Systematic Trading: Calibration Advances through Machine Learning

Systematic trading in finance uses computer models to define trade goals, risk controls and rules that can execute trade orders in a methodical way. This thesis investigates how performance in systematic trading can be crucially enhanced by both i) persistently reducing the bid-offer spread quoted by the trader through optimized and realistically backtested strategies and ii) improving the out-of-sample robustness of the strategy selected through the injection of theory into the typically data-driven calibration processes. While doing so it brings to the foreground sound scientific reasons that, for the first time to my knowledge, technically underpin popular academic observations about the recent nature of the financial markets. The thesis conducts consecutive experiments across strategies within the three important building blocks of systematic trading: a) execution, b) quoting and c) risk-reward allowing me to progressively generate more complex and accurate backtested scenarios as recently demanded in the literature (Cahan et al. (2010)). The three experiments conducted are: 1. Execution: an execution model based on support vector machines. The first experiment is deployed to improve the realism of the other two. It analyses a popular model of execution: the volume weighted average price (VWAP). The VWAP algorithm targets to split the size of an order along the trading session according to the expected intraday volume's profile since the activity in the markets typically resembles convex seasonality – with more activity around the open and the closing auctions than along the rest of the day. In doing so, the main challenge is to provide the model with a reasonable expected profile. After proving in my data sample that two simple static approaches to the profile overcome the PCA-ARMA from Bialkowski et al. (2008) (a popular two-fold model composed by a dynamic component around an unsupervised learning structure) a further combination of both through an index based on supervised learning is proposed. The Sample Sensitivity Index hence successfully allows estimating the expected volume's profile more accurately by selecting those ranges of time where the model shall be less sensitive to past data through the identification of patterns via support vector machines. Only once the intraday execution risk has been defined can the quoting policy of a mid-frequency (in general, up to a week) hedging strategy be accurately analysed. 2. Quoting: a quoting model built upon particle swarm optimization. The second experiment analyses for the first time to my knowledge how to achieve the disruptive 50% bid-offer spread discount observed in Menkveld (2013) without increasing the risk profile of a trading agent. The experiment depends crucially on a series of variables of which market impact and slippage are typically the most difficult to estimate. By adapting the market impact model in Almgren et al. (2005) to the VWAP developed in the previous experiment and by estimating its slippage through its errors' distribution a framework within which the bid-offer spread can be assessed is generated. First, a full-replication spread, (that set out following the strict definition of a product in order to hedge it completely) is calculated and fixed as a benchmark. Then, by allowing benefiting from a lower market impact at the cost of assuming deviation risk (tracking error and tail risk) a non-full-replication spread is calibrated through particle swarm optimization (PSO) as in Diez et al. (2012) and compared with the benchmark. Finally, it is shown that the latter can reach a discount of a 50% with respect to the benchmark if a certain number of trades is granted. This typically occurs on the most liquid securities. This result not only underpins Menkveld's observations but also points out that there is room for further reductions. When seeking additional performance, once the quoting policy has been defined, a further layer with a calibrated risk-reward policy shall be deployed. 3. Risk-Reward: a calibration model defined within a Q-learning framework. The third experiment analyses how the calibration process of a risk-reward policy can be enhanced to achieve a more robust out-of-sample performance – a cornerstone in quantitative trading. It successfully gives a response to the literature that recently focusses on the detrimental role of overfitting (Bailey et al. (2013a)). The experiment was motivated by the assumption that the techniques underpinned by financial theory shall show a better behaviour (a lower deviation between in-sample and out-of-sample performance) than the classical data-driven only processes. As such, both approaches are compared within a framework of active trading upon a novel indicator. The indicator, called the Expectations' Shift, is rooted on the expectations of the markets' evolution embedded in the dynamics of the prices. The crucial challenge of the experiment is the injection of theory within the calibration process. This is achieved through the usage of reinforcement learning (RL). RL is an area of ML inspired by behaviourist psychology concerned with how software agents take decisions in an specific environment incentivised by a policy of rewards. By analysing the Q-learning matrix that collects the set of state/actions learnt by the agent within the environment, defined by each combination of parameters considered within the calibration universe, the rationale that an autonomous agent would have learnt in terms of risk management can be generated. Finally, by then selecting the combination of parameters whose attached rationale is closest to that of the portfolio manager a data-driven solution that converges to the theory-driven solution can be found and this is shown to successfully outperform out-of-sample the classical approaches followed in Finance. The thesis contributes to science by addressing what techniques could underpin recent academic findings about the nature of the trading industry for which a scientific explanation was not yet given: • A novel agent-based approach that allows for a robust out-of-sampkle performance by crucially providing the trader with a way to inject financial insights into the generally data-driven only calibration processes. It this way benefits from surpassing the generic model limitations present in the literature (Bailey et al. (2013b), Schorfheid and Wolpin (2012), Van Belle and Kerr (2012) or Weiss and Kulikowski (1991)) by finding a point where theory-driven patterns (the trader's priors tend to enhance out-of-sample robustness) merge with data-driven ones (those that allow to exploit latent information). • The provision of a technique that, to the best of my knowledge, explains for the first time how to reduce the bid-offer spread quoted by a traditional trader without modifying her risk appetite. A reduction not previously addressed in the literature in spite of the fact that the increasing regulation against the assumption of risk by market makers (e.g. Dodd–Frank Wall Street Reform and Consumer Protection Act) does yet coincide with the aggressive discounts observed by Menkveld (2013). As a result, this thesis could further contribute to science by serving as a framework to conduct future analyses in the context of systematic trading. • The completion of a mid-frequency trading experiment with high frequency execution information. It is shown how the latter can have a significant effect on the former not only through the erosion of its performance but, more subtly, by changing its entire strategic design (both, optimal composition and parameterization). This tends to be highly disregarded by the financial literature. More importantly, the methodologies disclosed herein have been crucial to underpin the setup of a new unit in the industry, BBVA's Global Strategies & Data Science. This disruptive, global and cross-asset team gives an enhanced role to science by successfully becoming the main responsible for the risk management of the Bank's strategies both in electronic trading and electronic commerce. Other contributions include: the provision of a novel risk measure (flowVaR); the proposal of a novel trading indicator (Expectations’ Shift); and the definition of a novel index that allows to improve the estimation of the intraday volume’s profile (Sample Sensitivity Index)

