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arXiv2019

From Disequilibrium Markets to Equilibrium

The modeling of financial markets as disequilibrium models by ordinary differential equations has become a popular modeling tool. One famous example of such a model is the Beja-Goldman model(The Journal of Finance, 1980) which we consider in this paper. We study the passage from disequilibrium dynamics to equilibrium. Mathematically, this limit corresponds to an asymptotic limit also known as a Tikhonov-Fenichel reduction. Furthermore, we analyze the stability of the reduced equilibrium model and discuss the economic implications. We conduct several numerical examples to visualize and support our analysis.

econ.GN↗
arXiv2019

Design of High-Frequency Trading Algorithm Based on Machine Learning

Based on iterative optimization and activation function in deep learning, we proposed a new analytical framework of high-frequency trading information, that reduced structural loss in the assembly of Volume-synchronized probability of Informed Trading ($VPIN$), Generalized Autoregressive Conditional Heteroscedasticity (GARCH) and Support Vector Machine (SVM) to make full use of the order book information. Amongst the return acquisition procedure in market-making transactions, uncovering the relationship between discrete dimensional data from the projection of high-dimensional time-series would significantly improve the model effect. $VPIN$ would prejudge market liquidity, and this effectiveness backtested with CSI300 futures return.

q-fin.TR↗
arXiv2020

Conditional Correlations and Principal Regression Analysis for Futures

We explore the effect of past market movements on the instantaneous correlations between assets within the futures market. Quantifying this effect is of interest to estimate and manage the risk associated to portfolios of futures in a non-stationary context. We apply and extend a previously reported method called the Principal Regression Analysis (PRA) to a universe of $84$ futures contracts between $2009$ and $2019$. We show that the past up (resp. down) 10 day trends of a novel predictor -- the eigen-factor -- tend to reduce (resp. increase) instantaneous correlations. We then carry out a multifactor PRA on sectorial predictors corresponding to the four futures sectors (indexes, commodities, bonds and currencies), and show that the effect of past market movements on the future variations of the instantaneous correlations can be decomposed into two significant components. The first component is due to the market movements within the index sector, while the second component is due to the market movements within the bonds sector.

q-fin.ST↗
arXiv2019

An FBSDE approach to market impact games with stochastic parameters

We analyze a market impact game between $n$ risk averse agents who compete for liquidity in a market impact model with permanent price impact and additional slippage. Most market parameters, including volatility and drift, are allowed to vary stochastically. Our first main result characterizes the Nash equilibrium in terms of a fully coupled system of forward-backward stochastic differential equations (FBSDEs). Our second main result provides conditions under which this system of FBSDEs has indeed a unique solution, which in turn yields the unique Nash equilibrium. We furthermore obtain closed-form solutions in special situations and analyze them numerically

q-fin.TR↗
arXiv2019

Fairness in Multi-agent Reinforcement Learning for Stock Trading

Unfair stock trading strategies have been shown to be one of the most negative perceptions that customers can have concerning trading and may result in long-term losses for a company. Investment banks usually place trading orders for multiple clients with the same target assets but different order sizes and diverse requirements such as time frame and risk aversion level, thereby total earning and individual earning cannot be optimized at the same time. Orders executed earlier would affect the market price level, so late execution usually means additional implementation cost. In this paper, we propose a novel scheme that utilizes multi-agent reinforcement learning systems to derive stock trading strategies for all clients which keep a balance between revenue and fairness. First, we demonstrate that Reinforcement learning (RL) is able to learn from experience and adapt the trading strategies to the complex market environment. Secondly, we show that the Multi-agent RL system allows developing trading strategies for all clients individually, thus optimizing individual revenue. Thirdly, we use the Generalized Gini Index (GGI) aggregation function to control the fairness level of the revenue across all clients. Lastly, we empirically demonstrate the superiority of the novel scheme in improving fairness meanwhile maintaining optimization of revenue.

