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1 Statistical Arbitrage and Algorithmic Trading Statistical Arbitrage and Algorithmic Trading : Overview and Applications Miquel Noguer Alonso - Licenciado y Master en Administración y Dirección de Empresas – Universitat Ramon Llull - ESADE Facultad de Ciencias Económicas y Empresariales Departamento de Economía Aplicada Cuantitativa II UNED 2010 1 Facultad de Ciencias Económicas y Empresariales Departamento de Economía Aplicada Cuantitativa II Statistical Arbitrage and Algorithmic Trading : Overview and Applications Miquel Noguer Alonso - Licenciado y Master en Administración y Dirección de Empresas – Universitat Ramon Llull – ESADE - UBS AG Director : Andreu Pacheco Pages IFAE/CERN Codirector : Manuel Jose Sanchez Sanchez UNED 2 This PhD Thesis is a tribute to my family. To my mother and brother, whose confidence, support in me has been a constant in my life, to my wife Mima, whose love, patience, and understanding have been the foundations of this work. To the memory of my father, wherever he is, I love him so much. To my son Jordi who came early this year to inspire my work, bringing to our family such happiness that cannot be imagined. 3 Acknowledgements This PhD thesis is the result of more than a decade of work with my talented colleagues in UBS, Andbanc as many other people in the financial industry. Thanks to my Thesis Director, Andreu Pacheco Pages, for his knowledge, patience, help with ideas and devoting his precious time to my work! Thanks to Alberto Alvarez and Jose Manuel Sanchez for their guidance, dedication and support through all my PhD time at their university. Thanks to Christian Mazza, Jean Pierre Gabriel and Ales Janka for their collaboration in the research in Fribourg University. I am greatly indebted to Yi-Chen-Zhang and Damien Challet for bringing me there. Thanks to Lorenzo Moneta from CERN for his collaboration in the machine learning chapter of this PhD thesis. Thanks to Jose Miguel Dominguez for his collaboration in the factor models section of this work and the interesting discussions we have on quantitative investing. Thanks to Stephen Wolfram and Jason Cawley from Wolfram Research for their support and the research we did together in the NKS summer school back in 2008. My discussions and research with Martin Schaden have extremely useful to explore new ideas like quantum finance. My work wouldn’t have been the same without my conversations with Jean-Phillipe Bouchaud, Conrad Perez Vicente and other econophysicists. Whose contribution to economics science is changing the foundations of Finance. I am highly indebted to the Fisica i Finances research group from the Physics department at Universitat de Barcelona for their inspiring papers and books. 4 1. Introduction ................................................................................................................ 14 1.1. Scope.................................................................................................................................... 14 1.2. Definitions ........................................................................................................................... 16 1.2.1 Forecasting................................................................................................................................. 16 1.2.2 The ultimate goal: achieving high Sharpe ratios................................................................... 18 2. Algorithmic Trading strategies: track record, categories and disciplines 18 2.1. The industry of systematic traders: Barclay Systematic Traders Index ............ 18 2.2. Trading strategies categories : Mean reversion, momentum / Regime switching / Factor models .......................................................................................................... 20 2.2.1 Mean-reverting versus momentum strategies....................................................................... 20 2.2.2 Regime switching ...................................................................................................................... 25 2.2.3 Stationarity and cointegration.................................................................................................. 27 2.2.4 Factor models ............................................................................................................................ 28 2.2.5 High-frequency trading strategies........................................................................................... 30 2.2.6 What is your exit strategy?....................................................................................................... 32 2.2.7 Event trading.............................................................................................................................. 33 2.2.8 Volatility arbitrage...................................................................................................................... 34 2.3. Statistics and Finance: Econophysics and behavioral finance............................ 43 2.3.1 Statistics, econophysics and behavioural finance................................................................ 43 2.3.2 Agent-Based Modelling of Financial Markets........................................................................ 46 2.3.3 Game theory .............................................................................................................................. 47 2.3.4 Microstructure – Are the dynamics of financial markets endogenous or exogenous ? .. 48 2.3.5 Endogenous-Exogenous Market model................................................................................. 50 2.3.6 Statistics and Finance............................................................................................................... 50 3. P: discrete-time processes .................................................................................... 52 3.1. Random walk...................................................................................................................... 53 3.1.1 Continuous invariants ............................................................................................................... 54 3.1.2 Discrete invariants..................................................................................................................... 55 3.1.3 Generalized representations.................................................................................................... 56 3.1.4 Heavy tails.................................................................................................................................. 57 3.2. ARMA processes............................................................................................................... 59 3.3. Long memory ..................................................................................................................... 61 3.4. Volatility clustering........................................................................................................... 63 4. Part II Q: continuous-time processes.................................................................. 64 4.1. Levy processes.................................................................................................................. 65 4.1.1 Diffusion...................................................................................................................................... 65 4.1.2 Jumps.......................................................................................................................................... 66 4.1.3 Generalized representations.................................................................................................... 68 4.1.4 Notable examples...................................................................................................................... 69 4.2. Autocorrelated processes .............................................................................................. 71 4.3. Long memory ..................................................................................................................... 72 4.4. Volatility clustering........................................................................................................... 74 4.4.1 Stochastic volatility.................................................................................................................... 74 4.4.2 Subordination............................................................................................................................. 75 4.5. Markov Switching Models............................................................................................... 77 4.6. Fractals and multifractals in finance............................................................................ 78 5 4.6.1 Basic definitions......................................................................................................................... 78 4.6.2 Multifractals ................................................................................................................................81 4.6.3 Multifractal model of asset returns.......................................................................................... 84 4.6.4 Markov switching multifractal................................................................................................... 85 4.7. Quantum Finance.............................................................................................................. 86 4.8. State Space representation ............................................................................................ 86 4.9. Bayesian
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