An online adaptive learning algorithm for optimal trade execution in high-frequency markets

A thesis submitted in fulfilment of the requirements for the degree of Doctor of Philosophy in the Faculty of Science, School of Computer Science and Applied Mathematics University of the Witwatersrand. October 2016.Automated algorithmic trade execution is a central problem in modern financial markets, however finding and navigating optimal trajectories in this system is a non-trivial task. Many authors have developed exact analytical solutions by making simplifying assumptions regarding governing dynamics, however for practical feasibility and robustness, a more dynamic approach is needed to capture the spatial and temporal system complexity and adapt as intraday regimes change. This thesis aims to consolidate four key ideas: 1) the financial market as a complex adaptive system, where purposeful agents with varying system visibility collectively and simultaneously create and perceive their environment as they interact with it; 2) spin glass models as a tractable formalism to model phenomena in this complex system; 3) the multivariate Hawkes process as a candidate governing process for limit order book events; and 4) reinforcement learning as a framework for online, adaptive learning. Combined with the data and computational challenges of developing an efficient, machine-scale trading algorithm, we present a feasible scheme which systematically encodes these ideas. We first determine the efficacy of the proposed learning framework, under the conjecture of approximate Markovian dynamics in the equity market. We find that a simple lookup table Q-learning algorithm, with discrete state attributes and discrete actions, is able to improve post-trade implementation shortfall by adapting a typical static arrival-price volume trajectory with respect to prevailing market microstructure features streaming from the limit order book. To enumerate a scale-specific state space whilst avoiding the curse of dimensionality, we propose a novel approach to detect the intraday temporal financial market state at each decision point in the Q-learning algorithm, inspired by the complex adaptive system paradigm. A physical analogy to the ferromagnetic Potts model at thermal equilibrium is used to develop a high-speed maximum likelihood clustering algorithm, appropriate for measuring critical or near-critical temporal states in the financial system. State features are studied to extract time-scale-specific state signature vectors, which serve as low-dimensional state descriptors and enable online state detection. To assess the impact of agent interactions on the system, a multivariate Hawkes process is used to measure the resiliency of the limit order book with respect to liquidity-demand events of varying size. By studying the branching ratios associated with key quote replenishment intensities following trades, we ensure that the limit order book is expected to be resilient with respect to the maximum permissible trade executed by the agent. Finally we present a feasible scheme for unsupervised state discovery, state detection and online learning for high-frequency quantitative trading agents faced with a multifeatured, asynchronous market data feed. We provide a technique for enumerating the state space at the scale at which the agent interacts with the system, incorporating the effects of a live trading agent on limit order book dynamics into the market data feed, and hence the perceived state evolution.LG201

Impersonal efficiency and the dangers of a fully automated securities exchange

This report identifies impersonal efficiency as a driver of market automation during the past four decades, and speculates about the future problems it might pose. The ideology of impersonal efficiency is rooted in a mistrust of financial intermediaries such as floor brokers and specialists. Impersonal efficiency has guided the development of market automation towards transparency and impersonality, at the expense of human trading floors. The result has been an erosion of the informal norms and human judgment that characterize less anonymous markets. We call impersonal efficiency an ideology because we do not think that impersonal markets are always superior to markets built on social ties. This report traces the historical origins of this ideology, considers the problems it has already created in the recent Flash Crash of 2010, and asks what potential risks it might pose in the future

A comparison of different trading protocols in an agent-based market

We compare price dynamics of different market protocols (batch auction, continuous double auction and dealership) in an agent-based artificial exchange. In order to distinguish the effects of market architectures alone, we use a controlled environment where allocative and informational issues are neglected and agents do not optimize or learn. Hence, we rule out the possibility that the behaviour of traders drives the price dynamics. Aiming to compare price stability and execution quality in broad sense, we analyze standard deviation, excess kurtosis, tail exponent of returns, volume, perceived gain by traders and bid-ask spread. Overall, a dealership market appears to be the best candidate in this respect, generating low volume and volatility, virtually no excess kurtosis and high perceived gain.Artificial markets, Agent-based models, Microstructural architectures

Modelling Asset Prices for Algorithmic and High-Frequency Trading

Algorithmic trading (AT) and high-frequency (HF) trading, which are responsible for over 70% of US stocks trading volume, have greatly changed the microstructure dynamics of tick-by-tick stock data. In this article, we employ a hidden Markov model to examine how the intraday dynamics of the stock market have changed and how to use this information to develop trading strategies at high frequencies. In particular, we show how to employ our model to submit limit orders to profit from the bid–ask spread, and we also provide evidence of how HF traders may profit from liquidity incentives (liquidity rebates). We use data from February 2001 and February 2008 to show that while in 2001 the intraday states with the shortest average durations (waiting time between trades) were also the ones with very few trades, in 2008 the vast majority of trades took place in the states with the shortest average durations. Moreover, in 2008, the states with the shortest durations have the smallest price impact as measured by the volatility of price innovations

Modeling asset prices for algorithmic and high frequency trading.

Algorithmic Trading (AT) and High Frequency (HF) trading, which are responsible for over 70% of US stocks trading volume, have greatly changed the microstructure dynamics of tick-by-tick stock data. In this paper we employ a hidden Markov model to examine how the intra-day dynamics of the stock market have changed, and how to use this information to develop trading strategies at ultra-high frequencies. In particular, we show how to employ our model to submit limit-orders to profit from the bid-ask spread and we also provide evidence of how HF traders may profit from liquidity incentives (liquidity rebates). We use data from February 2001 and February 2008 to show that while in 2001 the intra-day states with shortest average durations were also the ones with very few trades, in 2008 the vast majority of trades took place in the states with shortest average durations. Moreover, in 2008 the fastest states have the smallest price impact as measured by the volatility of price innovationsHigh frequency traders; Algorithmic trading; Durations; Hidden Markov model;