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Main Authors:	Aït-Sahalia, Yacine (Author), Jacod, Jean 1944- (Author)
Format:	Book
Language:	English
Published:	Princeton, NJ [u.a.] Princeton Univ. Press 2014
Subjects:	Ökonometrie Ökonometrisches Modell Finanzwirtschaft
Links:	http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=027535608&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA
Physical Description:	XXIV, 659 S. graph. Darst.
ISBN:	9780691161433 0691161437

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adam_text	Contents Preface xvii Notation xxiii I Preliminary Material 1 1 From Diffusions to S emimartin gales 3 1.1 Diffusions .......................... 5 1.1.1 The Brownian Motion ............... 5 1.1.2 Stochastic Integrals ................ 8 1.1.3 A Central Example: Diffusion Processes ..... 12 1.2 Levy Processes ....................... 16 1.2.1 The Law of a Levy Process ............ 17 1.2.2 Examples ...................... 20 1.2.3 Poisson Random Measures ............. 24 1.2.4 Integrals with Respect to Poisson Random Mea¬ sures ......................... 27 1.2.5 Path Properties and Lévy-Itô Decomposition . . 30 1.3 Semimartingales ...................... 35 1.3.1 Definition and Stochastic Integrals ........ 35 1.3.2 Quadratic Variation ................ 38 1.3.3 Itô s Formula .................... 40 1.3.4 Characteristics of a Semimartingale and the Lévy- Itô Decomposition ................. 43 1.4 Ito Semimartingales .................... 44 1.4.1 The Definition ................... 44 1.4.2 Extension of the Probability Space ........ 46 1.4.3 The Grigelionis Form of an Ito Semimartingale . 47 vii viii Contents 1.4.4 A Fundamental Example: Stochastic Differential Equations Driven by a Levy Process ....... 49 1.5 Processes with Conditionally Independent Increments . 52 1.5.1 Processes with Independent Increments ..... 53 1.5.2 A Class of Processes with J7-Conditionally Inde¬ pendent Increments ................ 54 2 Data Considerations 57 2.1 Mechanisms for Price Determination ........... 58 2.1.1 Limit Order and Other Market Mechanisms ... 59 2.1.2 Market Rules and Jumps in Prices ........ 61 2.1.3 Sample Data: Transactions, Quotes and NBBO . 62 2.2 High-Frequency Data Distinctive Characteristics .... 64 2.2.1 Random Sampling Times ............. 65 2.2.2 Market Microstructure Noise and Data Errors . . 66 2.2.3 Non-normality ................... 67 2.3 Models for Market Microstructure Noise ......... 68 2.3.1 Additive Noise ................... 68 2.3.2 Rounding Errors .................. 72 2.4 Strategies to Mitigate the Impact of Noise ........ 73 2.4.1 Downsampling ................... 73 2.4.2 Filtering Transactions Using Quotes ....... 74 II Asymptotic Concepts 79 3 Introduction to Asymptotic Theory: Volatility Estima¬ tion for a Continuous Process 83 3.1 Estimating Integrated Volatility in Simple Cases .... 85 3.1.1 Constant Volatility ................. 85 3.1.2 Deterministic Time-Varying Volatility ...... 87 3-1.3 Stochastic Volatility Independent of the Driving Brownian Motion W ................ 88 3.1.4 From Independence to Dependence for the Stochastic Volatility ................ 90 3.2 Stable Convergence in Law ................ 91 3.3 Convergence for Stochastic Processes ........... 96 3.4 General Stochastic Volatility ............... 99 3.5 What If the Process Jumps? ................ 106 Contents їх 4 Vith Jumps: An Introduction to Power Variations 109 4.1 Power Variations ...................... 110 4.1.1 The Purely Discontinuous Case .......... Ill 4.1.2 The Continuous Case ............... 112 4.1.3 The Mixed Case .................. 113 4.2 Estimation in a Simple Parametric Example: Merton s Model ............................ 116 4.2.1 Some Intuition for the Identification or Lack Thereof: The Impact of High Frequency ..... 117 4.2.2 Asymptotic Efficiency in the Absence of Jumps . 119 4.2.3 Asymptotic Efficiency in the Presence of Jumps . 120 4.2.4 GMM Estimation .................. 