HEC Montréal Affiliated with the Université de Montréal. ThreeEssaysonHighFrequencyFinancialDataandTheirUsefor Risk Management. - PDF

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HEC Montréal Affiliated with the Université de Montréal ThreeEssaysonHighFrequencyFinancialDataandTheirUsefor Risk Management by Maria Pacurar Finance Department and Canada Research Chair in Risk Management

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HEC Montréal Affiliated with the Université de Montréal ThreeEssaysonHighFrequencyFinancialDataandTheirUsefor Risk Management by Maria Pacurar Finance Department and Canada Research Chair in Risk Management HEC Montréal This thesis is presented in partial fulfillment of the requirements for the degree of Philosophiæ Doctor (Ph.D.) in Business Administration June, 2006 c Maria Pacurar, 2006 HEC Montréal Affiliated with the Université de Montreal This thesis entitled: ThreeEssaysonHighFrequencyFinancialDataandTheirUsefor Risk Management By: Maria Pacurar Has been evaluated by the following jury: President-reviewer: Thesis supervisor: Thesis co-supervisor: Internal examiner: External examiner: Dr Joshua Slive HEC Montréal Dr Georges Dionne HEC Montréal Dr Pierre Duchesne Université de Montréal Dr Jean-Guy Simonato HEC Montréal Dr Christian Gouriéroux Université Paris IX et ENSAE Abstract This dissertation contains three essays investigating the modeling and use of financial tick-by-tick data. High-frequency finance has become a very active field of research over the last two decades. Research making use of irregularly timespaced transaction data has its roots in the seminal article of Engle and Russell (1998) that introduced the Autoregressive Conditional Duration (ACD) model for theanalysisofarrivaltimesbetweeneventsbasedonallpastinformation. The first essay provides an up-to-date survey of the main theoretical developments in ACD modeling and empirical studies using financial data. First, we discuss the properties of the standard ACD specification and its extensions, existing diagnostic tests, and joint models for the arrival times of events and some market characteristics. Then, we present the empirical applications of ACD models to different types of events, and identify possible directions for future research. The second essay proposes two classes of test statistics for duration clustering and one class of test statistics for the adequacy of ACD models, using a spectral approach. The tests for ACD effects of the first class are obtained by comparing a kernel-based normalized spectral density estimator and the normalized spectral density under the null hypothesis of no ACD effects, using a norm. The second class of test statistics for ACD effects exploits the one-sided nature of the alternative hypothesis. The class of tests for the adequacy of an ACD model is obtained by comparing a kernel-based spectral density estimator of the estimated standardized residuals and the null hypothesis of adequacy using a norm. With the L 2 norm and the truncated uniform kernel, we retrieve generalized versions of the classical Box-Pierce/Ljung-Box test statistics. However, using non-uniform kernels, we obtain more powerful test procedures in many situations. The proposed test statistics possess a convenient asymptotic normal distribution under the null hypothesis. We present a simulation experiment and an application iv on IBM transaction data. The third essay investigates the use of tick-by-tick data for market risk measurement. We propose an Intraday Value at Risk (IVaR) at different horizons based on irregularly time-spaced high-frequency data by using an intraday Monte Carlo simulation. An UHF-GARCH model extending the framework of Engle (2000) is used to specify the joint density of the marked point process of durations and high-frequency returns. We apply our methodology to transaction data for the Royal Bank and the Placer Dome stocks traded on the Toronto Stock Exchange. Results show that our approach constitutes reliable means of measuring intraday risk for traders who are very active on the market. The UHF-GARCH model performs well out-of-sample for almost all the time horizons and the confidence levels considered even when normality is assumed for the distribution of the error term, provided that intraday seasonality has been accounted for prior to the estimation. Keywords: tick-by-tick data, Autoregressive Conditional Duration model, duration clustering, model adequacy, spectral density, marked point process, Intraday Value at Risk, intraday market risk, UHF-GARCH models, intraday Monte Carlo simulation. Résumé Cette thèse est constituée de trois essais qui portent sur la modélisation et l utilisation des données financières transaction par transaction. La finance à haute fréquence est devenue un champ de recherche très actif au cours de deux dernières décennies. Les recherches empiriques utilisant des données de transaction irrégulièrement espacées trouvent leur origine dans le travail de Engle et Russell (1998) introduisant le modèle de durée conditionnelle