capturing both short- and long-term market trends to mitigate adverse selection risk. Subsequently, IMM formulates an expert strategy based on signals and trains the agent through the integration of RL and imitation learning techniques, leading to efficient learning. Extensive experimental results on four real-world market datasets demonstrate that IMM outperforms current RL-based market making strategies in terms of several financial criteria. The findings of the ablation study substantiate the effectiveness of the model components. ...

Improving Capital Efficiency and Impermanent Loss: Multi-Token Proactive Market Maker ArXiv ID: 2309.00632 “View on arXiv” Authors: Unknown Abstract Current approaches to the cryptocurrency automated market makers result in poor impermanent loss and capital efficiency. We analyze the mechanics underlying DODO Exchange’s proactive market maker (PMM) to probe for solutions to these issues, leading to our key insight of multi-token trading pools. We explore this paradigm primarily through the construction of a generalization of PMM, the multi-token token proactive market maker (MPMM). We show via simulations that MPMM has better impermanent loss and capital efficiency than comparable market makers under a variety of market scenarios. We also test multi-token generalizations of other common 2-token pool market makers. Overall, this work demonstrates several advantages of multi-token pools and introduces a novel multi-token pool market maker. ...

Semi-analytic pricing of American options in time-dependent jump-diffusion models with exponential jumps ArXiv ID: 2308.08760 “View on arXiv” Authors: Unknown Abstract In this paper we propose a semi-analytic approach to pricing American options for time-dependent jump-diffusions models with exponential jumps The idea of the method is to further generalize our approach developed for pricing barrier, [“Itkin et al., 2021”], and American, [“Carr and Itkin, 2021; Itkin and Muravey, 2023”], options in various time-dependent one factor and even stochastic volatility models. Our approach i) allows arbitrary dependencies of the model parameters on time; ii) reduces solution of the pricing problem for American options to a simpler problem of solving a system of an algebraic nonlinear equation for the exercise boundary and a linear Fredholm-Volterra equation for the the option price; iii) the options Greeks solve a similar Fredholm-Volterra linear equation obtained by just differentiating Eq. (25) by the required parameter. Once done, the American option price is presented in close form. ...

Detecting Financial Market Manipulation with Statistical Physics Tools ArXiv ID: 2308.08683 “View on arXiv” Authors: Unknown Abstract We take inspiration from statistical physics to develop a novel conceptual framework for the analysis of financial markets. We model the order book dynamics as a motion of particles and define the momentum measure of the system as a way to summarise and assess the state of the market. Our approach proves useful in capturing salient financial market phenomena: in particular, it helps detect the market manipulation activities called spoofing and layering. We apply our method to identify pathological order book behaviours during the flash crash of the LUNA cryptocurrency, uncovering widespread instances of spoofing and layering in the market. Furthermore, we establish that our technique outperforms the conventional Z-score-based anomaly detection method in identifying market manipulations across both LUNA and Bitcoin cryptocurrency markets. ...

Microstructure-Empowered Stock Factor Extraction and Utilization ArXiv ID: 2308.08135 “View on arXiv” Authors: Unknown Abstract High-frequency quantitative investment is a crucial aspect of stock investment. Notably, order flow data plays a critical role as it provides the most detailed level of information among high-frequency trading data, including comprehensive data from the order book and transaction records at the tick level. The order flow data is extremely valuable for market analysis as it equips traders with essential insights for making informed decisions. However, extracting and effectively utilizing order flow data present challenges due to the large volume of data involved and the limitations of traditional factor mining techniques, which are primarily designed for coarser-level stock data. To address these challenges, we propose a novel framework that aims to effectively extract essential factors from order flow data for diverse downstream tasks across different granularities and scenarios. Our method consists of a Context Encoder and an Factor Extractor. The Context Encoder learns an embedding for the current order flow data segment’s context by considering both the expected and actual market state. In addition, the Factor Extractor uses unsupervised learning methods to select such important signals that are most distinct from the majority within the given context. The extracted factors are then utilized for downstream tasks. In empirical studies, our proposed framework efficiently handles an entire year of stock order flow data across diverse scenarios, offering a broader range of applications compared to existing tick-level approaches that are limited to only a few days of stock data. We demonstrate that our method extracts superior factors from order flow data, enabling significant improvement for stock trend prediction and order execution tasks at the second and minute level. ...

