We introduce a prototype model in an attempt to capture some aspects of market dynamics simulating a trading mechanism. The model description starts with a discrete-space, continuous-time Markov process describing arrival and movement of orders with different prices. We then perform a re-scaling procedure leading to a deterministic dynamical system controlled by non-linear ordinary differential equations (ODEs). This allows us to introduce approximations for the equilibrium distribution of the model represented by fixed points of deterministic dynamics.
We analyze the relation between earning forecast accuracy and expected profitability of financial analysts. Modeling forecast errors with a multivariate Gaussian distribution, a complete characterization of the payoff of each analyst is provided. In particular, closed-form expressions for the probability density function, for the expectation, and, more generally, for moments of all orders are obtained. Our analysis shows that the relationship between forecast precision and trading profitability need not to be monotonic, and that, for any analyst, the impact on his expected payoff of the correl…
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…
Online financial markets can be represented as complex systems where trading dynamics can be captured and characterized at different resolutions and time scales. In this work, we develop a methodology based on non-negative tensor factorization (NTF) aimed at extracting and revealing the multi-timescale trading dynamics governing online financial systems. We demonstrate the advantage of our strategy first using synthetic data, and then on real-world data capturing all interbank transactions (over a million) occurred in an Italian online financial market (e-MID) between 2001 and 2015. Our result…
We empirically study the market impact of trading orders. We are specifically interested in large trading orders that are executed incrementally, which we call hidden orders. These are reconstructed based on information about market member codes using data from the Spanish Stock Market and the London Stock Exchange. We find that market impact is strongly concave, approximately increasing as the square root of order size. Furthermore, as a given order is executed, the impact grows in time according to a power-law; after the order is finished, it reverts to a level of about 0.5-0.7 of its value …
This work's purpose is to understand the dynamics of limit order books in order-driven markets. We try to illustrate a dynamical trading mechanism attached to the microstructure of limit order markets. We capture the iterative nature of trading processes, which is critical in the dynamics of bid-ask pairs and the switching laws between different traders' types and their orders. In general, after introducing the atomic trading scheme, we study a general iterated trading process in both combinatorial and stochastic ways, and state a few results on the stability of a dynamical trading system. We …
Prospect theory is widely viewed as the best available descriptive model of how people evaluate risk in experimental settings. According to prospect theory, people are risk-averse with respect to gains and risk-seeking with respect to losses, a phenomenon called "loss aversion". Despite of the fact that prospect theory has been well developed in behavioral economics at the theoretical level, there exist very few large-scale empirical studies and most of them have been undertaken with micro-panel data. Here we analyze over 28.5 million trades made by 81.3 thousand traders of an online financial…
We consider trading against a hedge fund or large trader that must liquidate a large position in a risky asset if the market price of the asset crosses a certain threshold. Liquidation occurs in a disorderly manner and negatively impacts the market price of the asset. We consider the perspective of small investors whose trades do not induce market impact and who possess different levels of information about the liquidation trigger mechanism and the market impact. We classify these market participants into three types: fully informed, partially informed and uninformed investors. We consider the…
We implement a market microstructure model including informed, uninformed and heuristic-driven investors, which latter behave in line with loss-aversion and mental accounting. We show that the probability of informed trading (PIN) varies significantly during 2008. In contrast, the probability of heuristic-driven trading (PH) remains constant both before and after the collapse of Lehman Brothers. Cross-sectional analysis yields that, unlike PIN, PH is not sensitive to size and volume effects. We show that heuristic-driven traders are universally present in all market segments and their presence…