122 4.2.5 GMM Estimation of Volatility with Power Varia¬ tions ......................... 124 4.3 References .......................... 130 5 High-Frequency Observations: Identifiability and Asymptotic Efficiency 131 5.1 Classical Parametric Models ................ 132 5.1.1 Identifiability .................... 133 5.1.2 Efficiency for Fully Identifiable Parametric Models 134 5.1.3 Efficiency for Partly Identifiable Parametric Mod¬ els ...... .................... 137 5.2 Identifiability for Levy Processes and the Blumenthal·- Getoor Indices ........................ 139 5.2.1 About Mutual Singularity of Laws of Levy Pro¬ cesses ........................ 139 5.2.2 The BlumenthaLGetoor Indices and Related Quantities for Levy Processes ........... 141 5.3 Discretely Observed Semimartingales: Identifiable Pa¬ rameters .......................... 144 5.3.1 Identifiable Parameters: A Definition ....... 145 5.3.2 Identifiable Parameters: Examples ........ 148 5.4 Tests: Asymptotic Properties ............... 151 5.5 Back to the Levy Case: Disentangling the Diffusion Part from Jumps ........................ 155 x Contents 5.5.1 The Parametric Case ............... 155 5.5.2 The Semi-Parametric Case ............ 156 5.6 Blumenthal-Getoor Indices for Levy Processes: Efficiency via Fisher s Information .................. 160 5.7 References .......................... 163 III Volatility 165 6 Estimating Integrated Volatility: The Base Case with. No Noise and Equidistant Observations 169 6.1 When the Process Is Continuous ............. 171 6.1-1 Feasible Estimation and Confidence Bounds . . . 173 6.1.2 The Multivariate Case ............... 176 6.1.3 About Estimation of the Quarticity ....... 177 6.2 When the Process Is Discontinuous ........... 179 6.2.1 Truncated Realized Volatility ........... 180 6.2.2 Choosing the Truncation Level: The One- Dimensional Case ................. 187 6.2.3 Multipower Variations ............... 191 6.2.4 Truncated Bipower Variations ........... 194 6.2.5 Comparing Truncated Realized Volatility and Multipower Variations .............. 196 6.3 Other Methods ....................... 197 6.3.1 Range-Based Volatility Estimators ........ 197 6.3.2 Range-Based Estimators in a Genuine High- Frequency Setting ................. 198 6.3.3 Nearest Neighbor Truncation ........... 199 6.3.4 Fourier-Based Estimators ............. 200 6.4 Finite Sample Refinements for Volatility Estimators . . 202 6.5 References .......................... 207 7 Volatility and IVIicrostructiire Noise 209 7.1 Models of Microstructure Noise .............. 211 7.1.1 Additive White Noise ............... 211 7.1.2 Additive Colored Noise .............. 212 7.1.3 Pure Rounding Noise ............... 213 7.1.4 A Mixed Case: Rounded White Noise ...... 215 7.1.5 Realized Volatility in the Presence of Noise . . . 216 Contents xi 7.2 Assumptions on the Noise ................. 220 7.3 Maximum-Likelihood and Quasi Maximum-Likelihood Estimation ......................... 224 7.3.1 A Toy Model: Gaussian Additive White Noise and Browman Motion ................. 224 7.3.2 Robustness of the MLE to Stochastic Volatility . 228 7.4 Quadratic Estimators ................... 231 7.5 Subsampling and Averaging: Two- S cales Realized Volatility .......................... 232 7.6 The Pre-averaging Method ................ 238 7.6.1 Pre- averaging and Optimality ........... 245 7.6.2 Adaptive Pre-averaging .............. 247 7.7 Flat Top Realized Kernels ................. 250 7.8 Multi-scales Estimators .................. 253 7.9 Estimation of the Quadratic Covariation ......... 254 7.10 References .......................... 256 8 Estimating Spot Volatility 259 8.1 Local Estimation of the Spot Volatility .......... 261 8.1.1 Some Heuristic Considerations .......... 261 8.1.2 Consistent Estimation ............... 265 8.1.3 Central Limit Theorem .............. 266 8.2 Global Methods for the Spot Volatility .......... 273 8.3 Volatility of Volatility ................... 274 8.4 Leverage: The Covariation between X and с ....... 