Company Similarity using Large Language Models ArXiv ID: 2308.08031 “View on arXiv” Authors: Unknown Abstract Identifying companies with similar profiles is a core task in finance with a wide range of applications in portfolio construction, asset pricing and risk attribution. When a rigorous definition of similarity is lacking, financial analysts usually resort to ’traditional’ industry classifications such as Global Industry Classification System (GICS) which assign a unique category to each company at different levels of granularity. Due to their discrete nature, though, GICS classifications do not allow for ranking companies in terms of similarity. In this paper, we explore the ability of pre-trained and finetuned large language models (LLMs) to learn company embeddings based on the business descriptions reported in SEC filings. We show that we can reproduce GICS classifications using the embeddings as features. We also benchmark these embeddings on various machine learning and financial metrics and conclude that the companies that are similar according to the embeddings are also similar in terms of financial performance metrics including return correlation. ...

Decentralized Token Economy Theory (DeTEcT) ArXiv ID: 2309.12330 “View on arXiv” Authors: Unknown Abstract This paper presents a pioneering approach for simulation of economic activity, policy implementation, and pricing of goods in token economies. The paper proposes a formal analysis framework for wealth distribution analysis and simulation of interactions between economic participants in an economy. Using this framework, we define a mechanism for identifying prices that achieve the desired wealth distribution according to some metric, and stability of economic dynamics. The motivation to study tokenomics theory is the increasing use of tokenization, specifically in financial infrastructures, where designing token economies is in the forefront. Tokenomics theory establishes a quantitative framework for wealth distribution amongst economic participants and implements the algorithmic regulatory controls mechanism that reacts to changes in economic conditions. In our framework, we introduce a concept of tokenomic taxonomy where agents in the economy are categorized into agent types and interactions between them. This novel approach is motivated by having a generalized model of the macroeconomy with controls being implemented through interactions and policies. The existence of such controls allows us to measure and readjust the wealth dynamics in the economy to suit the desired objectives. ...

Nested Multilevel Monte Carlo with Biased and Antithetic Sampling ArXiv ID: 2308.07835 “View on arXiv” Authors: Unknown Abstract We consider the problem of estimating a nested structure of two expectations taking the form $U_0 = E["\max{“U_1(Y), π(Y)"}”]$, where $U_1(Y) = E[“X\ |\ Y”]$. Terms of this form arise in financial risk estimation and option pricing. When $U_1(Y)$ requires approximation, but exact samples of $X$ and $Y$ are available, an antithetic multilevel Monte Carlo (MLMC) approach has been well-studied in the literature. Under general conditions, the antithetic MLMC estimator obtains a root mean squared error $\varepsilon$ with order $\varepsilon^{"-2"}$ cost. If, additionally, $X$ and $Y$ require approximate sampling, careful balancing of the various aspects of approximation is required to avoid a significant computational burden. Under strong convergence criteria on approximations to $X$ and $Y$, randomised multilevel Monte Carlo techniques can be used to construct unbiased Monte Carlo estimates of $U_1$, which can be paired with an antithetic MLMC estimate of $U_0$ to recover order $\varepsilon^{"-2"}$ computational cost. In this work, we instead consider biased multilevel approximations of $U_1(Y)$, which require less strict assumptions on the approximate samples of $X$. Extensions to the method consider an approximate and antithetic sampling of $Y$. Analysis shows the resulting estimator has order $\varepsilon^{"-2"}$ asymptotic cost under the conditions required by randomised MLMC and order $\varepsilon^{"-2"}|\log\varepsilon|^3$ cost under more general assumptions. ...

Online Universal Dirichlet Factor Portfolios ArXiv ID: 2308.07763 “View on arXiv” Authors: Unknown Abstract We revisit the online portfolio allocation problem and propose universal portfolios that use factor weighing to produce portfolios that out-perform uniform dirichlet allocation schemes. We show a few analytical results on the lower bounds of portfolio growth when the returns are known to follow a factor model. We also show analytically that factor weighted dirichlet sampled portfolios dominate the wealth generated by uniformly sampled dirichlet portfolios. We corroborate our analytical results with empirical studies on equity markets that are known to be driven by factors. ...