Multi-asset optimal execution and statistical arbitrage strategies under Ornstein-Uhlenbeck dynamics

In recent years, academics, regulators, and market practitioners have increasingly addressed liquidity issues. Amongst the numerous problems addressed, the optimal execution of large orders is probably the one that has attracted the most research works, mainly in the case of single-asset portfolios. In practice, however, optimal execution problems often involve large portfolios comprising numerous assets, and models should consequently account for risks at the portfolio level. In this paper, we address multi-asset optimal execution in a model where prices have multivariate Ornstein-Uhlenbeck dynamics and where the agent maximizes the expected (exponential) utility of her PnL. We use the tools of stochastic optimal control and simplify the initial multidimensional Hamilton-Jacobi-Bellman equation into a system of ordinary differential equations (ODEs) involving a Matrix Riccati ODE for which classical existence theorems do not apply. By using \textit{a priori} estimates obtained thanks to optimal control tools, we nevertheless prove an existence and uniqueness result for the latter ODE, and then deduce a verification theorem that provides a rigorous solution to the execution problem. Using examples based on data from the foreign exchange and stock markets, we eventually illustrate our results and discuss their implications for both optimal execution and statistical arbitrage

Theoretical and Practical Aspects of Algorithmic Trading

At today\u27s stock markets, most of the trading volume is traded electronically. Thus, also many market participants execute their order flow automatically with the help of trading algorithms. Hence, several important aspects concerning algorithmic trading are discussed. One of the main topics of the current work is the measurement and the analysis of the market impact of transactions performed by a trading algorithm. Another main topic is a model to predict the intraday trading volume

