High Frequency Trading (HFT) algorithms are automated feedback systems interacting with markets to maximize returns on investments. These systems have the potential to read different resolutions of market information at any given time, where Level I information is the minimal information about an equity--essentially its price--and Level II information is the full order book at that time for that equity. This paper presents a study of using Recurrent Neural Network (RNN) models to predict the spread of the DOW Industrial 30 index traded on NASDAQ, using Level I and Level II data as inputs. The results show that Level II data does not significantly improve the prediction of spread when predicting less than 100 millisecond into the future, while it is increasingly informative for spread predictions further into the future. This suggests that HFT algorithms should not attempt to make use of Level II information, and instead reallocate that computation power for improved trading performance, while slower trading algorithms may very well benefit from processing the complete order book.

<p> This dissertation consists of two topics. In chapter 1, we develop a discrete disaggregated model in which, the market maker can observe individual order flow instead of a batch order in Kyle (1985). The model suggests that the behavior of the uninformed traders play an important role in how the informed make the optimal trading strategy : when the uninformed is more likely to use large order, the informed will also trade large, no matter what size of signal he receives, and when the uninformed tend to trade with small size order, the informed will have to trade small quantity to maximize his expected profit, even if he receives the large value signal. When the uninformed does not prefer size of order, the informed will trade smaller (larger) quantities when receiving small(large) value signals. The result is consistent with the behavior of the informed in Kyle (1985). We further investigate order flow disaggregation on market liquidity by comparing aggregated order flow structure, in which market maker observes aggregated order flow. When the model setup is symmetric, the aggregated structure can provide more liquidity, while the disaggregated structure is more liquid under the asymmetric model setup. In chapter 2, we employ the type 2 joint power law distribution in Mardia (1962) to study the joint effect of the return and trading volume. The parameter estimate for marginal distribution in joint power-law exhibits the same pattern as in univariate power law literature for return and volume, but the value are smaller due to the joint effect of return and trading volume. However, we find the joint power law shows higher predictability than the univariate power law by employing the measure MSE (Means squared error). Additionally, the type 2 joint power law indicates the linear relationship between log absolute value of return and log trading volume , which suggests the none linear impact of trading volume on price. We also find that, as sampling interval shrinks from day to 15 seconds, the price impact will increase. And also as the waiting time for two consecutive transactions shrinks, the price impact will increase, which is in line with the result of Dufour and Engle (2000). </p>

We introduce a financial model for limit order book with two main features: First, the limit orders and market orders for the given asset both appear and interact with each other. Second, the high frequency trading (HFT, for short) activities are allowed and described by the scaling limit of nearly-unstable multi-dimensional Hawkes processes with power law decay. The model eventually becomes a stochastic partial differential equation (SPDE, for short) with the diffusion coefficient determined by a Volterra integral equation governed by a Hawkes process, whose Hurst exponent is less than 1/2, which makes the volatility path of the stochastic PDE rougher than that driven by a Brownian motion. We have further established the well-posedness of such a system so that a foundation is laid down for further studies in this direction.