We use statistically validated networks, a recently introduced method to validate links in a bipartite system, to identify clusters of investors trading in a financial market. Specifically, we investigate a special database allowing to track the trading activity of individual investors of the stock Nokia. We find that many statistically detected clusters of investors show a very high degree of synchronization in the time when they decide to trade and in the trading action taken. We investigate the composition of these clusters and we find that several of them show an over-expression of specifi…
The imbalance of buying and selling functions profoundly in the formation of market trends, however, a fine-granularity investigation of the imbalance is still missing. This paper investigates a unique transaction dataset that enables us to inspect the imbalance of buying and selling on the man-times level at high frequency, what we call 'trading polarity', for a large cross-section of stocks from Shenzhen Stock Exchange. The trading polarity measures the market sentiment toward stocks from a view of very essence of trading desire. When using the polarity to examine market crash, we find that …
A dynamic herding model with interactions of trading volumes is introduced. At time $t$, an agent trades with a probability, which depends on the ratio of the total trading volume at time $t-1$ to its own trading volume at its last trade. The price return is determined by the volume imbalance and number of trades. The model successfully reproduces the power-law distributions of the trading volume, number of trades and price return, and their relations. Moreover, the generated time series are long-range correlated. We demonstrate that the results are rather robust, and do not depend on the part…
Automated trading systems on developed and emerging capital markets are studied in this paper. The standard for developed market is automated trading system with 40-days simple moving average. We tested it for the index SIX Industrial for 1000 and 730 trading days of the slovak emerging capital market. The Buy and Hold trading system was 7.80 times more profitable than this etalon trading system for active trading. Taking of profitable standard trading system from a developed capital market does not lead to optimal results on the emerging capital markets. We then studied optimized standard tra…
This article comes up with an intraday trading strategy under T+1 using Markowitz optimization and Multilayer Perceptron (MLP) with published stock data obtained from the Shenzhen Stock Exchange and Shanghai Stock Exchange. The empirical results reveal the profitability of Markowitz portfolio optimization and validate the intraday stock price prediction using MLP. The findings further combine the Markowitz optimization, an MLP with the trading strategy, to clarify this strategy's feasibility.
We develop a single-period model for a large economic agent who trades with market makers at their utility indifference prices. A key role is played by a pair of conjugate saddle functions associated with the description of Pareto optimal allocations in terms of the utility function of a representative market maker.
This research analyses high-frequency data of the cryptocurrency market in regards to intraday trading patterns related to algorithmic trading and its impact on the European cryptocurrency market. We study trading quantitatives such as returns, traded volumes, volatility periodicity, and provide summary statistics of return correlations to CRIX (CRyptocurrency IndeX), as well as respective overall high-frequency based market statistics with respect to temporal aspects. Our results provide mandatory insight into a market, where the grand scale employment of automated trading algorithms and the …
We use standard physics techniques to model trading and price formation in a market under the assumption that order arrival and cancellations are Poisson random processes. This model makes testable predictions for the most basic properties of a market, such as the diffusion rate of prices, which is the standard measure of financial risk, and the spread and price impact functions, which are the main determinants of transaction cost. Guided by dimensional analysis, simulation, and mean field theory, we find scaling relations in terms of order flow rates. We show that even under completely random…
Using a data set which includes all transactions among banks in the Italian money market, we study their trading strategies and the dependence among them. We use the Fourier method to compute the variance-covariance matrix of trading strategies. Our results indicate that well defined patterns arise. Two main communities of banks, which can be coarsely identified as small and large banks, emerge.
