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arXiv2018

Cross-Sectional Variation of Intraday Liquidity, Cross-Impact, and their Effect on Portfolio Execution

The composition of natural liquidity has been changing over time. An analysis of intraday volumes for the S&P500 constituent stocks illustrates that (i) volume surprises, i.e., deviations from their respective forecasts, are correlated across stocks, and (ii) this correlation increases during the last few hours of the trading session. These observations could be attributed, in part, to the prevalence of portfolio trading activity that is implicit in the growth of ETF, passive and systematic investment strategies; and, to the increased trading intensity of such strategies towards the end of the trading session, e.g., due to execution of mutual fund inflows/outflows that are benchmarked to the closing price on each day. In this paper, we investigate the consequences of such portfolio liquidity on price impact and portfolio execution. We derive a linear cross-asset market impact from a stylized model that explicitly captures the fact that a certain fraction of natural liquidity providers only trade portfolios of stocks whenever they choose to execute. We find that due to cross-impact and its intraday variation, it is optimal for a risk-neutral, cost minimizing liquidator to execute a portfolio of orders in a coupled manner, as opposed to a separable VWAP-like execution that is often assumed. The optimal schedule couples the execution of the various orders so as to be able to take advantage of increased portfolio liquidity towards the end of the day. A worst case analysis shows that the potential cost reduction from this optimized execution schedule over the separable approach can be as high as 6% for plausible model parameters. Finally, we discuss how to estimate cross-sectional price impact if one had a dataset of realized portfolio transaction records that exploits the low-rank structure of its coefficient matrix suggested by our analysis.

q-fin.TR↗
arXiv2020

Asymptotics for Small Nonlinear Price Impact: a PDE Approach to the Multidimensional Case

We provide an asymptotic expansion of the value function of a multidimensional utility maximization problem from consumption with small non-linear price impact. In our model cross-impacts between assets are allowed. In the limit for small price impact, we determine the asymptotic expansion of the value function around its frictionless version. The leading order correction is characterized by a nonlinear second order PDE related to an ergodic control problem and a linear parabolic PDE. We illustrate our result on a multivariate geometric Brownian motion price model.

math.AP↗
arXiv2022

Practical Deep Reinforcement Learning Approach for Stock Trading

Stock trading strategy plays a crucial role in investment companies. However, it is challenging to obtain optimal strategy in the complex and dynamic stock market. We explore the potential of deep reinforcement learning to optimize stock trading strategy and thus maximize investment return. 30 stocks are selected as our trading stocks and their daily prices are used as the training and trading market environment. We train a deep reinforcement learning agent and obtain an adaptive trading strategy. The agent's performance is evaluated and compared with Dow Jones Industrial Average and the traditional min-variance portfolio allocation strategy. The proposed deep reinforcement learning approach is shown to outperform the two baselines in terms of both the Sharpe ratio and cumulative returns.

cs.LG↗
arXiv2019

Static vs Adaptive Strategies for Optimal Execution with Signals

We compare optimal static and dynamic solutions in trade execution. An optimal trade execution problem is considered where a trader is looking at a short-term price predictive signal while trading. When the trader creates an instantaneous market impact, it is shown that transaction costs of optimal adaptive strategies are substantially lower than the corresponding costs of the optimal static strategy. In the same spirit, in the case of transient impact it is shown that strategies that observe the signal a finite number of times can dramatically reduce the transaction costs and improve the performance of the optimal static strategy.

q-fin.TR↗
arXiv2023

Building Trust Takes Time: Limits to Arbitrage for Blockchain-Based Assets

A blockchain replaces central counterparties with time-consuming consensus protocols to record the transfer of ownership. This settlement latency slows cross-exchange trading, exposing arbitrageurs to price risk. Off-chain settlement, instead, exposes arbitrageurs to costly default risk. We show with Bitcoin network and order book data that cross-exchange price differences coincide with periods of high settlement latency, asset flows chase arbitrage opportunities, and price differences across exchanges with low default risk are smaller. Blockchain-based trading thus faces a dilemma: Reliable consensus protocols require time-consuming settlement latency, leading to arbitrage limits. Circumventing such arbitrage costs is possible only by reinstalling trusted intermediation, which mitigates default risk.

q-fin.TR↗
arXiv2018

General Compound Hawkes Processes in Limit Order Books

In this paper, we study various new Hawkes processes. Specifically, we construct general compound Hawkes processes and investigate their properties in limit order books. With regards to these general compound Hawkes processes, we prove a Law of Large Numbers (LLN) and a Functional Central Limit Theorems (FCLT) for several specific variations. We apply several of these FCLTs to limit order books to study the link between price volatility and order flow, where the volatility in mid-price changes is expressed in terms of parameters describing the arrival rates and mid-price process.