Submitted by Gustavo de Faro Colen Nunes (gustavocolennunes@gmail.com) on 2013-02-28T19:45:35Z No. of bitstreams: 1 MODELO DA DINÂMICA DE UM LIVRO DE ORDENS PARA APLICAÇÕES EM HIGH-FREQUENCY TRADING.pdf: 1769569 bytes, checksum: fcb41165f230caf02656cf7b8a709951 (MD5) / Approved for entry into archive by Suzinei Teles Garcia Garcia (suzinei.garcia@fgv.br) on 2013-02-28T21:30:40Z (GMT) No. of bitstreams: 1 MODELO DA DINÂMICA DE UM LIVRO DE ORDENS PARA APLICAÇÕES EM HIGH-FREQUENCY TRADING.pdf: 1769569 bytes, checksum: fcb41165f230caf02656cf7b8a709951 (MD5) / Made available in DSpace on 2013-03-01T11:06:28Z (GMT). No. of bitstreams: 1 MODELO DA DINÂMICA DE UM LIVRO DE ORDENS PARA APLICAÇÕES EM HIGH-FREQUENCY TRADING.pdf: 1769569 bytes, checksum: fcb41165f230caf02656cf7b8a709951 (MD5) Previous issue date: 2013-02-01 / As operações de alta frequência (High-Frequency Trading - HFT) estão crescendo cada vez mais na BOVESPA (Bolsa de Valores de São Paulo), porém seu volume ainda se encontra muito atrás do volume de operações similares realizadas em outras bolsas de relevância internacional. Este trabalho pretende criar oportunidades para futuras aplicações e pesquisas nesta área. Visando aplicações práticas, este trabalho foca na aplicação de um modelo que rege a dinâmica do livro de ordens a dados do mercado brasileiro. Tal modelo é construído com base em informações do próprio livro de ordens, apenas. Depois de construído o modelo, o mesmo é utilizado em uma simulação de uma estratégia de arbitragem estatística de alta frequência. A base de dados utilizada para a realização deste trabalho é constituída pelas ordens lançadas na BOVESPA para a ação PETR4. / High-frequency trading (HFT) are increasingly growing on BOVESPA (São Paulo Stock Exchange), but their volume is still far behind the volume of similar operations performed on other internationally relevant exchange markets. The main objective of this work is to create opportunities for future research and applications in this area. Aiming at practical applications, this work focuses on applying a model that governs the dynamics of the order book to the Brazilian market. This model is built based in the information of the order book alone. After building the model, a high frequency statistical arbitrage strategy is simulated to validate the model. The database used for this work consists on the orders posted on the equity PETR4 in BOVESPA.

This dissertation addresses the fundamental question of what factors drive equity prices and investigates the mechanisms through which the drivers influence the price dynamics. The studies are based on the two different frequency levels of financial data. The first part aims to identify what systematic risk factors affect the expected return of stocks based on historical data with frequency being daily or monthly. The second part aims to explain how the hidden supply-demand of a stock affects the stock price dynamics based on market data observed at frequency levels generally between a millisecond and a second. With more and more financial market data becoming available, it greatly facilitates quantitative approaches for analyzing asset price dynamics and market microstructure problems. In the first part, we propose an econometric measure, terms as modularity, for characterizing the cluster structure in a universe of stocks. A high level of modularity implies that the cluster structure of the universe of stocks is highly evident, and low modularity implies a blurred cluster structure. The modularity measure is shown to be related to the cycle of the economy. In addition, individual stock's sensitivity to the modularity measure is shown to be related to its expected return. From 1992 to 2011, the average annual return of stocks with the lowest sensitivity exceeds that of the stocks with highest sensitivities by approximately 7.6%. Considerations of modularity as an asset pricing factor expand the investment opportunity set to passive investors. In the second part, we analyze the effect of hidden demands/supplies in equity trading market on the stock price dynamics. We propose a statistical estimation model for average hidden liquidity based on the limit orderbook data. Not only the estimated hidden liquidity explains the probabilistic property in market microstructure better, it also refines the existing price impact model and achieves higher explanation powers. Our enhanced price impact model offers a base for devising optimal order execution strategies. After we develop an optimal execution strategy based on the price impact function, the advantage of this strategy over benchmark strategies is tested on a simulated stock trading model calibrated by historical data. Simulation tests indicate that our strategy yields significant savings in transaction cost over the benchmark strategies.