Negativna selekcija - Apsolutna mera algoritamskog izvršenja proizvoljnog naloga

Algorithmic trading is an automated process of order execution on electronic stock markets. It can be applied to a broad range of financial instruments, and it is  characterized by a signicant investors' control over the execution of his/her orders, with the principal goal of finding the right balance between costs and risk of not (fully) executing an order. As the measurement of execution performance gives information whether best execution is achieved, a signicant number of diffeerent benchmarks is  used in practice. The most frequently used are price benchmarks, where some of them are determined before trading (Pre-trade benchmarks), some during the trading  day (In-traday benchmarks), and some are determined after the trade (Post-trade benchmarks). The two most dominant are VWAP and Arrival Price, which is along with other pre-trade price benchmarks known as the Implementation Shortfall (IS). We introduce Negative Selection as a posteriori measure of the execution algorithm performance. It is based on the concept of Optimal Placement, which represents the ideal order that could be executed in a given time win-dow, where the notion of ideal means that it is an order with the best execution price considering  market  conditions  during the time window. Negative Selection is dened as a difference between vectors of optimal and executed orders, with vectors dened as a quantity of shares at specied price positionsin the order book. It is equal to zero when the order is optimally executed; negative if the order is not (completely) filled, and positive if the order is executed but at an unfavorable price. Negative Selection is based on the idea to offer a new, alternative performance measure, which will enable us to find the  optimal trajectories and construct optimal execution of an order. The first chapter of the thesis includes a list of notation and an overview of denitions and theorems that will be used further in the thesis. Chapters 2 and 3 follow with a  theoretical overview of concepts related to market microstructure, basic information regarding benchmarks, and theoretical background of algorithmic trading. Original results are presented in chapters 4 and 5. Chapter 4 includes a construction of optimal placement, definition and properties of Negative Selection. The results regarding the properties of a Negative Selection are given in [35]. Chapter 5 contains the theoretical background for stochastic optimization, a model of the optimal execution formulated as a stochastic optimization problem with regard to Negative Selection, as well as original work on nonmonotone line search method [31], while numerical results are in the last, 6th chapter.Algoritamsko trgovanje je automatizovani proces izvršavanja naloga na elektronskim berzama. Može se primeniti na širok spektar nansijskih instrumenata kojima se trguje na berzi i karakteriše ga značajna kontrola investitora nad izvršavanjem njegovih naloga, pri čemu se teži nalaženju pravog balansa izmedu troška i rizika u vezi sa izvršenjem naloga. S ozirom da se merenjem performasi izvršenja naloga određuje da li je postignuto najbolje izvršenje, u praksi postoji značajan broj različitih pokazatelja. Najčešće su to pokazatelji cena, neki od njih se određuju pre trgovanja (eng. Pre-trade), neki u toku trgovanja (eng. Intraday), a neki nakon trgovanja (eng. Post-trade). Dva najdominantnija pokazatelja cena su VWAP i Arrival Price koji je zajedno sa ostalim "pre-trade" pokazateljima cena poznat kao Implementation shortfall (IS). Pojam negative selekcije se uvodi kao "post-trade" mera performansi algoritama izvršenja, polazeći od pojma optimalnog naloga, koji predstavlja idealni nalog koji se  mogao izvrsiti u datom vremenskom intervalu, pri ćemu se pod pojmom "idealni" podrazumeva nalog kojim se postiže najbolja cena u tržišnim uslovima koji su vladali  u toku tog vremenskog intervala. Negativna selekcija se definiše kao razlika vektora optimalnog i izvršenog naloga, pri čemu su vektori naloga defisani kao količine akcija na odgovarajućim pozicijama cena knjige naloga. Ona je jednaka nuli kada je nalog optimalno izvršen; negativna, ako nalog nije (u potpunosti) izvršen, a pozitivna ako je nalog izvršen, ali po nepovoljnoj ceni. Uvođenje mere negativne selekcije zasnovano je na ideji da se ponudi nova, alternativna, mera performansi i da se u odnosu na nju nađe optimalna trajektorija i konstruiše optimalno izvršenje naloga. U prvom poglavlju teze dati su lista notacija kao i pregled definicija i teorema  neophodnih za izlaganje materije. Poglavlja 2 i 3 bave se teorijskim pregledom pojmova i literature u vezi sa mikrostrukturom tržišta, pokazateljima trgovanja i algoritamskim trgovanjem. Originalni rezultati su predstavljeni u 4. i 5. poglavlju. Poglavlje 4 sadrži konstrukciju optimalnog naloga, definiciju i osobine negativne selekcije. Teorijski i praktični rezultati u vezi sa osobinama negativna selekcije dati su u [35]. Poglavlje 5 sadrži teorijske osnove stohastičke optimizacije, definiciju modela za optimalno izvršenje, kao i originalni rad u vezi sa metodom nemonotonog linijskog pretraživanja [31], dok 6. poglavlje sadrži empirijske rezultate

