Essays in Volatility Research Tristan Linke
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ESSAYS IN VOLATILITY RESEARCH by TRISTAN LINKE MSc in Quantitative Finance, Lancaster University (2011) THESIS SUBMITTED TO THE DEPARTMENT OF ACCOUNTING AND FINANCE IN PARTIAL FULFILLMENT OF THE REQUIREMENTS FOR THE DEGREE OF DOCTOR OF PHILOSOPHY IN FINANCE at THE MANAGEMENT SCHOOL, LANCASTER UNIVERSITY 2017 c Tristan Linke, MMXVI. All rights reserved. Supervisor: Stephen J. Taylor, Professor of Finance Thesis Advisor: Prof. Ser{huang Poon, Professor of Finance External Examiner: Prof. Nick Taylor, Professor of Finance Internal Examiner: Prof. Ingmar Nolte, Professor of Finance and Econometrics Preface This thesis has been written during my time as a Ph.D. candidate in Finance at Lancaster University and as a visiting Ph.D. scholar at the Econometrics Department of the Univer- sity of Amsterdam. This Ph.D. thesis starts with an introduction to finance for a general audience. Followed by an extensive literature overview, which I have continued to enrich over the years, of interesting topics in the econometrics{intense field of finance so I felt the need to incorporate it into my Ph.D.|which is a documentation of my work over the last years. I then start with a very brief teaser regarding finite sample properties of the classical skewness estimator and a robust alternative. This paves the way to the first paper in this thesis on Realized Skewness, Asymmetric Volatility and Risk Management which is co{authored with my supervisor and was influenced by my time spent in Amsterdam. The next paper, asymmetric dynamics in index volatility and constituent correlation was my first work after completing my M.Sc. in Quantitative Finance at Lancaster University on jump detection methodologies. It largely developed during the first period of my Ph.D. with the great support of my supervisor and my thesis advisor. These two papers are linked by an overarching theme: the asymmetric effects of returns on future volatility and vice versa. The last chapter, co{authored with Cisil Sarisoy, developed more recently and concentrates on transformations of the covariance matrix, also known as the beta, in a noisy setting. i PREFACE Acknowledgements Of course this thesis would not have existed if it were not for the support from so many different people over the years. I would here like to take the opportunity to thank in particular my supervisor Stephen J. Taylor for his invaluable guidance, his advice with applications, and his insightful contributions to our joint research projects. Without knowing of my existence, Stephen already guided me through my undergrad- uate thesis on volatility spreads at the ESB Business School through his book Asset Price Dynamics, Volatility and Prediction, which ultimately draw me into the newly opened master degree programme in quantitative finance at Lancaster and I felt like Robert Cole visiting Ibn Sina in the book the Physician by Noah Gordon when he offered to supervise me for my M.Sc. and later on for my Ph.D. dissertation. Very special thanks also goes to my thesis advisor Ser{huang Poon at Manchester Business School who was guiding me very well and shared lots of interesting research ideas over the course of my studies and providing me the opportunity to present my work at Manchester, and to my sponsor at the University of Amsterdam Peter Boswijk, who enabled me to stay for nine months at the University at Amsterdam and always seemed curious in my research and gave many insightful comments and suggestions for improvements. I would also like to thank Mark Shackleton and Ingmar Nolte for guiding me through the literature and commenting on many research ideas and for their open door policy. The Department of Accounting and Finance at Lancaster University, the Department of Econometrics at the University of Amsterdam, and the Department of Finance at Manch- ester Business School have all been very stimulating and interesting environments to work in. The great seminar series and brown bag seminars have been very inspiring for my work. I am also grateful for the financial support throughout my studies provided by the Department of Accounting and Finance at Lancaster, the scholarship by Lancaster Uni- versity Management School, scholarshop by the Northwest Doctoral Training Center of the ESRC and in particular I would like to thank Steve Young or enabling me to teach on the departmental programmes, and the trust in me in supervising several master dissertations. No matter where I have been, I have had the privilege to be surrounded by great Ph.D. colleagues, and I have very much enjoyed their company during this endeavor. Thank you to my officemates Rui Fan, Xi Fu, Yang Liu, Andrei Lalu and in particular Tobias Langenberg for academic and non{academic discussions. ii ESSAYS