This thesis examines an impact of high frequency trading on equity market qualities. As an indicator of market quality, stock prices realized volatility is used. To estimate the high frequency trading activity, we implement a special method of identification of high frequency orders from quote data. Study of relation between high frequency trading and market qualities is incited by growing concerns about the welfare impacts of high frequency trading and connected activities. In order to test the dependence and causality between high frequency trading activity and volatility, we implement time-scale estimation techniques. Wavelet coherence is used to study localized dependence. The analysis is amended by a robustness check, using wavelet correlation. Results show inconsistent dependence at short trading horizons and regions of significant continuous dependence at trading horizons within hours. Powered by TCPDF (www.tcpdf.org)

On propose une perspective originale d'analyser les différents flux hautes fréquences d'information provenant des marchés financiers et fournit des modèles simples et intuitives qui reflètent étroitement la réalité. On observe les données empiriques et note certains faits stylisés et propose des modèles pour capturer ces faits. Dans le chapitre 1, on passe en revue les définitions et propriétés de base des marchés électroniques. En particulier, on revoit les travaux de microstructure et de modélisation du marché, et leurs relations à ce travail. On introduit la taille du "tick", qu'on utilise pour classifier les actifs et interpréter les différents résultats. Dans le chapitre 2, on montre empiriquement que l'impact d'une seule transaction dépend de la durée inter-transactions. En effet, lorsque le taux des échanges devient plus rapide, la variance des rendements des transactions augmente fortement et que ce comportement persiste à des échelles de temps plus grossières. On montre également que la valeur du spread augmente avec l'activité et on en déduit que les carnets d'ordres sont plus vide lorsque le taux des échanges est élevé. Dans le chapitre 3, on présente un modèle pour capturer le bruit de microstructure. Les prix des actifs sont représentés par la somme des rendements "tick" arrivant à des temps de Poisson aléatoires. Le modèle se compose d'une martingale diffusive contaminée par un bruit autocorrélé mais disparaissant aux échelles grossières. On est capable de capturer la signature de la variance et l'autocorrélation faible mais significative des rendements "tick". Dans le chapitre 4, on utilise les processus ponctuels de Hawkes pour modéliser l'arrivée aléatoire des transactions. On modélise la transformation échelle fine - échelle grossière des prix et en particulier l'effet sur les moments des rendements des prix. On propose une technique simple d'estimation non paramétrique de la structure de dépendance des processus de Hawkes dans le cas unidimensionnel et dans quelques cas particuliers multidimensionnels. On applique la méthode à des actifs de Future et trouve des noyaux de dépendance en loi de puissance.

Over the last decade, researchers have attempted to show how efficient the markets are by using Fama’s Efficiency Market Hypothesis (EMH). The theory states that an investor cannot increase his returns without taking additional risk. The markets can be efficient in different forms depending on the information included in the traded asset. It is quoted that: "There ain't no such thing as a free lunch". However, the topic still remains disputable since researchers have introduced controversial findings after investigating different markets. Overall, emerging markets have been characterized with higher volatility which consequently declares for market imperfections. Commonly, these market inefficiencies are quickly captured by the eye of the investors who are lurking for potential benefits through exploiting them. These are the so called arbitrage opportunities which exist on different level of impact, depending on the attitude of the market. The existence of arbitrage is clear evidence against Fama’s theory and it has been documented in numerous studies. Unfortunately those events occur rarely and disappear in a matter of seconds, thus; is highly competitive to capitalize. Over the last decade high frequency trading (HFT) became popular on different markets and it allowed traders to make decisions and execute transactions in a matter of milliseconds using algorithms. The market we are interested in is the Forex market which is a decentralized market where currencies from all over the world are traded. Main participants include multinational banks which rely heavily on HFT. The method used to benefit from inefficiency is called triangular arbitrage and it involves selling and buying 3 sets of currency pairs in times when a parity is violated. The goal of this study is to answer the following research question, “Is there a difference in triangular arbitrage opportunities between emerging markets and developed ones?” The main objective of this research is to examine how the number of arbitrage occurrences varies considering different market characteristics. Furthermore, the originality of the research stems from the comparison between strategies using currencies from developed economies and emerging ones. Moreover, the additional academic value comes from the analysis of a new dataset that has not yet been examined. Lastly, our results make an empirical contribution into a country’s economy by reducing market inefficiencies and increasing economic stability. Our sample consists of quantitative data totaling to 2.4 million observations per quotation taken from 2011 and 2013 for currencies picked using a non-probability convenience method based on their property to be converted to EUR and USD currency and availability of information. The research revealed that differences between the two types of market exist, and indicates that the “early” markets possess higher arbitrage activity in contrast to the mature economies. These results should boost the potential for a better trading management and upgrade the profit growth.

