We consider the Brownian market model and the problem of expected utility maximization of terminal wealth. We, specifically, examine the problem of maximizing the utility of terminal wealth under the presence of transaction costs of a fund/agent investing in futures markets. We offer some preliminary remarks about statistical arbitrage strategies and we set the framework for futures markets, and introduce concepts such as margin, gearing and slippage. The setting is of discrete time, and the price evolution of the futures prices is modelled as discrete random sequence involving Ito's sums. We assume the drift and the Brownian motion driving the return process are non-observable and the transaction costs are represented by the bid-ask spread. We provide explicit solution to the optimal portfolio process, and we offer an example using logarithmic utility.
The paper considers trading with proportional transaction costs. We give a necessary and sufficient condition for A, the cone of claims attainable from zero endowment, to be closed, and show, in general, how to represent its closure in such a way that it is the cone of claims attainable for zero endowment, for a different set of trading prices. The new representation obeys the Fundamental Theorem of Asset Pricing. We then show how to represent claims and in a final section show how any such setup corresponds to a coherent risk measure.
Quantitative trading is an integral part of financial markets with high calculation speed requirements, while no quantum algorithms have been introduced into this field yet. We propose quantum algorithms for high-frequency statistical arbitrage trading in this work by utilizing variable time condition number estimation and quantum linear regression.The algorithm complexity has been reduced from the classical benchmark O(N^2d) to O(sqrt(d)(kappa)^2(log(1/epsilon))^2 )). It shows quantum advantage, where N is the length of trading data, and d is the number of stocks, kappa is the condition numbe…
Signature-Based Optimal Execution for Statistical Arbitrage with Path-Dependent Trading Signals
Deep Blue Capital B.V.（深蓝资本有限公司）；Informatics Institute, University of Amsterdam（阿姆斯特丹大学信息学研究所）；Korteweg-de Vries Institute for Mathematics, University of Amsterdam（阿姆斯特丹大学科特韦格-德弗里斯数学研究所）
The theory of optimal trading under proportional transaction costs has been considered from a variety of perspectives. In this paper, we show that all the results can be interpreted using a universal law, illustrating the results in trading algorithm design.
Decentralized Exchanges (DEXes) enable users to create markets for exchanging any pair of cryptocurrencies. The direct exchange rate of two tokens may not match the cross-exchange rate in the market, and such price discrepancies open up arbitrage possibilities with trading through different cryptocurrencies cyclically. In this paper, we conduct a systematic investigation on cyclic arbitrages in DEXes. We propose a theoretical framework for studying cyclic arbitrage. With our framework, we analyze the profitability conditions and optimal trading strategies of cyclic transactions. We further exa…
We prove the existence of an equilibrium in a model with transaction costs and price impact where two agents are incentivized to trade towards a target. The two types of frictions -- price impact and transaction costs -- lead the agents to two distinct changes in their optimal investment approach: price impact causes agents to continuously trade in smaller amounts, while transaction costs cause the agents to cease trading before the end of the trading period. As the agents lose wealth because of transaction costs, the exchange makes a profit. We prove the existence of a strictly positive optim…
In the present work we develop a formalism to tackle the problem of optimal execution when trading market securities. More precisely, we introduce a utility function that balances market impact and timing risk, with this last being modelled as the very negative transaction costs incurred by our order execution. The framework is built upon existing theory on optimal trading strategies, but incorporates characteristics that enable distinctive execution strategies. The formalism is complemented by an analysis of various impact models and different distributional properties of market returns.