IN VOLATILITY RESEARCH Most importantly, I would like to thank Cisil Sarisoy for all her support and all our inspiring research talks over all these years. Lastly, I wish to thank my friends, my parents and my sister for your patience and support over the years, and for bearing over with me being slightly absentminded at times. Declaration This thesis is submitted to Lancaster University in support of my application for the degree of Doctor of Philosophy. It has been composed by myself and has not been submitted in any previous application for any degree. The work presented including data generated and data analysis was carried out by the author. TRISTAN LINKE iii Contents Preface i Abstract......................................... i Acknowledgements................................... ii Declaration....................................... iii Table of Contents.................................... vii Introduction1 Introduction to the Financial Economic Setting................... 1 Financial Econometric Rationale for Chapters 1, 2, 3................ 2 Chapter 1: Realized Skewness, Asymmetric Volatility, and Volatility Feedback2 Chapter 2: Reconciling Asymmetric Dynamics in Index Volatility and Con- stituent Correlations........................... 5 Chapter 3: The Role of Noise in the Estimation of Betas........... 8 Financial Econometric Literature Review ...................... 9 Time Deformation ................................ 10 Stochastic Volatility ............................... 11 Risk{Neutral Skewness from Implied Volatility Curves............ 16 From Implied Volatility Surface back to Data Generating Process . 19 Measurement Theory & Applications: Realized Methodology . 21 Test Statistics for Jumps, Identification, Implications............. 27 ARCH{type Models and Long Memory Properties .............. 33 Multivariate ARCH{type Models and Correlation Modelling......... 34 Economic Explanations of Asymmetric Volatility and Skewness . 42 A review of the classical skewness estimator, estimates, and a robust alternvative 47 Daily Skewness and its Quantile{based Variations............... 47 Skewness as a Function of the Return Horizon................. 50 Skewness of Large Cap Stocks at Monthly Return Horizon.......... 51 iv CONTENTS Finite Sample Properties and Alternative (Robust) Skewness Measure . 52 Preliminary Take{away ............................. 55 1 Realized Skewness, Asymmetric Volatility, and Volatility Feedback 59 1.1 Introduction: A New Estimator of Realized Skewness..................... 60 1.2 Literature Review: Skewness, Realized Skewness, and the Statistical Leverage Effect . 62 1.3 Methodology: Designing Realized Skewness Estimators.................... 67 1.3.1 Model{free Realized Skewness...................... 67 1.3.2 Addressing the periodicity component in intraday volatility . 76 1.3.3 Semi{parametric and model{based approaches ............ 79 1.4 Empirical Results................................. 89 1.4.1 Data.................................... 89 1.4.2 Intra{weekday and macroeconomic announcement day volatility pat- terns.................................... 92 1.4.3 The Class of Non{parametric Realized Skewness Estimators . 97 1.5 Conclusions....................................109 Appendix 113 1.A Proofs for Chapter1...............................113 1.A.1 Decompositional & aggregational results of realized skewness measures113 1.A.2 Properties and analytical moments of SV{type models . 116 1.B Tables for Chapter1...............................131 1.C Figures for Chapter1 ..............................138 1.D Robustness Checks................................185 1.D.1 Extended Trading Hours.........................185 2 Reconciling Asymmetric Dynamics in Index Volatility and Constituent Correlations 191 2.1 Introduction....................................192 2.2 Literature review: Asymmetric return{volatility innovations ...................193 TRISTAN LINKE v CONTENTS 2.2.1 The leverage effect............................193 2.2.2 The volatility feedback effect ......................195 2.2.3 Simultaneous comparison and differentiation of the two effects . 196 2.2.4 Economic explanations and 'investor sentiment' . 198 2.3 Methodology ...................................200 2.3.1 Generalized ARCH{type model setup . 200 2.3.2 Empirical Model Specification......................201 2.3.3 Statistical Properties...........................203 2.3.4 Correlations................................204 2.4 Empirical Analysis................................207 2.4.1 Data Description.............................207 2.4.2 Aggregate market & constituent returns summary statistics . 211 2.4.3 Asymmetric dynamics in index and constituent return volatility . 214 2.4.4 Analysing asymmetric correlations...................222 2.5 Concluding remarks ...............................225