In modern society, the trading methods and strategies used in financial market have gradually changed from traditional on-site trading to electronic remote trading, and even online automatic trading performed by a pre-programmed computer programs because the continuous development of network and computer computing technology. The quantitative trading, which the main purpose is to automatically formulate people's investment decisions into a fixed and quantifiable operation logic that eliminates all emotional interference and the influence of subjective thoughts and applies this logic to financi…
In this article, the long-term behavior of the stock market index of the New York Stock Exchange is studied, for the period 1950 to 2013. Specifically, the CRSP Value-Weighted and CRSP Equal-Weighted index are analyzed in terms of market efficiency, using the standard ratio variance test, considering over 1600 one week rolling windows. For the equally weighted index, the null hypothesis of random walk is rejected in the whole period, while for the weighted market value index, the null hypothesis start to be accepted from the 1990s. In order to explain this difference, we raised the hypothesis …
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…
We develop a fundamentally different stochastic dynamic programming model of trading costs. Built on a strong theoretical foundation, our model provides insights to market participants by splitting the overall move of the security price during the duration of an order into the Market Impact (price move caused by their actions) and Market Timing (price move caused by everyone else) components. We derive formulations of this model under different laws of motion of the security prices, starting with a simple benchmark scenario and extending this to include multiple sources of uncertainty, liquidi…
In this paper, we employ the Heston stochastic volatility model to describe the stock's volatility and apply the model to derive and analyze the optimal trading strategies for dealers in a security market. We also extend our study to option market making for options written on stocks in the presence of stochastic volatility. Mathematically, the problem is formulated as a stochastic optimal control problem and the controlled state process is the dealer's mark-to-market wealth. Dealers in the security market can optimally determine their ask and bid quotes on the underlying stocks or options con…
The purpose of this paper is to showcase trading strategies that give solutions to three difficult and intriguing problems in business finance, economics and statistics. The paper discusses trading strategies for both commodities and stocks but the main focus is on stock market trading at the New York Stock Exchange. Problem 1: Buy Low and Sell High. The buy low and sell high problem can be summarized like this: suppose the price of a commodity or stock fluctuates indefinitely, is there any explicit strategy for a trader to "ride the price waves" by buying low and selling high to eventually wi…
FLAG-Trader: Fusion LLM-Agent with Gradient-based Reinforcement Learning for Financial Trading
Harvard University（哈佛大学）；Stevens Institute of Technology（史蒂文斯理工学院）；Columbia University（哥伦比亚大学）；University of Minnesota（明尼苏达大学）；NVIDIA（英伟达公司）；Rensselaer Polytechnic Institute（伦斯勒理工学院）；TheFinAI；University of Manchester（曼彻斯特大学）
We consider the problem of optimal trading for a power producer in the context of intraday electricity markets. The aim is to minimize the imbalance cost induced by the random residual demand in electricity, i.e. the consumption from the clients minus the production from renewable energy. For a simple linear price impact model and a quadratic criterion, we explicitly obtain approximate optimal strategies in the intraday market and thermal power generation, and exhibit some remarkable properties of the trading rate. Furthermore, we study the case when there are jumps on the demand forecast and …
Nearly one-half of all trades in financial markets are executed by high-speed, autonomous computer programs -- a type of trading often called high-frequency trading (HFT). Although evidence suggests that HFT increases the efficiency of markets, it is unclear how or why it produces this outcome. Here we create a simple model to study the impact of HFT on investors who trade similar securities in different markets. We show that HFT can improve liquidity by allowing more transactions to take place without adversely affecting pricing or volatility. In the model, HFT synchronizes the prices of the …
We study the relation between the trading behavior of agents and volatility in toy markets of adaptive inductively rational agents. We show that excess volatility, in such simplified markets, arises as a consequence of {\em i)} the neglect of market impact implicit in price taking behavior and of {\em ii)} excessive reactivity of agents. These issues are dealt with in detail in the simple case without public information. We also derive, for the general case, the critical learning rate above which trading behavior leads to turbulent dynamics of the market.
