Executing a basket of co-integrated assets is an important task facing investors. Here, we show how to do this accounting for the informational advantage gained from assets within and outside the basket, as well as for the permanent price impact of market orders (MOs) from all market participants, and the temporary impact that the agent's MOs have on prices. The execution problem is posed as an optimal stochastic control problem and we demonstrate that, under some mild conditions, the value function admits a closed-form solution, and prove a verification theorem. Furthermore, we use data of five stocks traded in the Nasdaq exchange to estimate the model parameters and use simulations to illustrate the performance of the strategy. As an example, the agent liquidates a portfolio consisting of shares in Intel Corporation (INTC) and Market Vectors Semiconductor ETF (SMH). We show that including the information provided by three additional assets, FARO Technologies (FARO), NetApp (NTAP) and Oracle Corporation (ORCL), considerably improves the strategy's performance; for the portfolio we execute, it outperforms the multi-asset version of Almgren-Chriss by approximately 4 to 4.5 basis points.
In this study, we applied a stochastic spread pairs trading strategy on the Indian commodity market. The complete set of commodities were taken whose spot price was available for the period of January 1st 2010 to December 31st 2018 including energy, metals and the agricultural commodity sector. Spot data was taken from the MCX pooled spot prices for 17 commodities. The data was split into training period (January 1st 2010 to 14th March 2017) and testing period(15th Match 2017 to 31st December 2018). The splitting was done using a 80:20 split.Johanssen Cointegration tests were done on training …
We establish connections between optimal transport theory and the dynamic version of the Kyle model, including new characterizations of informed trading profits via conjugate duality and Monge-Kantorovich duality. We use these connections to extend the model to multiple assets, general distributions, and risk-averse market makers. With risk-averse market makers, liquidity is lower, assets exhibit short-term reversals, and risk premia depend on market maker inventories, which are mean reverting. We illustrate the model by showing that implied volatilities predict stock returns when there is inf…
In recent years, the tendency of the number of financial institutions including cryptocurrencies in their portfolios has accelerated. Cryptocurrencies are the first pure digital assets to be included by asset managers. Although they have some commonalities with more traditional assets, they have their own separate nature and their behaviour as an asset is still in the process of being understood. It is therefore important to summarise existing research papers and results on cryptocurrency trading, including available trading platforms, trading signals, trading strategy research and risk manage…
Financial trading has been widely analyzed for decades with market participants and academics always looking for advanced methods to improve trading performance. Deep reinforcement learning (DRL), a recently reinvigorated method with significant success in multiple domains, still has to show its benefit in the financial markets. We use a deep Q-network (DQN) to design long-short trading strategies for futures contracts. The state space consists of volatility-normalized daily returns, with buying or selling being the reinforcement learning action and the total reward defined as the cumulative p…
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…
In this article, we provide a flexible framework for optimal trading in an asset listed on different venues. We take into account the dependencies between the imbalance and spread of the venues, and allow for partial execution of limit orders at different limits as well as market orders. We present a Bayesian update of the model parameters to take into account possibly changing market conditions and propose extensions to include short/long trading signals, market impact or hidden liquidity. To solve the stochastic control problem of the trader we apply the finite difference method and also dev…
Financial trading aims to build profitable strategies to make wise investment decisions in the financial market. It has attracted interests in the machine learning community for a long time. This paper proposes to trade financial assets automatically using feature preprocessing skills and Recurrent Reinforcement Learning (RRL) algorithm. The strategy starts from technical indicators extracted from assets' market information. Then these technical indicators are preprocessed by Principal Component Analysis (PCA) and Discrete Wavelet Transform (DWT) and eventually inputted to the RRL algorithm to…
Institute of Science and Technology Austria (ISTA)（奥地利科学技术研究所（ISTA））；TRALITY GmbH（Trality有限公司）；University of Trieste（的里雅斯特大学）
We investigate the potential of Multi-Objective, Deep Reinforcement Learning for stock and cryptocurrency single-asset trading: in particular, we consider a Multi-Objective algorithm which generalizes the reward functions and discount factor (i.e., these components are not specified a priori, but incorporated in the learning process). Firstly, using several important assets (cryptocurrency pairs BTCUSD, ETHUSDT, XRPUSDT, and stock indexes AAPL, SPY, NIFTY50), we verify the reward generalization property of the proposed Multi-Objective algorithm, and provide preliminary statistical evidence sho…
School of Engineering（工程学院）；Zurich University of Applied Sciences（苏黎世应用科技大学）
This paper presents a Double Deep Q-Network algorithm for trading single assets, namely the E-mini S&P 500 continuous futures contract. We use a proven setup as the foundation for our environment with multiple extensions. The features of our trading agent are constantly being expanded to include additional assets such as commodities, resulting in four models. We also respond to environmental conditions, including costs and crises. Our trading agent is first trained for a specific time period and tested on new data and compared with the long-and-hold strategy as a benchmark (market). We analyze…