Titel:  Flash-krascher – ett allvarligt problem på Stockholmsbörsen? Författare:  Madelene Söderström &amp; Sebastian Roth Handledare: Bo Sjö Ämne:  Nationalekonomi – Kandidatuppsats inom finans Syfte:  Syftet med arbetet är att fördjupa förståelsen kring flash-krascher och vilken påverkan dessa har på handeln av värdepapper som sker på Stockholmsbörsen. Vi hoppas också att studien ger en klarare bild av hur flash-krascher påverkar olika aktörer med koppling till aktiehandeln i Sverige. Metod:  Uppsatsen är baserad på en kvalitativ studie utförd med intervjurespondenter med varierande koppling till Stockholmsbörsen och den svenska finansmarknaden. Teori:  Uppsatsen utgår främst från tidigare forskning inom ämnet bestående av studier baserade på händelser och data från USA. Annan ekonomisk teori som presenteras i studien är adverse selection. Empiri:  Uppsatsen är bestående av sju semistrukturerade intervjuer med aktörer på finansmarknaden. Intervjuerna jämförs med tidigare inträffade händelser i USA för att diskutera möjliga slutsatser om flash-krascher på Stockholmsbörsen. Slutsats:  Studien kommer fram till att det är osannolikt att flash-krascher av den magnituden som inträffat i USA 6 maj 2010 inträffar på Stockholmsbörsen idag. Vidare så verkar flash-krascher inte ha särskilt stor påverkan på aktörer på Stockholmsbörsen, däremot kan det finnas en viss oros- och förtroendeproblematik kopplad till flash-krascher som bör tas på allvar. I studien av tidigare forskning finner vi intressanta teorier för hur flash-krascher kan förutses. Vi kan däremot inte dra några slutsatser kring dessa teorier kopplat till Stockholmsbörsen. / Title:  Flash crashes – a severe problem at Nasdaq OMX Stockholm? Authors:  Madelene Söderström &amp; Sebastian Roth Advisor:  Bo Sjö Subject:  Bachelor thesis in finance Purpose:  The purpose of this study is to understand and critically examine the impact flash crashes might have on the market for securities at Nasdaq OMX Stockholm. Our goal is to provide a clearer view on how flash crashes affect the trade and the market participants. Method:  This thesis is a qualitative study based on interviews with respondents with different approach to both Nasdaq OMX Stockholm and the financial market in Sweden. Theory:  The thesis is based on earlier studies within the subject made from data and events from United States of America. Other economic theories that the thesis involve is adverse selection. Empirics:  The study is predicated around seven semi structured interviews with participants on the financial market in Sweden. The interviews are compared with the earlier events from USA to make for conclusions about flash crashes on Nasdaq OMX Stockholm. Conclusion:  We find that it is unlikely that a flash crash of the same magnitude as the May 6, 2010 flash crash will occur on the Nasdaq OMX Stockholm exchange today. Furthermore, flash crashes appear to have little impact on the market participants at Nasdaq OMX Stockholm, though there may be concerns about trust issues following flash crashes that should be considered. While studying some of the earlier research we find interesting theories about ways to predict flash crashes before they have occurred, we can’t make any conclusions about these theories connected to Nasdaq OMX Stockholm though.