q-fin.TR↗
arXiv2019

Continual Learning Augmented Investment Decisions

Investment decisions can benefit from incorporating an accumulated knowledge of the past to drive future decision making. We introduce Continual Learning Augmentation (CLA) which is based on an explicit memory structure and a feed forward neural network (FFNN) base model and used to drive long term financial investment decisions. We demonstrate that our approach improves accuracy in investment decision making while memory is addressed in an explainable way. Our approach introduces novel remember cues, consisting of empirically learned change points in the absolute error series of the FFNN. Memory recall is also novel, with contextual similarity assessed over time by sampling distances using dynamic time warping (DTW). We demonstrate the benefits of our approach by using it in an expected return forecasting task to drive investment decisions. In an investment simulation in a broad international equity universe between 2003-2017, our approach significantly outperforms FFNN base models. We also illustrate how CLA's memory addressing works in practice, using a worked example to demonstrate the explainability of our approach.

cs.LG↗
arXiv2019

Simulation of Stylized Facts in Agent-Based Computational Economic Market Models

We study the qualitative and quantitative appearance of stylized facts in several agent-based computational economic market (ABCEM) models. We perform our simulations with the SABCEMM (Simulator for Agent-Based Computational Economic Market Models) tool recently introduced by the authors (Trimborn et al. 2019). Furthermore, we present novel ABCEM models created by recombining existing models and study them with respect to stylized facts as well. This can be efficiently performed by the SABCEMM tool thanks to its object-oriented software design. The code is available on GitHub (Trimborn et al. 2018), such that all results can be reproduced by the reader.

econ.GN↗
arXiv2020

Double Deep Q-Learning for Optimal Execution

Optimal trade execution is an important problem faced by essentially all traders. Much research into optimal execution uses stringent model assumptions and applies continuous time stochastic control to solve them. Here, we instead take a model free approach and develop a variation of Deep Q-Learning to estimate the optimal actions of a trader. The model is a fully connected Neural Network trained using Experience Replay and Double DQN with input features given by the current state of the limit order book, other trading signals, and available execution actions, while the output is the Q-value function estimating the future rewards under an arbitrary action. We apply our model to nine different stocks and find that it outperforms the standard benchmark approach on most stocks using the measures of (i) mean and median out-performance, (ii) probability of out-performance, and (iii) gain-loss ratios.

q-fin.TR↗
arXiv2018

Emergence of stylized facts during the opening of stock markets

Financial markets show a number of non-stationarities, ranging from volatility fluctuations over ever changing technical and regulatory market conditions to seasonalities. On the other hand, financial markets show various stylized facts which are remarkably stable. It is thus an intriguing question to find out how these stylized facts emerge. As a first example, we here investigate how the bid-ask-spread between best sell and best buy offer for stocks develops during the trading day. For rescaled and properly smoothed data we observe collapsing curves for many different NASDAQ stocks, with a slow power law decline of the spread during the whole trading day. This effect emerges robustly after a highly fluctuating opening period. Some so called large-tick stocks behave differently because of technical boundaries. Their spread closes to one tick shortly after the market opening. We use our findings for identifying the duration of the market opening which we find to vary largely from stock to stock.

q-fin.TR↗
arXiv2021

On pricing rules and optimal strategies in general Kyle-Back models

The folk result in Kyle-Back models states that the value function of the insider remains unchanged when her admissible strategies are restricted to absolutely continuous ones. In this paper we show that, for a large class of pricing rules used in current literature, the value function of the insider can be finite when her strategies are restricted to be absolutely continuous and infinite when this restriction is not imposed. This implies that the folk result doesn't hold for those pricing rules and that they are not consistent with equilibrium. We derive the necessary conditions for a pricing rule to be consistent with equilibrium and prove that, when a pricing rule satisfies these necessary conditions, the insider's optimal strategy is absolutely continuous, thus obtaining the classical result in a more general setting. This, furthermore, allows us to justify the standard assumption of absolute continuity of insider's strategies since one can construct a pricing rule satisfying the necessary conditions derived in the paper that yield the same price process as the pricing rules employed in the modern literature when insider's strategies are absolutely continuous.

q-fin.TR↗
arXiv2018

Optimizing Market Making using Multi-Agent Reinforcement Learning

In this paper, reinforcement learning is applied to the problem of optimizing market making. A multi-agent reinforcement learning framework is used to optimally place limit orders that lead to successful trades. The framework consists of two agents. The macro-agent optimizes on making the decision to buy, sell, or hold an asset. The micro-agent optimizes on placing limit orders within the limit order book. For the context of this paper, the proposed framework is applied and studied on the Bitcoin cryptocurrency market. The goal of this paper is to show that reinforcement learning is a viable strategy that can be applied to complex problems (with complex environments) such as market making.

