Statistical Arbitrage

Automated Market Making and Decentralized Finance ArXiv ID: 2407.16885 “View on arXiv” Authors: Unknown Abstract Automated market makers (AMMs) are a new type of trading venues which are revolutionising the way market participants interact. At present, the majority of AMMs are constant function market makers (CFMMs) where a deterministic trading function determines how markets are cleared. Within CFMMs, we focus on constant product market makers (CPMMs) which implements the concentrated liquidity (CL) feature. In this thesis we formalise and study the trading mechanism of CPMMs with CL, and we develop liquidity provision and liquidity taking strategies. Our models are motivated and tested with market data. We derive optimal strategies for liquidity takers (LTs) who trade orders of large size and execute statistical arbitrages. First, we consider an LT who trades in a CPMM with CL and uses the dynamics of prices in competing venues as market signals. We use Uniswap v3 data to study price, liquidity, and trading cost dynamics, and to motivate the model. Next, we consider an LT who trades a basket of crypto-currencies whose constituents co-move. We use market data to study lead-lag effects, spillover effects, and causality between trading venues. We derive optimal strategies for strategic liquidity providers (LPs) who provide liquidity in CPMM with CL. First, we use stochastic control tools to derive a self-financing and closed-form optimal liquidity provision strategy where the width of the LP’s liquidity range is determined by the profitability of the pool, the dynamics of the LP’s position, and concentration risk. Next, we use a model-free approach to solve the problem of an LP who provides liquidity in multiple CPMMs with CL. We do not specify a model for the stochastic processes observed by LPs, and use a long short-term memory (LSTM) neural network to approximate the optimal liquidity provision strategy. ...

Reinforcement Learning Pair Trading: A Dynamic Scaling approach ArXiv ID: 2407.16103 “View on arXiv” Authors: Unknown Abstract Cryptocurrency is a cryptography-based digital asset with extremely volatile prices. Around USD 70 billion worth of cryptocurrency is traded daily on exchanges. Trading cryptocurrency is difficult due to the inherent volatility of the crypto market. This study investigates whether Reinforcement Learning (RL) can enhance decision-making in cryptocurrency algorithmic trading compared to traditional methods. In order to address this question, we combined reinforcement learning with a statistical arbitrage trading technique, pair trading, which exploits the price difference between statistically correlated assets. We constructed RL environments and trained RL agents to determine when and how to trade pairs of cryptocurrencies. We developed new reward shaping and observation/action spaces for reinforcement learning. We performed experiments with the developed reinforcement learner on pairs of BTC-GBP and BTC-EUR data separated by 1 min intervals (n=263,520). The traditional non-RL pair trading technique achieved an annualized profit of 8.33%, while the proposed RL-based pair trading technique achieved annualized profits from 9.94% to 31.53%, depending upon the RL learner. Our results show that RL can significantly outperform manual and traditional pair trading techniques when applied to volatile markets such as~cryptocurrencies. ...

Is the difference between deep hedging and delta hedging a statistical arbitrage? ArXiv ID: 2407.14736 “View on arXiv” Authors: Unknown Abstract The recent work of Horikawa and Nakagawa (2024) claims that under a complete market admitting statistical arbitrage, the difference between the hedging position provided by deep hedging and that of the replicating portfolio is a statistical arbitrage. This raises concerns as it entails that deep hedging can include a speculative component aimed simply at exploiting the structure of the risk measure guiding the hedging optimisation problem. We test whether such finding remains true in a GARCH-based market model, which is an illustrative case departing from complete market dynamics. We observe that the difference between deep hedging and delta hedging is a speculative overlay if the risk measure considered does not put sufficient relative weight on adverse outcomes. Nevertheless, a suitable choice of risk measure can prevent the deep hedging agent from engaging in speculation. ...

Statistical arbitrage in multi-pair trading strategy based on graph clustering algorithms in US equities market ArXiv ID: 2406.10695 “View on arXiv” Authors: Unknown Abstract The study seeks to develop an effective strategy based on the novel framework of statistical arbitrage based on graph clustering algorithms. Amalgamation of quantitative and machine learning methods, including the Kelly criterion, and an ensemble of machine learning classifiers have been used to improve risk-adjusted returns and increase immunity to transaction costs over existing approaches. The study seeks to provide an integrated approach to optimal signal detection and risk management. As a part of this approach, innovative ways of optimizing take profit and stop loss functions for daily frequency trading strategies have been proposed and tested. All of the tested approaches outperformed appropriate benchmarks. The best combinations of the techniques and parameters demonstrated significantly better performance metrics than the relevant benchmarks. The results have been obtained under the assumption of realistic transaction costs, but are sensitive to changes in some key parameters. ...

Application of Black-Litterman Bayesian in Statistical Arbitrage ArXiv ID: 2406.06706 “View on arXiv” Authors: Unknown Abstract \begin{“abstract”} In this paper, we integrated the statistical arbitrage strategy, pairs trading, into the Black-Litterman model and constructed efficient mean-variance portfolios. Typically, pairs trading underperforms under volatile or distressed market condition because the selected asset pairs fail to revert to equilibrium within the investment horizon. By enhancing this strategy with the Black-Litterman portfolio optimization, we achieved superior performance compared to the S&P 500 market index under both normal and extreme market conditions. Furthermore, this research presents an innovative idea of incorporating traditional pairs trading strategies into the portfolio optimization framework in a scalable and systematic manner. ...