Exchanges implement intentional trade delays to limit the harmful impact of low-latency trading. Do such "speed bumps" curb investment in fast trading technology? Data is scarce since trading technologies are proprietary. We build an experimental trading platform where participants face speed bumps and can invest in fast trading technology. We find that asymmetric speed bumps, on average, reduce investment in speed by only 20%. Increasing the magnitude of the speed bump by one standard deviation further reduces low-latency investment by 8.33%. Finally, introducing a symmetric speed bump leads …
This paper investigates the equilibrium interactions between trading targets and private information in a multi-period Kyle (1985) market. There are two investors who each follow dynamic trading strategies: A strategic portfolio rebalancer who engages in order splitting to reach a cumulative trading target and an unconstrained strategic insider who trades on long-lived information. We consider cases in which the constrained rebalancer is partially informed as well as the special case in which the rebalancer is ex ante uninformed. We derive a linear Bayesian Nash equilibrium, describe an algori…
Trading Electrons: Predicting DART Spread Spikes in ISO Electricity Markets
CEREMADE, Université Paris Dauphine & PSL Research University（巴黎第九大学与PSL研究大学）；Department of Operations Research & Financial Engineering, Princeton University（普林斯顿大学运筹学与金融工程系）
A great deal of academic and theoretical work has been dedicated to optimal liquidation of large orders these last twenty years. The optimal split of an order through time (`optimal trade scheduling') and space (`smart order routing') is of high interest \rred{to} practitioners because of the increasing complexity of the market micro structure because of the evolution recently of regulations and liquidity worldwide. This paper translates into quantitative terms these regulatory issues and, more broadly, current market design. It relates the recent advances in optimal trading, order-book simula…
In this paper we extend the analysis of an agent-based model for adaptive trading, called asynchronous stochastic price pump (ASPP) introduced by Perepelitsa and Timofeyev (2019), to the model with heterogeneous distribution of psychological parameters of speculative optimism and pessimism across the population of traders. We show that the new model has a range of qualitatively different dynamics when the correlation between those factors ranges from low negative to large positive values. A statistical parameter estimation suggests a heterogeneous ASPP with negative correlation as a model of p…
With the development of artificial intelligence,more and more financial practitioners apply deep reinforcement learning to financial trading strategies.However,It is difficult to extract accurate features due to the characteristics of considerable noise,highly non-stationary,and non-linearity of single-scale time series,which makes it hard to obtain high returns.In this paper,we extract a multi-scale feature matrix on multiple time scales of financial time series,according to the classic financial theory-Chan Theory,and put forward to an approach of multi-scale stroke deep deterministic policy…
The dynamics of a stock market with heterogeneous agents is discussed in the framework of a recently proposed spin model for the emergence of bubbles and crashes. We relate the log returns of stock prices to magnetization in the model and find that it is closely related to trading volume as observed in real markets. The cumulative distribution of log returns exhibits scaling with exponents steeper than 2 and scaling is observed in the distribution of transition times between bull and bear markets.
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 show that filling an order with a large number of distinct counterparts incurs additional market impact, as opposed to filling the order with a small number of counterparts. For best execution, therefore, it may be beneficial to opportunistically fill orders with as few counterparts as possible in Large-in-scale (LIS) venues. This article introduces the concept of concentrated trading, a situation that occurs when a large fraction of buying or selling in a given time period is done by one or a few traders, for example when executing a large order. Using London Stock Exchange data, we show t…
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…
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.
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.