q-fin.TR↗
arXiv2020

A simple microstructural explanation of the concavity of price impact

This article provides a simple explanation of the asymptotic concavity of the price impact of a meta-order via the microstructural properties of the market. This explanation is made more precise by a model in which the local relationship between the order flow and the fundamental price (i.e. the local price impact) is linear, with a constant slope, which makes the model dynamically consistent. Nevertheless, the expected impact on midprice from a large sequence of co-directional trades is nonlinear and asymptotically concave. The main practical conclusion of the proposed explanation is that, throughout a meta-order, the volumes at the best bid and ask prices change (on average) in favor of the executor. This conclusion, in turn, relies on two more concrete predictions, one of which can be tested, at least for large-tick stocks, using publicly available market data.

q-fin.TR↗
arXiv2020

Zooming In on Equity Factor Crowding

Crowding is most likely an important factor in the deterioration of strategy performance, the increase of trading costs and the development of systemic risk. We study the imprints of \emph{crowding} on both anonymous market data and a large database of metaorders from institutional investors in the U.S. equity market. We propose direct metrics of crowding that capture the presence of investors contemporaneously trading the same stock in the same direction by looking at fluctuations of the imbalances of trades executed on the market. We identify significant signs of crowding in well known equity signals, such as Fama-French factors and especially Momentum. We show that the rebalancing of a Momentum portfolio can explain between 1-2\% of order flow, and that this percentage has been significantly increasing in recent years.

q-fin.TR↗
arXiv2020

Corporate Governance, Noise Trading and Liquidity of Stocks

Our main task is to study the effect of corporate governance on the market liquidity of listed companies' stocks. We establish a theoretical model that contains the heterogeneity of investors' beliefs to explain the mechanisms by which corporate governance improves liquidity of the corporate stocks. In this process we found that the existence of noise traders who are semi-informed in the market is an important condition for corporate governance to have the effect of improving liquidity of the stocks. We further find that the strength of this effect is affected by the degree of noise traders' participation in market transactions. Our model reveals that corporate governance and the degree of noise traders' participation in transactions have a synergistic effect on improving the liquidity of the stocks.

q-fin.TR↗
arXiv2020

Trading on the Floor after Sweeping the Book

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 for informed traders to extract the full value of their private info.

q-fin.TR↗
arXiv2020

Optimal liquidation trajectories for the Almgren-Chriss model with Levy processes

We consider an optimal liquidation problem with infinite horizon in the Almgren-Chriss framework, where the unaffected asset price follows a Levy process. The temporary price impact is described by a general function which satisfies some reasonable conditions. We consider an investor with constant absolute risk aversion, who wants to maximise the expected utility of the cash received from the sale of his assets, and show that this problem can be reduced to a deterministic optimisation problem which we are able to solve explicitly. In order to compare our results with exponential Levy models, which provides a very good statistical fit with observed asset price data for short time horizons, we derive the (linear) Levy process approximation of such models. In particular we derive expressions for the Levy process approximation of the exponential Variance-Gamma Levy process, and study properties of the corresponding optimal liquidation strategy. We then provide a comparison of the liquidation trajectories for reasonable parameters between the Levy process model and the classical Almgren-Chriss model. In particular, we obtain an explicit expression for the connection between the temporary impact function for the Levy model and the temporary impact function for the Brownian motion model (the classical Almgren-Chriss model), for which the optimal liquidation trajectories for the two models coincide.

q-fin.TR↗
arXiv2020

Optimal liquidation for a risk averse investor in a one-sided limit order book driven by a Levy process

In a one-sided limit order book, satisfying some realistic assumptions, where the unaffected price process follows a Levy process, we consider a market agent that wants to liquidate a large position of shares. We assume that the agent has constant absolute risk aversion and aims at maximising the expected utility of the cash position at the end of time. The agent is then faced with the problem of balancing the market risk and the cost of a rapid execution. In particular we are interested in how the agent should go about optimally submitting orders. Since liquidation normally takes place within a short period of time, modelling the risk as a Levy process should provide a realistic model with good statistical fit to observed market data, and thus the model should provide a realistic reflection of the agent's market risk. We reduce the optimisation problem to a deterministic two-dimensional singular problem, to which we are able to derive an explicit solution in terms of the model data. In particular we find an expression for the optimal intervention boundary, which completely characterise the optimal liquidation strategy.

q-fin.TR↗
arXiv2020

Price impact equilibrium with transaction costs and TWAP trading

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 optimal transaction cost from the exchange's perspective.