On a fundamental statistical edge principle ArXiv ID: 2404.14252 “View on arXiv” Authors: Unknown Abstract This paper establishes that conditioning the probability of execution of new orders on the self-generated historical trading information (HTI) of a trading strategy is a necessary condition for a statistical trading edge. It is shown, in particular, that, given any trading strategy S that does not use its own HTI, it is always possible to construct a new strategy S* that yields a systematically increasing improvement over S in terms of profit and loss (PnL) by using the self-generated HTI. This holds true under rather general conditions that are frequently met in practice, and it is proven through a decision mechanism specifically designed to formally prove this idea. Simulations and real-world trading evidence are included for validation and illustration, respectively. ...

Advanced Statistical Arbitrage with Reinforcement Learning ArXiv ID: 2403.12180 “View on arXiv” Authors: Unknown Abstract Statistical arbitrage is a prevalent trading strategy which takes advantage of mean reverse property of spread of paired stocks. Studies on this strategy often rely heavily on model assumption. In this study, we introduce an innovative model-free and reinforcement learning based framework for statistical arbitrage. For the construction of mean reversion spreads, we establish an empirical reversion time metric and optimize asset coefficients by minimizing this empirical mean reversion time. In the trading phase, we employ a reinforcement learning framework to identify the optimal mean reversion strategy. Diverging from traditional mean reversion strategies that primarily focus on price deviations from a long-term mean, our methodology creatively constructs the state space to encapsulate the recent trends in price movements. Additionally, the reward function is carefully tailored to reflect the unique characteristics of mean reversion trading. ...

Pairs Trading Using a Novel Graphical Matching Approach ArXiv ID: 2403.07998 “View on arXiv” Authors: Unknown Abstract Pairs trading, a strategy that capitalizes on price movements of asset pairs driven by similar factors, has gained significant popularity among traders. Common practice involves selecting highly cointegrated pairs to form a portfolio, which often leads to the inclusion of multiple pairs sharing common assets. This approach, while intuitive, inadvertently elevates portfolio variance and diminishes risk-adjusted returns by concentrating on a small number of highly cointegrated assets. Our study introduces an innovative pair selection method employing graphical matchings designed to tackle this challenge. We model all assets and their cointegration levels with a weighted graph, where edges signify pairs and their weights indicate the extent of cointegration. A portfolio of pairs is a subgraph of this graph. We construct a portfolio which is a maximum weighted matching of this graph to select pairs which have strong cointegration while simultaneously ensuring that there are no shared assets within any pair of pairs. This approach ensures each asset is included in just one pair, leading to a significantly lower variance in the matching-based portfolio compared to a baseline approach that selects pairs purely based on cointegration. Theoretical analysis and empirical testing using data from the S&P 500 between 2017 and 2023, affirm the efficacy of our method. Notably, our matching-based strategy showcases a marked improvement in risk-adjusted performance, evidenced by a gross Sharpe ratio of 1.23, a significant enhancement over the baseline value of 0.48 and market value of 0.59. Additionally, our approach demonstrates reduced trading costs attributable to lower turnover, alongside minimized single asset risk due to a more diversified asset base. ...

End-to-End Policy Learning of a Statistical Arbitrage Autoencoder Architecture ArXiv ID: 2402.08233 “View on arXiv” Authors: Unknown Abstract In Statistical Arbitrage (StatArb), classical mean reversion trading strategies typically hinge on asset-pricing or PCA based models to identify the mean of a synthetic asset. Once such a (linear) model is identified, a separate mean reversion strategy is then devised to generate a trading signal. With a view of generalising such an approach and turning it truly data-driven, we study the utility of Autoencoder architectures in StatArb. As a first approach, we employ a standard Autoencoder trained on US stock returns to derive trading strategies based on the Ornstein-Uhlenbeck (OU) process. To further enhance this model, we take a policy-learning approach and embed the Autoencoder network into a neural network representation of a space of portfolio trading policies. This integration outputs portfolio allocations directly and is end-to-end trainable by backpropagation of the risk-adjusted returns of the neural policy. Our findings demonstrate that this innovative end-to-end policy learning approach not only simplifies the strategy development process, but also yields superior gross returns over its competitors illustrating the potential of end-to-end training over classical two-stage approaches. ...

Finding Moving-Band Statistical Arbitrages via Convex-Concave Optimization ArXiv ID: 2402.08108 “View on arXiv” Authors: Unknown Abstract We propose a new method for finding statistical arbitrages that can contain more assets than just the traditional pair. We formulate the problem as seeking a portfolio with the highest volatility, subject to its price remaining in a band and a leverage limit. This optimization problem is not convex, but can be approximately solved using the convex-concave procedure, a specific sequential convex programming method. We show how the method generalizes to finding moving-band statistical arbitrages, where the price band midpoint varies over time. ...