autorégressive ACD pour l analyse du temps entre deux événements qui surviennent sur le marché. Le premier essai propose une revue de la littérature théorique et empirique concernant les modèles ACD. Nous présentons d abord les propriétés du modèle ACD de base et de ses extensions, les tests de diagnostic existants et les modèles joints d une durée et d une caractéristique. Ensuite, nous considérons les applications empiriques des modèles ACD à plusieurs types d événements et nous identifions des pistes de recherche future. Le deuxième essai propose deux classes de statistiques de test pour les effets ACD et une classe de statistiques de test pour l ajustement des modèles ACD, en utilisant une approche spectrale. Les tests d effets ACD de la première classe sont obtenus en comparant un estimateur à noyau de la densité spectrale normalisée et la densité spectrale normalisée sous l hypothèse nulle d absence d effets ACD, en utilisant une métrique. La deuxième classe de tests d effets ACD exploite la nature unilatérale de l hypothèse alternative. La classe de tests d ajustement d un modèle ACD est obtenue en comparant un estimateur à noyau de la densité spectrale des résidus estimés standardisés et l hypothèse nulle d ajustement en utilisant unemétrique. EnutilisantlenoyauuniformetronquéetlamétriqueL 2,nous obtenons des versions généralisées des tests Box-Pierce/Ljung-Box. Cependant, plusieurs noyaux permettent d obtenir une meilleure puissance. Les statistiques de test proposées possèdent une distribution asymptotique normale rigoureusement vi établie sous l hypothèse nulle. Nous réalisons une étude par simulation ainsi qu une application avec des données de transaction sur l action IBM. Dans le troisième essai nous étudions l utilisation des données transaction par transaction pour mesurer le risque de marché. Nous proposons une Valeur à Risque intrajournalière à horizons différents, basée sur des données à haute fréquence irrégulièrement espacées dans le temps. Les résultats sont obtenus en utilisant une simulation Monte Carlo intrajournalière. La densité jointe du processus de points marqués des durées et des rendements à haute fréquence est spécifiée au moyen d une extension du modèle UHF-GARCH de Engle (2000). Nous appliquons notre méthodologie à des données sur les actions de la Banque Royale et de Placer Dome transigées à la Bourse de Toronto. Les résultats montrent que notre approche propose une mesure robuste du risque intrajournalier auquel sont confrontés les cambistes très actifs sur le marché. Le modèle UHF- GARCH performe bien hors échantillon pour presque tous les horizons temporels et les degrés de confiance considérés, même lorsque l hypothèse de normalité est supposée pour la distribution du terme d erreur, à condition que la saisonnalité intrajournalière ait été prise en compte avant l estimation. Mots clés : données transaction par transaction, modèle ACD, effets ACD, ajustement d un modèle, densité spectrale, processus de points marqués, Valeur à Risque intrajournalière, risque de marché intrajournalier, modèles UHF-GARCH, simulation Monte Carlo intrajournalière Table of contents Abstract Résumé List of Tables List of Figures Acknowledgements iii v x xii xiv Chapter 1: Autoregressive Conditional Duration (ACD) models in finance: A survey of the theoretical and empirical literature Introduction TheACDmodel:theoreticaldevelopments Generalsetup Modelsforthedurations Modelsfordurationsandmarks Applications of ACD models in finance Intradayseasonality Applicationstotradedurations Applicationstopricedurations Applications to volume durations and other economic events Conclusion References viii Chapter 2: On testing for duration clustering and diagnostic checking of models for irregularly spaced transaction data Introduction Preliminariesandframework Preliminaries Autoregressive conditional duration models Two classes of test statistics for testing for ACD effects Tests based on a kernel-based spectral density estimator of therawdurationsandanorm Tests based on the spectral density evaluated at the zero frequency ClassofteststatisticsfortheadequacyofACDmodels Tests based on a kernel-based spectral density estimator of theestimatedresidualsandanorm Simulationresults Description of the experiment when testing for ACD effects Discussion of the level study (ACD effects) Discussion of the power study (ACD effects) Description of the experiment when testing for the adequacy ofacdmodels Discussion of the level study (adequacy of ACD models) Discussion of the power study (adequacy of ACD models) ApplicationwithIBMdata Conclusion References Appendix... 