q-fin.MF↗
arXiv2022

Optimal Signal-Adaptive Trading with Temporary and Transient Price Impact

We study optimal liquidation in the presence of linear temporary and transient price impact along with taking into account a general price predicting finite-variation signal. We formulate this problem as minimization of a cost-risk functional over a class of absolutely continuous and signal-adaptive strategies. The stochastic control problem is solved by following a probabilistic and convex analytic approach. We show that the optimal trading strategy is given by a system of four coupled forward-backward SDEs, which can be solved explicitly. Our results reveal how the induced transient price distortion provides together with the predictive signal an additional predictor about future price changes. As a consequence, the optimal signal-adaptive trading rate trades off exploiting the predictive signal against incurring the transient displacement of the execution price from its unaffected level. This answers an open question from Lehalle and Neuman [29] as we show how to derive the unique optimal signal-adaptive liquidation strategy when price impact is not only temporary but also transient.

q-fin.TR↗
arXiv2020

Novel Insights in the Levy-Levy-Solomon Agent-Based Economic Market Model

The Levy-Levy-Solomon model (A microscopic model of the stock market: cycles, booms, and crashes, Economic Letters 45 (1))is one of the most influential agent-based economic market models. In several publications this model has been discussed and analyzed. Especially Lux and Zschischang (Some new results on the Levy, Levy and Solomon microscopic stock market model, Physica A, 291(1-4)) have shown that the model exhibits finite-size effects. In this study we extend existing work in several directions. First, we show simulations which reveal finite-size effects of the model. Secondly, we shed light on the origin of these finite-size effects. Furthermore, we demonstrate the sensitivity of the Levy-Levy-Solomon model with respect to random numbers. Especially, we can conclude that a low-quality pseudo random number generator has a huge impact on the simulation results. Finally, we study the impact of the stopping criteria in the market clearance mechanism of the Levy-Levy-Solomon model.

q-fin.TR↗
arXiv2020

SHIFT: A Highly Realistic Financial Market Simulation Platform

This paper presents a new financial market simulator that may be used as a tool in both industry and academia for research in market microstructure. It allows multiple automated traders and/or researchers to simultaneously connect to an exchange-like environment, where they are able to asynchronously trade several financial assets at the same time. In its current iteration, this order-driven market implements the basic rules of U.S. equity markets, supporting both market and limit orders, and executing them in a first-in-first-out fashion. We overview the system architecture and we present possible use cases. We demonstrate how a set of automated agents is capable of producing a price process with characteristics similar to the statistics of real price from financial markets. Finally, we detail a market stress scenario and we draw, what we believe to be, interesting conclusions about crash events.

q-fin.TR↗
arXiv2020

Empirical Analysis of Indirect Internal Conversions in Cryptocurrency Exchanges

Algorithmic trading is well studied in traditional financial markets. However, it has received less attention in centralized cryptocurrency exchanges. The Commodity Futures Trading Commission (CFTC) attributed the $2010$ flash crash, one of the most turbulent periods in the history of financial markets that saw the Dow Jones Industrial Average lose $9\%$ of its value within minutes, to automated order "spoofing" algorithms. In this paper, we build a set of methodologies to characterize and empirically measure different algorithmic trading strategies in Binance, a large centralized cryptocurrency exchange, using a complete data set of historical trades. We find that a sub-strategy of triangular arbitrage is widespread, where bots convert between two coins through an intermediary coin, and obtain a favorable exchange rate compared to the direct one. We measure the profitability of this strategy, characterize its risks, and outline two strategies that algorithmic trading bots use to mitigate their losses. We find that this strategy yields an exchange ratio that is $0.144\%$, or $14.4$ basis points (bps) better than the direct exchange ratio. $2.71\%$ of all trades on Binance are attributable to this strategy.

q-fin.TR↗
arXiv2020

Transformers for Limit Order Books

We introduce a new deep learning architecture for predicting price movements from limit order books. This architecture uses a causal convolutional network for feature extraction in combination with masked self-attention to update features based on relevant contextual information. This architecture is shown to significantly outperform existing architectures such as those using convolutional networks (CNN) and Long-Short Term Memory (LSTM) establishing a new state-of-the-art benchmark for the FI-2010 dataset.

q-fin.CP↗