Few assets in financial history have been as notoriously volatile as cryptocurrencies. While the long term outlook for this asset class remains unclear, we are successful in making short term price predictions for several major crypto assets. Using historical data from July 2015 to November 2019, we develop a large number of technical indicators to capture patterns in the cryptocurrency market. We then test various classification methods to forecast short-term future price movements based on these indicators. On both PPV and NPV metrics, our classifiers do well in identifying up and down marke…
We consider the general problem of a set of agents trading a portfolio of assets in the presence of transient price impact and additional quadratic transaction costs and we study, with analytical and numerical methods, the resulting Nash equilibria. Extending significantly the framework of Schied & Zhang (2019) and Luo & Schied (2020), who considered the single asset case, we prove the existence and uniqueness of the corresponding Nash equilibria for the related mean-variance optimization problem. We then focus our attention on the conditions on the model parameters making the trading profile …
Trading a financial asset pushes its price as well as the prices of other assets, a phenomenon known as cross-impact. We consider a general class of kernel-based cross-impact models and investigate suitable parameterisations for trading purposes. We focus on kernels that guarantee that prices are martingales and anticipate future order flow (martingale-admissible kernels) and those that ensure there is no possible price manipulation (no-statistical-arbitrage-admissible kernels). We determine the overlap between these two classes and provide formulas for calibration of cross-impact kernels on d…
A leveraged ETF is a fund aimed at achieving a rate of return several times greater than that of the underlying asset such as Nikkei 225 futures. Recently, it has been suggested that rebalancing trades of a leveraged ETF may destabilize the financial markets. An empirical study using an agent-based simulation indicated that a rebalancing trade strategy could affect the price formation of an underlying asset market. However, no leveraged ETF trading method for suppressing the increase in volatility as much as possible has yet been proposed. In this paper, we compare different strategies of trad…
We study optimal trading in an Almgren-Chriss model with running and terminal inventory costs and general predictive signals about price changes. As a special case, this allows to treat optimal liquidation in "target zone models": asset prices with a reflecting boundary enforced by regulatory interventions. In this case, the optimal liquidation rate is the "theta" of a lookback option, leading to explicit formulas for Bachelier or Black-Scholes dynamics.
Universidade de São Paulo（圣保罗大学）；Centro Universitário FEI（FEI大学中心）
The feasibility of making profitable trades on a single asset on stock exchanges based on patterns identification has long attracted researchers. Reinforcement Learning (RL) and Natural Language Processing have gained notoriety in these single-asset trading tasks, but only a few works have explored their combination. Moreover, some issues are still not addressed, such as extracting market sentiment momentum through the explicit capture of sentiment features that reflect the market condition over time and assessing the consistency and stability of RL results in different situations. Filling thi…
We consider an agent who needs to buy (or sell) a relatively small amount of asset over some fixed short time interval. We work at the highest frequency meaning that we wish to find the optimal tactic to execute our quantity using limit orders, market orders and cancellations. To solve the agent's control problem, we build an order book model and optimize an expected utility function based on our price impact. We derive the equations satisfied by the optimal strategy and solve them numerically. Moreover, we show that our optimal tactic enables us to outperform significantly naive execution str…
This research aims to demonstrate a dynamic cointegration-based pairs trading strategy, including an optimal look-back window framework in the cryptocurrency market, and evaluate its return and risk by applying three different scenarios. We employ the Engle-Granger methodology, the Kapetanios-Snell-Shin (KSS) test, and the Johansen test as cointegration tests in different scenarios. We calibrate the mean-reversion speed of the Ornstein-Uhlenbeck process to obtain the half-life used for the asset selection phase and look-back window estimation. By considering the main limitations in the market …
While attention is a predictor for digital asset prices, and jumps in Bitcoin prices are well-known, we know little about its alternatives. Studying high frequency crypto data gives us the unique possibility to confirm that cross market digital asset returns are driven by high frequency jumps clustered around black swan events, resembling volatility and trading volume seasonalities. Regressions show that intra-day jumps significantly influence end of day returns in size and direction. This provides fundamental research for crypto option pricing models. However, we need better econometric metho…
Trading a financial instrument pushes its price and those of other assets, a phenomenon known as cross-impact. To be of use, cross-impact models must fit data and be well-behaved so they can be applied in applications such as optimal trading. To address these issues, we introduce a set of desirable properties which constrain cross-impact models. We classify cross-impact models according to which properties they satisfy and stress them on three different asset classes to evaluate goodness-of-fit. We find that two models are robust across markets, but only one satisfies all desirable properties …
We formulate and solve a multi-player stochastic differential game between financial agents who seek to cost-efficiently liquidate their position in a risky asset in the presence of jointly aggregated transient price impact, along with taking into account a common general price predicting signal. The unique Nash-equilibrium strategies reveal how each agent's liquidation policy adjusts the predictive trading signal to the aggregated transient price impact induced by all other agents. This unfolds a quantitative relation between trading signals and the order flow in crowded markets. We also form…