96 ix Chapter 3: Intraday Value at Risk (IVaR) using tick-by-tick data with application to the Toronto Stock Exchange Introduction Thegeneraleconometricmodel TheACDandthelog-ACDmodels TheUHF-GARCHmodel MonteCarloIVaR IVaR: definition TheextendedUHF-GARCHmodel IntradayMonteCarlosimulation Empiricalstudy Data Seasonaladjustment Estimationresults IVaRbacktesting Conclusion References List of Tables 2.1 Empirical levels at the 5% level for tests of ACD effects Level-adjusted powers against ACD(1) at 5% level for tests of ACD effects Level-adjusted powers against ACD(4) at 5% level for tests of ACD effects Level-adjusted powers against ACD(12) at 5% level for tests of ACD effects Level-adjusted powers against ACD(1,1) at 5% level for tests of ACD effects Empirical levels at the 5% level for tests of adjustment when the modelisacd(1,1) Level-adjusted powers against ACD(2,1) at 5% level for tests of adjustmentwhenthemodelisacd(1,1) Level-adjusted powers against ACD(2,2) a at 5% level for tests of adjustmentwhenthemodelisacd(1,1) Level-adjusted powers against ACD(2,2) b at 5% level for tests of adjustmentwhenthemodelisacd(1,1) Level-adjusted powers against ACD(4,4) at 5% level for tests of adjustmentwhenthemodelisacd(1,1) DescriptivestatisticsofIBMdurations(inseconds) Test statistics for ACD effects for IBM trade durations Test statistics for ACD effects for IBM volume durations Test statistics for adjustment of EACD(1,1) and EACD(2,2) models foribmtradedurations Test statistics for adjustment of WACD(1,1) and WACD(2,2) modelsforibmtradedurations xi 2.16 Test statistics for adjustment of GACD(1,1) and GACD(2,2) modelsforibmtradedurations Test statistics for adjustment of EACD(1,1) and EACD(2,2) models foribmvolumedurations Test statistics for adjustment of WACD(1,1) and WACD(2,2) modelsforibmvolumedurations Test statistics for adjustment of GACD(1,1) and GACD(2,2) modelsforibmvolumedurations Descriptive statistics of raw data for Royal Bank (RY) and Placer Dome(PDG)Stocks Descriptive statistics of deseasonalised data for Royal Bank (RY) andplacerdome(pdg)stocks EstimatesofACD-GARCHmodels IVaRresultsforRY IVaRresultsforPDG List of Figures 3.1 Illustration of the intraday Monte Carlo simulation approach Histograms of intraday returns for Royal Bank (RY) and Placer Dome(PDG) EstimatedintradayfactorsforRYdurations EstimatedintradayfactorsforRYsquaredreturns Intraday returns vs IVaR for RY (interval = 45 or 22 minutes).. 149 To my family whose love, sacrifice, and patience have made this project possible, To Greg who has been with me every step of the way, You are all my source of motivation, Thank you for everything Acknowledgements Setting down my acknowledgments has definitely been the moment I have dreamt of most often over the past several years - not because it is associated with the end of my dissertation (is a dissertation ever finished?), but because of all the people who have contributed to its completion. I could hardly wait for the moment when Iwouldfinally be able to say Thank you to you all. First, I would like to express my gratitude to my supervisors, Georges Dionne and Pierre Duchesne, for guiding me through this process. My first year at HEC Montréal has been particularly difficult but it would certainly have been more difficult without Dr. Dionne s support and patience. His research experience, dedication, and wisdom proved to be extremely valuable over all these years. I thank him for offering me detailed comments and insights, especially for the discussions and time invested in chapter three, for giving me freedom in research while always being there to assist, for trusting me enough to push me forward gently when I struggled with doubt (particularly before presentations), for generously supporting me in my job search, and for providing financing for my participation to conferences and for the completion of the thesis. Pierre stepped enthusiastically into this project when I greatly needed a boost and played a vital role in its completion. He patiently introduced me to the world of statistical testing and provided excellent guidance and sound advice that shaped my development as a researcher. The second chapter of this thesis is the direct consequence of our collaboration and I thank him for guiding my interest in ACD models. He challenged me every step of the way, yet supported and instilled confidence in me. Evenings I spent working late in my office during a cold winter holiday while he sent me suggestions online as well as his stimulating questions on chapter three will remain among the precious memories of this journey. I am extremely grateful to the other members of my thesis committee: to Jean-Guy Simonato for the gift of his time, his valuable comments, and his support in my job search, and to Alain Guay for many helpful suggestions and his extraordinary kindness. I am also very thankful to my mentor, Jean Bénéteau, who initially encouraged me to pursue doctoral studies. I could never have discovered the intellectual challenge of such an enterprise as well as the associated rewards were it not for his trust and visionary style. He remained supportive in every possible way, buoying me with his confidence. Meeting him has resulted in a career choice. Mercidetoutcoeur. I also thank Jean-Yves Le Louarn for his crucial assistance in the starting of this project and for his great support and encouragement. I would like to thank Jacqueline Lemay (Head of International Student Affairs) for her encouragement, support