Essays in empirical finance

This thesis contains three essays on the role of incentives in financial decisions. The first essay documents how airlines financial choices are affected by the threat of future competition. The second essay explores the role of cross-trading in mutual fund families. The third essay shows the effect of stock undepricing on innovation spending

Algorithmic trading, market quality and information : a dual -process account

One of the primary challenges encountered when conducting theoretical research on the subject of algorithmic trading is the wide array of strategies employed by practitioners. Current theoretical models treat algorithmic traders as a homogenous trader group, resulting in a gap between theoretical discourse and empirical evidence on algorithmic trading practices. In order to address this, the current study introduces an organisational framework from which to conceptualise and synthesise the vast amount of algorithmic trading strategies. More precisely, using the principles of contemporary cognitive science, it is argued that the dual process paradigm - the most prevalent contemporary interpretation of the nature and function of human decision making - lends itself well to a novel taxonomy of algorithmic trading. This taxonomy serves primarily as a heuristic to inform a theoretical market microstructure model of algorithmic trading. Accordingly, this thesis presents the first unified, all-inclusive theoretical model of algorithmic trading; the overall aim of which is to determine the evolving nature of financial market quality as a consequence of this practice. In accordance with the literature on both cognitive science and algorithmic trading, this thesis espouses that there exists two distinct types of algorithmic trader; one (System 1) having fast processing characteristics, and the other (System 2) having slower, more analytic or reflective processing characteristics. Concomitantly, the current microstructure literature suggests that a trader can be superiorly informed as a result of either (1) their superior speed in accessing or exploiting information, or (2) their superior ability to more accurately forecast future variables. To date, microstructure models focus on either one aspect but not both. This common modelling assumption is also evident in theoretical models of algorithmic trading. Theoretical papers on the topic have coalesced around the idea that algorithmic traders possess a comparative advantage relative to their human counterparts. However, the literature is yet to reach consensus as to what this advantage entails, nor its subsequent effects on financial market quality. Notably, the key assumptions underlying the dual-process taxonomy of algorithmic trading suggest that two distinct informational advantages underlie algorithmic trading. The possibility then follows that System 1 algorithmic traders possess an inherent speed advantage and System 2 algorithmic traders, an inherent accuracy advantage. Inevitably, the various strategies associated with algorithmic trading correspond to their own respective system, and by implication, informational advantage. A model that incorporates both types of informational advantage is a challenging problem in the context of a microstructure model of trade. Models typically eschew this issue entirely by restricting themselves to the analysis of one type of information variable in isolation. This is done solely for the sake of tractability and simplicity (models can in theory include both variables). Thus, including both types of private information within a single microstructure model serves to enhance the novel contribution of this work. To prepare for the final theoretical model of this thesis, the present study will first conjecture and verify a benchmark model with only one type/system of algorithmic trader. More formally, iv a System 2 algorithmic trader will be introduced into Kyle’s (1985) static Bayesian Nash Equilibrium (BNE) model. The behavioral and informational characteristics of this agent emanate from the key assumptions reflected in the taxonomy. The final dual-process microstructure model, presented in the concluding chapter of this thesis, extends the benchmark model (which builds on Kyle (1985)) by introducing the System 1 algorithmic trader; thereby, incorporating both algorithmic trader systems. As said above: the benchmark model nests the Kyle (1985) model. In a limiting case of the benchmark model, where the System 2 algorithmic trader does not have access to this particular form of private information, the equilibrium reduces to the equilibrium of the static model of Kyle (1985). Likewise, in the final model, when the System 1 algorithmic trader’s information is negligible, the model collapses to the benchmark model. Interestingly, this thesis was able to determine how the strategic interplay between two differentially informed algorithmic traders impact market quality over time. The results indicate that a disparity exists between each distinctive algorithmic trading system and its relative impact on financial market quality. The unique findings of this thesis are addressed in the concluding chapter. Empirical implications of the final model will also be discussed.GR201