We extend the "No-dynamic-arbitrage and market impact"-framework of Jim Gatheral [Quantitative Finance, 10(7): 749-759 (2010)] to the multi-dimensional case where trading in one asset has a cross-impact on the price of other assets. From the condition of absence of dynamical arbitrage we derive theoretical limits for the size and form of cross-impact that can be directly verified on data. For bounded decay kernels we find that cross-impact must be an odd and linear function of trading intensity and cross-impact from asset $i$ to asset $j$ must be equal to the one from $j$ to $i$. To test these…
Optimal trading strategies for pairs trading have been studied by models that try to find either optimal shares of stocks by assuming no transaction costs or optimal timing of trading fixed numbers of shares of stocks with transaction costs. To find optimal strategies which determine optimally both trade times and number of shares in pairs trading process, we use a singular stochastic control approach to study an optimal pairs trading problem with proportional transaction costs. Assuming a cointegrated relationship for a pair of stock log-prices, we consider a portfolio optimization problem wh…
We study the optimal timing strategies for trading a mean-reverting price process with afinite deadline to enter and a separate finite deadline to exit the market. The price process is modeled by a diffusion with an affine drift that encapsulates a number of well-known models,including the Ornstein-Uhlenbeck (OU) model, Cox-Ingersoll-Ross (CIR) model, Jacobi model,and inhomogeneous geometric Brownian motion (IGBM) model.We analyze three types of trading strategies: (i) the long-short (long to open, short to close) strategy; (ii) the short-long(short to open, long to close) strategy, and (iii) …
We use an adversarial expert based online learning algorithm to learn the optimal parameters required to maximise wealth trading zero-cost portfolio strategies. The learning algorithm is used to determine the relative population dynamics of technical trading strategies that can survive historical back-testing as well as form an overall aggregated portfolio trading strategy from the set of underlying trading strategies implemented on daily and intraday Johannesburg Stock Exchange data. The resulting population time-series are investigated using unsupervised learning for dimensionality reduction…
We study how transaction cost affects to the equilibrium return and optimal stock holdings in equilibrium. To this end, we develop a continuous-time risk-sharing model where heterogenous agents trade toward terminal target holdings subject to a quadratic transaction cost. The equilibrium stock holdings and trading rate under transaction cost are characterized by a unique solution to a forward-backward stochastic differential equation (FBSDE). The equilibrium return is also characterized as the unique solution of a system of coupled but linear FBSDEs.
Proportional transaction costs present difficult theoretical problems in trading algorithm design, on account of their lack of analytical tractability. The author derives a solution of DT-NT-DT form for an arbitrary model in which the the traded asset has diffusive dynamics described by one or more stochastic risk factors. The width of the NT zone is found to be, as expected, proportional to the cube root of the transaction cost. It is also proportional to the 2/3 power of the volatility of the target position, thereby causing a faster trading strategy to be buffered more than a slower one. Th…
PolySwarm: A Multi-Agent Large Language Model Framework for Prediction Market Trading and Latency Arbitrage
Department of Computer Science, State University of New York, Binghamton（纽约州立大学宾汉姆顿分校计算机科学系）；Department of Software Engineering, Arizona State University（亚利桑那州立大学软件工程系）
Motivated by how transaction amount constrain trading volume and price volatility in stock market, we, in this paper, study the relation between volume and price if amount of transaction is given. We find that accumulative trading volume gradually emerges a kurtosis near the price mean value over a trading price range when it takes a longer trading time, regardless of actual price fluctuation path, time series, or total transaction volume in the time interval. To explain the volume-price behavior, we, in terms of physics, propose a transaction energy hypothesis, derive a time-independent trans…
We model an informed agent with information about the future value of an asset trying to maximize profits when subjected to a transaction cost as well as a market maker tasked with setting fair transaction prices. In a single auction model, equilibrium is characterized by the unique root of a particular polynomial. Analysis of this polynomial with small levels of risk-aversion and transaction costs reveal a dimensionless parameter which captures several orders of asymptotic accuracy of the equilibrium behaviour. In a continuous time analogue of the single auction model, incorporation of a tran…
The possibility of latency arbitrage in financial markets has led to the deployment of high-speed communication links between distant financial centers. These links are noisy and so there is a need for coding. In this paper, we develop a gametheoretic model of trading behavior where two traders compete to capture latency arbitrage opportunities using binary signalling. Different coding schemes are strategies that trade off between reliability and latency. When one trader has a better channel, the second trader should not compete. With statistically identical channels, we find there are two dif…
We introduce a microscopic model which describes the dynamics of each dealer in multiple foreign exchange markets, taking account of the triangular arbitrage transaction. The model reproduces the interaction among the markets well. We explore the relation between the parameters of the present microscopic model and the spring constant of a macroscopic model that we proposed previously.