Le but de cette thèse est de répondre au vrai besoin de prédire les fluctuations futures des prix d'actions. En effet, l'aléatoire régissant ces fluctuations constitue pour des acteurs de la finance, tels que les Market Maker, une des plus grandes sources de risque. Tout au long de cette étude, nous mettons en évidence la possibilité de réduire l'incertitude sur les prix futurs par l'usage des modèles mathématiques appropriés. Cette étude est rendue possible grâce à une grande base de données financières et une puissante grille de calcul mises à notre disposition par l'équipe Automatic Market Making de BNP Paribas. Dans ce document, nous présentons uniquement les résultats de la recherche concernant le trading haute fréquence. Les résultats concernant la partie basse fréquence présentent un intérêt scientifique moindre pour le monde académique et rentrent par ailleurs dans le cadre des résultats confidentiels. Ces résultats seront donc volontairement omis.Dans le premier chapitre, nous présentons le contexte et les objectifs de cette étude. Nous présentons, également, les différentes méthodes utilisées, ainsi que les principaux résultats obtenus. Dans le chapitre 2, nous nous intéressons à l'apport de la supériorité technologique en trading haute fréquence. Dans ce but, nous simulons un trader ultra rapide, omniscient, et agressif, puis nous calculons son gain total sur 3 ans. Les gains obtenus sont très modestes et reflètent l'apport limité de la technologie en trading haute fréquence. Ce résultat souligne l'intérêt primordial de la recherche et de la modélisation dans ce domaine.Dans le chapitre 3, nous étudions la prédictibilité des prix à partir des indicateurs de carnet d'ordre. Nous présentons, à l'aide des espérances conditionnelles, des preuves empiriques de dépendances statistiques entre les prix et les différents indicateurs. L'importance de ces dépendances résulte de la simplicité de la méthode, éliminant tout risque de surapprentissage des données. Nous nous intéressons, ensuite, à la combinaison des différents indicateurs par une régression linéaire et nous analysons les différents problèmes numériques et statistiques liés à cette méthode. Enfin, nous concluons que les prix sont prédictibles pour un horizon de quelques minutes et nous mettons en question l'hypothèse de l'efficience du marché.Dans le chapitre 4, nous nous intéressons au mécanisme de formation du prix à partir des arrivés des évènements dans le carnet d'ordre. Nous classifions les ordres en douze types dont nous analysons les propriétés statistiques. Nous étudions par la suite les dépendances entre ces différents types d'ordres et nous proposons un modèle de carnet d'ordre en ligne avec les observations empiriques. Enfin, nous utilisons ce modèle pour prédire les prix et nous appuyons l'hypothèse de la non-efficience des marchés, suggérée au chapitre 3. / The aim of this thesis is to address the real need of predicting the prices of stocks. In fact, the randomness governing the evolution of prices is, for financial players like market makers, one of the largest sources of risk. In this context, we highlight the possibility of reducing the uncertainty of the future prices using appropriate mathematical models. This study was made possible by a large base of high frequency data and a powerful computational grid provided by the Automatic Market Making team at BNP Paribas. In this paper, we present only the results of high frequency tests. Tests are of less scientific interest in the academic world and are confidential. Therefore, these results will be deliberately omitted.In the first chapter, the background and the objectives of this study are presented along with the different methods used and the main results obtained.The focus of chapter 2 is on the contribution of technological superiority in high frequency trading. In order to do this, an omniscient trader is simulated and the total gain over three years is calculated. The obtained gain is very modest and reflects the limited contribution of technology in high frequency trading. This result underlines the primary role of research and modeling in this field.In Chapter 3, the predictability of prices using some order book indicators is studied. Using conditional expectations, the empirical evidence of the statistical dependencies between the prices and indicators is presented. The importance of these dependencies results from the simplicity of the method, eliminating any risk of over fitting the data. Then the combination of the various indicators is tested using a linear regression and the various numerical and statistical problems associated with this method are analyzed. Finally, it can be concluded that the prices are predictable for a period of a few minutes and the assumption of market efficiency is questioned.In Chapter 4, the mechanism of price formation from the arrival of events in the order book is investigated. The orders are classified in twelve types and their statistical properties are analyzed. The dependencies between these different types of orders are studied and a model of order book in line with the empirical observations is proposed. Finally, this model is used to predict prices and confirm the assumption of market inefficiency suggested in Chapter 3.