Stochastic Models of Limit Order Markets

During the last two decades most stock and derivatives exchanges in the world transitioned to electronic trading in limit order books, creating a need for a new set of quantitative models to describe these order-driven markets. This dissertation offers a collection of models that provide insight into the structure of modern financial markets, and can help to optimize trading decisions in practical applications. In the first part of the thesis we study the dynamics of prices, order flows and liquidity in limit order markets over short timescales. We propose a stylized order book model that predicts a particularly simple linear relation between price changes and order flow imbalance, defined as a difference between net changes in supply and demand. The slope in this linear relation, called a price impact coefficient, is inversely proportional in our model to market depth - a measure of liquidity. Our empirical results confirm both of these predictions. The linear relation between order flow imbalance and price changes holds for time intervals between 50 milliseconds and 5 minutes. The inverse relation between the price impact coefficient and market depth holds on longer timescales. These findings shed a new light on intraday variations in market volatility. According to our model volatility fluctuates due to changes in market depth or in order flow variance. Previous studies also found a positive correlation between volatility and trading volume, but in order-driven markets prices are determined by the limit order book activity, so the association between trading volume and volatility is unclear. We show how a spurious correlation between these variables can indeed emerge in our linear model due to time aggregation of high-frequency data. Finally, we observe short-term positive autocorrelation in order flow imbalance and discuss an application of this variable as a measure of adverse selection in limit order executions. Our results suggest that monitoring recent order flow can improve the quality of order executions in practice. In the second part of the thesis we study the problem of optimal order placement in a fragmented limit order market. To execute a trade, market participants can submit limit orders or market orders across various exchanges where a stock is traded. In practice these decisions are influenced by sizes of order queues and by statistical properties of order flows in each limit order book, and also by rebates that exchanges pay for limit order submissions. We present a realistic model of limit order executions and formalize the search for an optimal order placement policy as a convex optimization problem. Based on this formulation we study how various factors determine investor's order placement decisions. In a case when a single exchange is used for order execution, we derive an explicit formula for the optimal limit and market order quantities. Our solution shows that the optimal split between market and limit orders largely depends on one's tolerance to execution risk. Market orders help to alleviate this risk because they execute with certainty. Correspondingly, we find that an optimal order allocation shifts to these more expensive orders when the execution risk is of primary concern, for example when the intended trade quantity is large or when it is costly to catch up on the quantity after limit order execution fails. We also characterize the optimal solution in the general case of simultaneous order placement on multiple exchanges, and show that it sets execution shortfall probabilities to specific threshold values computed with model parameters. Finally, we propose a non-parametric stochastic algorithm that computes an optimal solution by resampling historical data and does not require specifying order flow distributions. A numerical implementation of this algorithm is used to study the sensitivity of an optimal solution to changes in model parameters. Our numerical results show that order placement optimization can bring a substantial reduction in trading costs, especially for small orders and in cases when order flows are relatively uncorrelated across trading venues. The order placement optimization framework developed in this thesis can also be used to quantify the costs and benefits of financial market fragmentation from the point of view of an individual investor. For instance, we find that a positive correlation between order flows, which is empirically observed in a fragmented U.S. equity market, increases the costs of trading. As the correlation increases it may become more expensive to trade in a fragmented market than it is in a consolidated market. In the third part of the thesis we analyze the dynamics of limit order queues at the best bid or ask of an exchange. These queues consist of orders submitted by a variety of market participants, yet existing order book models commonly assume that all orders have similar dynamics. In practice, some orders are submitted by trade execution algorithms in an attempt to buy or sell a certain quantity of assets under time constraints, and these orders are canceled if their realized waiting time exceeds a patience threshold. In contrast, high-frequency traders submit and cancel orders depending on the order book state and their orders are not driven by patience. The interaction between these two order types within a single FIFO queue leads bursts of order cancelations for small queues and anomalously long waiting times in large queues. We analyze a fluid model that describes the evolution of large order queues in liquid markets, taking into account the heterogeneity between order submission and cancelation strategies of different traders. Our results show that after a finite initial time interval, the queue reaches a specific structure where all orders from high-frequency traders stay in the queue until execution but most orders from execution algorithms exceed their patience thresholds and are canceled. This "order crowding" effect has been previously noted by participants in highly liquid stock and futures markets and was attributed to a large participation of high-frequency traders. In our model, their presence creates an additional workload, which increases queue waiting times for new orders. Our analysis of the fluid model leads to waiting time estimates that take into account the distribution of order types in a queue. These estimates are tested against a large dataset of realized limit order waiting times collected by a U.S. equity brokerage firm. The queue composition at a moment of order submission noticeably affects its waiting time and we find that assuming a single order type for all orders in the queue leads to unrealistic results. Estimates that assume instead a mix of heterogeneous orders in the queue are closer to empirical data. Our model for a limit order queue with heterogeneous order types also appears to be interesting from a methodological point of view. It introduces a new type of behavior in a queueing system where one class of jobs has state-dependent dynamics, while others are driven by patience. Although this model is motivated by the analysis of limit order books, it may find applications in studying other service systems with state-dependent abandonments