We study price formation in intraday electricity markets in the presence of intermittent renewable generation. We consider the setting where a major producer may interact strategically with a large number of small producers. Using stochastic control theory we identify the optimal strategies of agents with market impact and exhibit the Nash equilibrium in closed form in the asymptotic framework of mean field games with a major player. This is a companion paper to [Féron, Tankov, and Tinsi, Price formation and optimal trading in intraday electricity markets, arXiv:2009.04786, 2020], where a simi…
An automatic program that generates constant profit from the financial market is lucrative for every market practitioner. Recent advance in deep reinforcement learning provides a framework toward end-to-end training of such trading agent. In this paper, we propose an Markov Decision Process (MDP) model suitable for the financial trading task and solve it with the state-of-the-art deep recurrent Q-network (DRQN) algorithm. We propose several modifications to the existing learning algorithm to make it more suitable under the financial trading setting, namely 1. We employ a substantially small re…
High-speed computerized trading, often called "high-frequency trading" (HFT), has increased dramatically in financial markets over the last decade. In the US and Europe, it now accounts for nearly one-half of all trades. Although evidence suggests that HFT contributes to the efficiency of markets, there are concerns it also adds to market instability, especially during times of stress. Currently, it is unclear how or why HFT produces these outcomes. In this paper, I use data from NASDAQ to show that HFT synchronizes prices in financial markets, making the values of related securities change co…
We study the problem of optimal trading using general alpha predictors with linear costs and temporary impact. We do this within the framework of stochastic optimization with finite horizon using both limit and market orders. Consistently with other studies, we find that the presence of linear costs induces a no-trading zone when using market orders, and a corresponding market-making zone when using limit orders. We show that, when combining both market and limit orders, the problem is further divided into zones in which we trade more aggressively using market orders. Even though we do not sol…
Informed traders need to trade fast in order to profit from their private information before it becomes public. Fast electronic markets provide such liquidity. Slow markets provide execution in an auction based trading floor. Hybrid markets combine both execution venues. In its main result, the paper shows that to compensate for their slow and risky executions, trading floors need to be at least twice as deep as the sweeping facility. Furthermore, when a stand-alone trading floor is enhanced with the addition of a sweeping facility, overall informed trading will decline because it is easier fo…
University College London（伦敦大学学院）；University of Manchester（曼彻斯特大学）
Systematic financial trading strategies account for over 80% of trade volume in equities and a large chunk of the foreign exchange market. In spite of the availability of data from multiple markets, current approaches in trading rely mainly on learning trading strategies per individual market. In this paper, we take a step towards developing fully end-to-end global trading strategies that leverage systematic trends to produce superior market-specific trading strategies. We introduce QuantNet: an architecture that learns market-agnostic trends and use these to learn superior market-specific tra…
We show how a multi-agent simulator can support two important but distinct methods for assessing a trading strategy: Market Replay and Interactive Agent-Based Simulation (IABS). Our solution is important because each method offers strengths and weaknesses that expose or conceal flaws in the subject strategy. A key weakness of Market Replay is that the simulated market does not substantially adapt to or respond to the presence of the experimental strategy. IABS methods provide an artificial market for the experimental strategy using a population of background trading agents. Because the backgro…
Market manipulation is a strategy used by traders to alter the price of financial securities. One type of manipulation is based on the process of buying or selling assets by using several trading strategies, among them spoofing is a popular strategy and is considered illegal by market regulators. Some promising tools have been developed to detect manipulation, but cases can still be found in the markets. In this paper we model spoofing and pinging trading, two strategies that differ in the legal background but share the same elemental concept of market manipulation. We use a reinforcement lear…
We present a new model for prediction markets, in which we use risk measures to model agents and introduce a market maker to describe the trading process. This specific choice on modelling tools brings us mathematical convenience. The analysis shows that the whole market effectively approaches a global objective, despite that the market is designed such that each agent only cares about its own goal. Additionally, the market dynamics provides a sensible algorithm for optimising the global objective. An intimate connection between machine learning and our markets is thus established, such that w…
In financial markets, abnormal trading behaviors pose a serious challenge to market surveillance and risk management. What is worse, there is an increasing emergence of abnormal trading events that some experienced traders constitute a collusive clique and collaborate to manipulate some instruments, thus mislead other investors by applying similar trading behaviors for maximizing their personal benefits. In this paper, a method is proposed to detect the hidden collusive cliques involved in an instrument of future markets by first calculating the correlation coefficient between any two eligible…
The continuous-time version of Kyle's (1985) model is studied, in which market makers are not fiduciaries. They have some market power which they utilize to set the price to their advantage, resulting in positive expected profits. This has several implications for the equilibrium, the most important being that by setting a modest fee conditional of the order flow, the market maker is able to obtain a profit of the order of magnitude, and even better than, a perfectly informed insider. Our model also indicates why speculative prices are more volatile than predicted by fundamentals.