and exceptional empathy. She has been always available for listening and seeking solutions, and has never doubted my capability to succeed. I truly cannot imagine my life at HEC without her. Jacqueline, words are simply not enough to express my gratitude! xv I also thank all my professors in the PhD program who have helped me in various ways and moments to move towards my goal. A special thanks goes to Michele Breton and the CREF for the assistance I received in purchasing the tick-by-tick data and participating to conferences, and to Mohamed for his words of encouragement and for offering me support in SAS. I also give my warmest thanks to the staff at HEC, especially to Claire Boisvert for her smiling graciousness in helping me at any time and to Lise Cloutier-Delage for smoothing theadministrativeproceduresaswellasforfriendlyadviceandsupport. I gratefully acknowledge financial support from the Agence Universitaire de la Francophonie, HEC Montréal, the Canada Research Chair in Risk Management, the Institut de Finance Mathématique de Montréal (IFM2), thefonds Québécois de la Recherche sur la Société et la Culture (FQRSC) and the Center for Research on E-finance (CREF). Furthermore, I am grateful to all my friends and fellow colleagues in the PhD program, particularly to: Adrian, for many thought-provoking (non-finance) conversations; Cristi and Mihai for their great support and help; Khemmais for sharing the office, some of his knowledge (and even his birthday); Nabil, Nadia, Thouraya, and Sophia for the good and bad times we have been through together from the very beginning; Marlei for being an example of determination and optimism, always ready to cheer me up; Maria for her friendship and comforting presence. My office-mate and dear friend Denitsa deserves a special heartfelt thanks for always being supportive, discrete and honest. Not only has she read various parts of my thesis making suggestions, she also looked for solutions with me when things got even worse than I imagined while patiently listening to my groans. Our lunches were always something I looked forward to. I also wish to express my gratitude to all my friends all over the world for their moral support and patience. Among them, I especially thank Daniela, Iuliana, and Mira for their constant encouragement, and Cornel for offering me help when the world was looming dark. A thank-you is just not enough for my best friends, so far away but always there for me: Monica for her emotional support ever since we first met more than thirteen years ago, for forgiving me for writing her shorter and shorter s and for trying hard to keep me connected totheworldwhentheonlythingsihadinmindweresimulationsandcodeerrors; and Georgiana for inspiring me through her courage in completing her thesis under difficult conditions, for giving me almost daily support over the past years, for listening to my complaints and sharing my joys with the same dedication. I would have never made it up to this point without my extraordinary family. I am grateful to my parents for always supporting and encouraging me and for raising me to be the person I am today, to my sister and her family for their love and constant support, to my grandmothers who missed sharing this moment but will always be in my heart. And to Greg who has given me a new sense of life. He made numerous sacrifices so that I can complete this journey and yet has never ceased to show me love, patience and support. This thesis is as much his, as it is mine. Chapter 1 Autoregressive Conditional Duration (ACD) models in finance: A survey of the theoretical and empirical literature 1.1 Introduction Until two decades ago, most empirical studies in finance employed, as the finest frequency, daily data obtained by retaining either the first or the last observation of the day for the variable of interest (i.e., the closing price), thus neglecting all intraday events. However, due to the increased automatization of financial markets and the rapid developments in raising computer power, more and more exchanges have set up intraday databases that record every single transaction together with its characteristics (such as price, volume etc.). The availability of these low-cost intraday datasets fueled the development of a new area of financial research: high-frequency finance. Embracing finance, econometrics, and time series statistics, the analysis of high-frequency data (HFD) rapidly appeared as a promising avenue for research by facilitating a deeper understanding of market activity. 1 Interestingly,thesedevelopmentshavenotbeenlimitedtoacademia, but have also affected the current trading environment. years the speed of trading has been constantly increasing. Over the last several Day-trading, once the exclusive territory of floor-traders, is now available to all investors. High frequency finance hedge funds have emerged as a new and successful category of hedge funds. The intrinsic limit of high-frequency data is represented by the transaction 1 E
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