Analysis of new sentiment and its application to finance

This thesis was submitted for the degree of Doctor of philosophy and awarded by Brunel UniversityWe report our investigation of how news stories influence the behaviour of tradable financial assets, in particular, equities. We consider the established methods of turning news events into a quantifiable measure and explore the models which connect these measures to financial decision making and risk control. The study of our thesis is built around two practical, as well as, research problems which are determining trading strategies and quantifying trading risk. We have constructed a new measure which takes into consideration (i) the volume of news and (ii) the decaying effect of news sentiment. In this way we derive the impact of aggregated news events for a given asset; we have defined this as the impact score. We also characterise the behaviour of assets using three parameters, which are return, volatility and liquidity, and construct predictive models which incorporate impact scores. The derivation of the impact measure and the characterisation of asset behaviour by introducing liquidity are two innovations reported in this thesis and are claimed to be contributions to knowledge. The impact of news on asset behaviour is explored using two sets of predictive models: the univariate models and the multivariate models. In our univariate predictive models, a universe of 53 assets were considered in order to justify the relationship of news and assets across 9 different sectors. For the multivariate case, we have selected 5 stocks from the financial sector only as this is relevant for the purpose of constructing trading strategies. We have analysed the celebrated Black-Litterman model (1991) and constructed our Bayesian multivariate predictive models such that we can incorporate domain expertise to improve the predictions. Not only does this suggest one of the best ways to choose priors in Bayesian inference for financial models using news sentiment, but it also allows the use of current and synchronised data with market information. This is also a novel aspect of our work and a further contribution to knowledge.Engineering and Physical Sciences Research Council (EPSRC) and OptiRisk Systems

Essays in statistical arbitrage

This three-paper thesis explores the important relationship between arbitrage and price efficiency. Chapter 3 investigates the risk-bearing capacity of arbitrageurs under varying degrees and types of risk. A novel stochastic process is introduced to the literature that is capable of jointly capturing fundamental risk factors which are absent from extant specifications. Using stochastic optimal control theory, the degree to which arbitrageurs' investment behaviour is affected by aversion to these risks is analytically characterized, as well as conditions under which arbitrageurs cut losses, effectively exacerbating pricing disequilibria. Chapter 4 explores the role of arbitrage in enforcing price parity between cross-listed securities. This work employs an overlooked mechanism by which arbitrage can maintain parity, namely pairs-trading, which is cheaper to implement than the mechanism most commonly employed in the literature on cross-listed securities. This work shows that arbitrage is successful at enforcing parity between cross-listed securities, and also documents the main limits to arbitrage in this market setting. Chapter 5 examines the extent to which arbitrage contributes to the flow of information across markets. It is shown that microscopic lead/lag relationships of the order of a few hundred milliseconds exist across three major international index futures. Importantly, these delays last long enough, and induce pricing anomalies large enough, to compensate arbitrageurs for appropriating pricing disequilibria. These results accord with the view that temporary disequilibria incentivise arbitrageurs to correct pricing anomalies

Application of Machine Learning to Financial Time Series Analysis

This multidisciplinary thesis investigates the application of machine learning to financial time series analysis. The research is motivated by the following thesis question: ‘Can one improve upon the state of the art in financial time series analysis through the application of machine learning?’ The work is split according to the following time series trichotomy: 1) characterization — determine the fundamental properties of the time series; 2) modelling — find a description that accurately captures features of the long-term behaviour of the system; and 3) forecasting — accurately predict the short-term evolution of the system