Motivated by the industry practice of pairs trading, we study the optimal timing strategies for trading a mean-reverting price spread. An optimal double stopping problem is formulated to analyze the timing to start and subsequently liquidate the position subject to transaction costs. Modeling the price spread by an Ornstein-Uhlenbeck process, we apply a probabilistic methodology and rigorously derive the optimal price intervals for market entry and exit. As an extension, we incorporate a stop-loss constraint to limit the maximum loss. We show that the entry region is characterized by a bounded…
In recent years, a wide range of investment models have been created using artificial intelligence. Automatic trading by artificial intelligence can expand the range of trading methods, such as by conferring the ability to operate 24 hours a day and the ability to trade with high frequency. Automatic trading can also be expected to trade with more information than is available to humans if it can sufficiently consider past data. In this paper, we propose an investment agent based on a deep reinforcement learning model, which is an artificial intelligence model. The model considers the transact…
This paper studies the timing of trades under mean-reverting price dynamics subject to fixed transaction costs. We solve an optimal double stopping problem to determine the optimal times to enter and subsequently exit the market, when prices are driven by an exponential Ornstein-Uhlenbeck process. In addition, we analyze a related optimal switching problem that involves an infinite sequence of trades, and identify the conditions under which the double stopping and switching problems admit the same optimal entry and/or exit timing strategies. Among our results, we find that the investor general…
In this paper we examine inefficiencies and information disparity in the Japanese stock market. By carefully analysing information publicly available on the internet, an `outsider' to conventional statistical arbitrage strategies--which are based on market microstructure, company releases, or analyst reports--can nevertheless pursue a profitable trading strategy. A large volume of blog data is used to demonstrate the existence of an inefficiency in the market. An information-based model that replicates the trading strategy is developed to estimate the degree of information disparity.
We empirically study the trading activity in the electronic on-book segment and in the dealership off-book segment of the London Stock Exchange, investigating separately the trading of active market members and of other market participants which are non-members. We find that (i) the volume distribution of off-book transactions has a significantly fatter tail than the one of on-book transactions, (ii) groups of members and non-members can be classified in categories according to their trading profile (iii) there is a strong anticorrelation between the daily inventory variation of a market membe…
The market impact (MI) of Volume Weighted Average Price (VWAP) orders is a convex function of a trading rate, but most empirical estimates of transaction cost are concave functions. How is this possible? We show that isochronic (constant trading time) MI is slightly convex, and isochoric (constant trading volume) MI is concave. We suggest a model that fits all trading regimes and guarantees no-dynamic-arbitrage.