279 8.5 Optimal Estimation of a Function of Volatility ..... 284 8.6 State-Dependent Volatility ................. 289 8.7 Spot Volatility and Microstructuxe Noise ......... 293 8.8 References .......................... 296 9 Volatility and Irregularly Spaced Observations 299 9.1 Irregular Observation Times: The One-Dimensional Case 301 9.1.1 About Irregular Sampling Schemes ........ 302 9.1.2 Estimation of the Integrated Volatility and Other Integrated Volatility Powers ............ 305 9.1.3 Irregular Observation Schemes: Time Changes . 309 9.2 The Multivariate Case: Non-synchronous Observations . 313 9.2.1 The Epps Effect .................. 314 9.2.2 The Hayashi-Yoshida Method ........... 315 9.2.3 Other Methods and Extensions .......... 320 хи Contents 9.3 References .......................... 323 IV Jumps 325 10 Testing for Jumps 329 10.1 Introduction ......................... 331 10.2 Relative Sizes of the Jump and Continuous Parts and Testing for Jumps ..................... 334 10.2.1 The Mathematical Tools .............. 334 10.2.2 A Linear Test for Jumps ............ 336 10.2.3 A Ratio Test for Jumps ............ 340 10.2.4 Relative Sizes of the Jump and Brownian Parts . 342 10.2.5 Testing the Null П^с) instead of Q^w) ..... 352 10.3 A Symmetrical Test for Jumps .............. 353 10.3.1 The Test Statistics Based on Power Variations . 353 10.3.2 Some Central Limit Theorems .......... 356 10.3.3 Testing the Null Hypothesis of No Jump ..... 360 10.3.4 Testing the Null Hypothesis of Presence of Jumps 362 10.3.5 Comparison of the Tests .............. 366 10.4 Detection of Jumps ..................... 368 10.4.1 Mathematical Background ............. 369 10.4.2 A Test for Jumps .................. 372 10.4.3 Finding the Jumps: The Finite Activity Case . . 373 10.4.4 The General Case ................. 376 10.5 Detection of Volatility Jumps ............... 378 10.6 Microstructure Noise and Jumps ............. 381 10.6.1 A Noise-Robust Jump Test Statistic ....... 382 10.6.2 The Central Limit Theorems for the Noise-Robust Jump Test ...................... 384 10.6.3 Testing the Null Hypothesis of No Jump in the Presence of Noise ................. 386 10.6.4 Testing the Null Hypothesis of Presence of Jumps in the Presence of Noise .............. 388 10.7 References .......................... 390 11 Finer Analysis of Jumps: The Degree of Jump Activity 393 11.1 The Model Assumptions .................. 395 11.2 Estimation of the First B G Index and of the Related Intensity ........................... 399 Contents xiii 11.2.1 Construction of the Estimators .......... 399 11.2.2 Asymptotic Properties ............... 404 11.2.3 How Far from Asymptotic Optimality ? ..... 407 11.2.4 The Truly Non-symmetric Case .......... 415 11.3 Successive B G Indices ................... 419 11.3 Л Preliminaries .................... 420 11.3.2 First Estimators .................. 422 11.3.3 Improved Estimators ................ 424 11.4 References .......................... 427 12 Finite or Infinite Activity for Jumps? 429 12.1 When the Null Hypothesis Is Finite Jump Activity . . . 430 12.2 When the Null Hypothesis Is Infinite Jump Activity . . 437 12.3 References .......................... 439 13 Is Brownian IVlotion Really Necessary? 441 13.1 Tests for the Null Hypothesis That the Brownian Is Present ........................... 443 13.2 Tests for the Null Hypothesis That the Brownian Is Absent 446 13.2.1 Adding a Fictitious Brownian ........... 448 13.2.2 Tests Based on Power Variations ......... 449 13.3 References .......................... 451 14 Co-jumps 453 14.1 Co-jumps for the Underlying Process . ......... 453 14.1.1 The Setting ..................... 453 14.1.2 Testing for Common Jumps ............ 456 14.1.3 Testing for Disjoint Jumps ............ 459 14.1.4 Some Open Problems ............... 463 14.2 Co-jumps between the Process and Its Volatility .... 464 14.2.1 Limit Theorems for Functionals of Jumps and Volatility ...................... 