q-fin.TR↗
arXiv2019

Optimal VWAP execution under transient price impact

We solve the problem of optimal liquidation with volume weighted average price (VWAP) benchmark when the market impact is linear and transient. Our setting is indeed more general as it considers the case when the trading interval is not necessarily coincident with the benchmark interval: Implementation Shortfall and Target Close execution are shown to be particular cases of our setting. We find explicit solutions in continuous and discrete time considering risk averse investors having a CARA utility function. Finally, we show that, contrary to what is observed for Implementation Shortfall, the optimal VWAP solution contains both buy and sell trades also when the decay kernel is convex.

q-fin.TR↗
arXiv2019

An Agent-Based Model to Explain the Emergence of Stylised Facts in Log Returns

This paper outlines an agent-based model of a simple financial market in which a single asset is available for trade by three different types of traders. The model was first introduced in the PhD thesis of one of the authors, see reference [1]. The simulated log returns are examined for the presence of the stylised facts of financial data. The features of leptokurtosis, volatility clustering and aggregational Gaussianity are especially highlighted and studied in detail. The following ingredients are found to be essential for the production of these stylised facts: the memory of noise traders who make random trade decisions; the inclusion of technical traders that trade in line with trends in the price and the inclusion of fundamental traders who know the "fundamental value" of the stock and trade accordingly. When these three basic types of traders are included log returns are produced with a leptokurtic distribution and volatility clustering as well as some further statistical features of empirical data. This enhances and broadens our understanding of the fundamental processes involved in the production of empirical data by the market.

q-fin.TR↗
arXiv2019

Slow decay of impact in equity markets: insights from the ANcerno database

We present an empirical study of price reversion after the executed metaorders. We use a data set with more than 8 million metaorders executed by institutional investors in the US equity market. We show that relaxation takes place as soon as the metaorder ends:{while at the end of the same day it is on average $\approx 2/3$ of the peak impact, the decay continues the next days, following a power-law function at short time scales, and converges to a non-zero asymptotic value at long time scales (${\sim 50}$ days) equal to $\approx 1/2$ of the impact at the end of the first day.} Due to a significant, multiday correlation of the sign of executed metaorders, a careful deconvolution of the \emph{observed} impact must be performed to extract the estimate of the impact decay of isolated metaorders.

q-fin.TR↗
arXiv2019

Queue-reactive Hawkes models for the order flow

In this work we introduce two variants of multivariate Hawkes models with an explicit dependency on various queue sizes aimed at modeling the stochastic time evolution of a limit order book. The models we propose thus integrate the influence of both the current book state and the past order flow. The first variant considers the flow of order arrivals at a specific price level as independent from the other one and describes this flow by adding a Hawkes component to the arrival rates provided by the continuous time Markov "Queue Reactive" model of Huang et al. Empirical calibration using Level-I order book data from Eurex future assets (Bund and DAX) show that the Hawkes term dramatically improves the pure "Queue-Reactive" model not only for the description of the order flow properties (as e.g. the statistics of inter-event times) but also with respect to the shape of the queue distributions. The second variant we introduce describes the joint dynamics of all events occurring at best bid and ask sides of some order book during a trading day. This model can be considered as a queue dependent extension of the multivariate Hawkes order-book model of Bacry et al. We provide an explicit way to calibrate this model either with a Maximum-Likelihood method or with a Least-Square approach. Empirical estimation from Bund and DAX level-I order book data allow us to recover the main features of Hawkes interactions uncovered in Bacry et al. but also to unveil their joint dependence on bid and ask queue sizes. We notably find that while the market order or mid-price changes rates can mainly be functions on the volume imbalance this is not the case for the arrival rate of limit or cancel orders. Our findings also allows us to clearly bring to light various features that distinguish small and large tick assets.

q-fin.TR↗
arXiv2018

Investigating Limit Order Book Characteristics for Short Term Price Prediction: a Machine Learning Approach

With the proliferation of algorithmic high-frequency trading in financial markets, the Limit Order Book has generated increased research interest. Research is still at an early stage and there is much we do not understand about the dynamics of Limit Order Books. In this paper, we employ a machine learning approach to investigate Limit Order Book features and their potential to predict short term price movements. This is an initial broad-based investigation that results in some novel observations about LOB dynamics and identifies several promising directions for further research. Furthermore, we obtain prediction results that are significantly superior to a baseline predictor.

q-fin.TR↗