Machine Learning-Based Bitcoin Trading Under Transaction Costs: Evidence From Walk-Forward Forecasting
Quantitative Finance Research Group, Faculty of Economic Sciences, University of Warsaw（经济科学学院量化金融研究组，华沙大学）；Quantitative Finance Research Group, Department of Quantitative Finance and Machine Learning, Faculty of Economic Sciences, University of Warsaw（经济科学学院量化金融与机器学习系量化金融研究组，华沙大学）
We consider a Nash equilibrium between two high-frequency traders in a simple market impact model with transient price impact and additional quadratic transaction costs. Extending a result by Schöneborn (2008), we prove existence and uniqueness of the Nash equilibrium and show that for small transaction costs the high-frequency traders engage in a "hot-potato game", in which the same asset position is sold back and forth. We then identify a critical value for the size of the transaction costs above which all oscillations disappear and strategies become buy-only or sell-only. Numerical simulati…
The asymmetric price impact between the institutional purchases and sales of 32 liquid stocks in Chinese stock markets in year 2003 is carefully studied. We analyze the price impact in both drawup and drawdown trends with consecutive positive and negative daily price changes, and test the dependence of the price impact asymmetry on the market condition. For most of the stocks institutional sales have a larger price impact than institutional purchases, and larger impact of institutional purchases only exists in few stocks with primarily increasing tendencies. We further study the mean return of…
The algorithmic trading comes from digitalisation of the processing of trading assets on financial markets. Since 1980 the computerization of the stock market offers real time processing of financial information. This technological revolution has offered processes and mathematic methods to identify best return on transactions. Current research relates to autonomous transaction systems programmed in certain periods and some algorithms. This offers return opportunities where traders can not intervene. There are about thirty algorithms to assist the traders, the best known are the VWAP, the TWAP,…
This paper conducts an empirically study on the trade package composed of a sequence of consecutive purchases or sales of 23 stocks in Chinese stock market. We investigate the probability distributions of the execution time, the number of trades and the total trading volume of trade packages, and analyze the possible scaling relations between them. Quantitative differences are observed between the institutional and individual investors. The trading profile of trade packages is investigated to reveal the preference of large trades on trading volumes and transaction time of the day, and the diff…
We model the impact costs of a strategy that trades a basket of correlated instruments, by extending to the multivariate case the linear propagator model previously used for single instruments. Our specification allows us to calibrate a cost model that is free of arbitrage and price manipulation. We illustrate our results using a pool of US stocks and show that neglecting cross-impact effects leads to an incorrect estimation of the liquidity and suboptimal execution strategies. We show in particular the importance of synchronizing the execution of correlated contracts.
Domain-adapted Learning and Imitation: DRL for Power Arbitrage
University College London（伦敦大学学院）；Shell Global Solutions International（壳牌全球解决方案国际公司）；Shell Shared Service Center Chennai（壳牌金奈共享服务中心）；Shell Energy North America（壳牌能源北美公司）
Attempts to accurately measure the monetary velocity or related properties of bitcoin used in transactions have often attempted to either directly apply definitions from traditional macroeconomic theory or to use specialized metrics relative to the properties of the Blockchain like bitcoin days destroyed. In this paper, it is demonstrated that beyond being a useful metric, bitcoin days destroyed has mathematical properties that allow you to calculate the average dormancy (time since last use in a transaction) of the bitcoins used in transactions over a given time period. In addition, bitcoin d…
If financial markets displayed the informational efficiency postulated in the efficient markets hypothesis (EMH), arbitrage operations would be self-extinguishing. The present paper considers arbitrage sequences in foreign exchange (FX) markets, in which trading platforms and information are fragmented. In Kozyakin et al. (2010) and Cross et al. (2012) it was shown that sequences of triangular arbitrage operations in FX markets containing 4 currencies and trader-arbitrageurs tend to display periodicity or grow exponentially rather than being self-extinguishing. This paper extends the analysis …
Generalized statistical arbitrage concepts are introduced corresponding to trading strategies which yield positive gains on average in a class of scenarios rather than almost surely. The relevant scenarios or market states are specified via an information system given by a $σ$-algebra and so this notion contains classical arbitrage as a special case. It also covers the notion of statistical arbitrage introduced in Bondarenko (2003). Relaxing these notions further we introduce generalized profitable strategies which include also static or semi-static strategies. Under standard no-arbitrage ther…
We present the use of the fitted Q iteration in algorithmic trading. We show that the fitted Q iteration helps alleviate the dimension problem that the basic Q-learning algorithm faces in application to trading. Furthermore, we introduce a procedure including model fitting and data simulation to enrich training data as the lack of data is often a problem in realistic application. We experiment our method on both simulated environment that permits arbitrage opportunity and real-world environment by using prices of 450 stocks. In the former environment, the method performs well, implying that ou…