466 14.2.2 Testing the Null Hypothesis of No Cc-jump . . . 469 14.2.3 Testing the Null Hypothesis of the Presence of Co-jumps ...................... 473 14.3 References .......................... 474 A Asymptotic Results for Power Variations 477 A.I Setting and Assumptions ................. 477 A. 2 Laws of Large Numbers .................. 480 Contents Α. 2.1 LLNs for Power Variations and Related Function- als .......................... 480 A. 2.2 LLNs for the Integrated Volatility ........ 484 A. 2.3 LLNs for Estimating the Spot Volatility ..... 485 A.3 Central Limit Theorems .................. 488 A.3.1 CLTs for the Processes B{f,An) and £(ƒ, Δη) . 488 A.3. 2 A Degenerate Case ................. 490 A. 3.3 CLTs for the Processes B (f, Δη) and Л (/, Δη) 492 Α. 3.4 CLTs for the Quadratic Variation ......... 495 A. 4 Noise and Ρ re-aver aging: Limit Theorems ........ 496 A. 4.1 Assumptions on Noise and Pre- averaging Schemes 497 A.4.2 LLNs for Noise ................... 498 A. 4.3 CLTs for Noise ................... 500 A. 5 Localization and Strengthened Assumptions ....... 502 В Miscellaneous Proofs 507 B.I Proofs for Chapter 5.................... 507 B.I.I Proofs for Sections 5.2 and 5.3.......... 507 B.I. 2 Proofs for Section 5.5 ............... 513 B.1.3 Proof of Theorem 5.25............... 520 B.2 Proofs for Chapter 8.................... 531 B.2.1 Preliminaries .................... 531 B.2. 2 Estimates for the Increments of X and с ..... 535 В. 2.3 Estimates for the Spot Volatility Estimators . . . 538 B.2. 4 A Key Decomposition for Theorems 8.11 and 8.14 540 B.2. 5 Proof of Theorems 8.11 and 8.14 and Remark 8.15 547 B.2. 6 Proof of Theorems 8.12 and 8.17......... 553 B.2. 7 Proof of Theorem 8.20............... 554 B.3 Proofs for Chapter 10 ................... 557 B.3.1 Proof of Theorem 10.12.............. 557 B.3. 2 Proofs for Section 10.3............... 564 B.3.3 Proofs for Section 10.4............... 568 B.3. 4 Proofs for Section 10.5................ 573 B.4 Limit Theorems for the Jumps of an Ito Semimartingale 578 B.5 A Comparison Between Jumps and Increments ..... 583 B.6 Proofs for Chapter 11 ................... 593 B.6.1 Proof of Theorems 11.11, 11.12, 11.18, 11.19, and Remark 11.14.................... 593 B.6. 2 Proof of Theorem 11.21.............. 597 B.6.3 Proof of Theorem 11.23.............. 600 Contents xv В. 7 Proofs for Chapter 12 ................... 604 B.8 Proofs for Chapter 13 ................... 612 B.9 Proofs for Chapter 14................... 614 B.9.1 Proofs for Section 14.1............... 614 B.9. 2 Proofs for Section 14.2............... 619 Bibliography 633 Index 657
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spellingShingle	Aït-Sahalia, Yacine Jacod, Jean 1944- High frequency financial econometrics Ökonometrie (DE-588)4132280-0 gnd Ökonometrisches Modell (DE-588)4043212-9 gnd Finanzwirtschaft (DE-588)4017214-4 gnd
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title	High frequency financial econometrics
title_alt	High-frequency financial econometrics
title_auth	High frequency financial econometrics
title_exact_search	High frequency financial econometrics
title_full	High frequency financial econometrics Yacine Aït-Sahalia & Jean Jacod
title_fullStr	High frequency financial econometrics Yacine Aït-Sahalia & Jean Jacod
title_full_unstemmed	High frequency financial econometrics Yacine Aït-Sahalia & Jean Jacod
title_short	High frequency financial econometrics
title_sort	high frequency financial econometrics
topic	Ökonometrie (DE-588)4132280-0 gnd Ökonometrisches Modell (DE-588)4043212-9 gnd Finanzwirtschaft (DE-588)4017214-4 gnd
topic_facet	Ökonometrie Ökonometrisches Modell Finanzwirtschaft
url	http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=027535608&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA
work_keys_str_mv	AT aitsahaliayacine highfrequencyfinancialeconometrics AT jacodjean highfrequencyfinancialeconometrics

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