A complete guide to the theory and practice of volatility models in financial engineering
Volatility has become a hot topic in this era of instant communications, spawning a great deal of research in empirical finance and time series econometrics. Providing an overview of the most recent advances, Handbook of Volatility Models and Their Applications explores key concepts and topics essential for modeling the volatility of financial time series, both univariate and multivariate, parametric and non-parametric, high-frequency and low-frequency.
Featuring contributions from international experts in the field, the book features numerous examples and applications from real-world projects and cutting-edge research, showing step by step how to use various methods accurately and efficiently when assessing volatility rates. Following a comprehensive introduction to the topic, readers are provided with three distinct sections that unify the statistical and practical aspects of volatility:
* Autoregressive Conditional Heteroskedasticity and Stochastic Volatility presents ARCH and stochastic volatility models, with a focus on recent research topics including mean, volatility, and skewness spillovers in equity markets
* Other Models and Methods presents alternative approaches, such as multiplicative error models, nonparametric and semi-parametric models, and copula-based models of (co)volatilities
* Realized Volatility explores issues of the measurement of volatility by realized variances and covariances, guiding readers on how to successfully model and forecast these measures
Handbook of Volatility Models and Their Applications is an essential reference for academics and practitioners in finance, business, and econometrics who work with volatility models in their everyday work. The book also serves as a supplement for courses on risk management and volatility at the upper-undergraduate and graduate levels.

1. Volatility Models 1

1.1 Introduction 1

1.2 GARCH 1

1.3 Stochastic Volatility 31

1.4 Realized Volatility 42

Part I. ARCH and SV

2. Nonlinear ARCH Models 63

2.1 Introduction 63

2.2 Standard GARCH model 64

2.3 Predecessors to Nonlinear GARCH 65

2.4 Nonlinear ARCH and GARCH 67

2.5 Testing 76

2.6 Estimation 81

2.7 Forecasting 83

2.8 Multiplicative Decomposition 86

2.9 Conclusion 88

3. Mixture and Regime-switching GARCH Models 89

3.1 Introduction 89

3.2 Regime-switching GARCH models 92

3.3 Stationarity and Moment Structure 102

3.4 Regime Inference, Likelihood Functions, and Volatility Forecasting 111

3.5 Application of Mixture GARCH Models 119

3.6 Conclusion 124

4. Forecasting High Dimensional Covariance Matrices 129

4.1 Introduction 129

4.2 Notation 130

4.3 Rolling-Window Forecasts 131

4.4 Dynamic Models 136

4.5 High-Frequency Based Forecasts 147

4.6 Forecast Evaluation 154

4.7 Conclusion 157

5. Mean, Volatility and Skewness Spillovers in Equity Markets 159

5.1 Introduction 159

5.2 Data and Summary Statistics 162

5.3 Empirical Results 171

5.4 Conclusion 177

6. Relating Stochastic Volatility Estimation Methods 185

6.1 Introduction 185

6.2 Theory and Methodology 188

6.3 Comparison of Methods 201

6.4 Estimating Volatility Models in Practice 209

6.5 Conclusion 217

7. Multivariate Stochastic Volatility Models 221

7.1 Introduction 221

7.2 MSV model 223

7.3 Factor MSV model 231

7.4 Applications to Stock Indices Returns 237

7.5 Conclusion 244

8. Model Selection and Testing of Volatility Models 249

8.1 Introduction 249

8.2 Model Selection and Testing 252

8.3 Empirical Example 265

8.4 Conclusion 277

Part II. Other models and methods

9. Multiplicative Error Models 281

9.1 Introduction 281

9.2 Theory and Methodology 283

9.3 MEM Application 293

9.4 MEM Extensions 302

9.5 Conclusion 308

10. Locally Stationary Volatility Modeling 311

10.1 Introduction 311

10.2 Empirical evidences 314

10.3 Locally Stationary Processes 319

10.4 Locally Stationary Volatility Models 323

10.5 Multivariate Models for Locally Stationary Volatility 331

10.6 Conclusion 333

11. Nonparametric and Semiparametric Volatility Models 335

11.1 Introduction 335

11.2 Nonparametric and Semiparametric Univariate Models 338

11.3 Nonparametric and Semiparametric Multivariate Volatility Models 354

11.4 Empirical Analysis 360

11.5 Conclusion 363

12. Copula-based Volatility Models 367

12.1 Introduction 367

12.2 Definition and Properties of Copulas 369

12.3 Estimation 375

12.4 Dynamic Copulas 381

12.5 Value-at-Risk 387

12.6 Multivariate Static copulas 389

12.7 Conclusion 395

Part III. Realized Volatility

13. Realized Volatility: Theory and Applications 399

13.1 Introduction 399

13.2 Modelling Framework 400

13.3 Issues in Handling Intra-day Transaction Databases 404

13.4 Realized Variance and Covariance 411

14.5 Modelling and Forecasting 422

13.6 Asset Pricing 426

13.7 Estimating Continuous Time Models 431

14. Likelihood-Based Volatility Estimators 435

14.1 Introduction 435

14.2 Volatility Estimation 438

14.3 Covariance Estimation 447

14.4 Empirical Application 450

14.5 Conclusion 452

15. HAR Modeling for Realized Volatility Forecasting 453

15.1 Introduction 453

15.2 Stylized Facts 455

15.3 Heterogeneity and Volatility Persistence 457

15.4 HAR Extensions 463

15.5 Multivariate Models 469

15.6 Applications 473

15.7 Conclusion 478

16. Forecasting volatility with MIDAS 481

16.1 Introduction 481

16.2 MIDAS Regression Models and Volatility Forecasting 482

16.3 Likelihood-based Methods 492

16.4 Multivariate Models 505

16.5 Conclusion 507

17. Jumps 509

17.1 Introduction 509

17.2 Estimators of Integrated Variance and Integrated Covariance 519

17.3 Testing for the Presence of Jumps 548

17.4 Conclusion 563

18. Jumps, Periodicity and Microstructure Noise 565

18.1 Introduction 565

18.2 Model 568

18.3 Price Jump Detection Method 570

18.4 Simulation Study 576

18.5 Comparison on NYSE-Stock Prices 581

18.6 Conclusion 583

19. Volatility Forecasts Evaluation and Comparison 585

19.1 Introduction 585

19.2 Notation 588

19.3 Single Forecast Evaluation 590

19.4 Loss Functions and the Latent Variable Problem 593

19.5 Pairwise Comparison 597

19.6 Multiple Comparison 601

19.7 Consistency of the Ordering and Inference on Forecast Performances 607

19.8 Conclusion 613

Index 615

Bibliography 629 

Luc Bauwens, PhD, is Professor of Economics at the Université catholique de Louvain (Belgium), where he is also President of the Center for Operations Research and Econometrics (CORE). He has written more than 100 published papers on the topics of econometrics, statistics, and microeconomics.

Christian Hafner, PhD, is Professor and President of the Louvain School of Statistics, Biostatistics, and Actuarial Science (LSBA) at the Université catholique de Louvain (Belgium). He has published extensively in the areas of time series econometrics, applied nonparametric statistics, and empirical finance.

Sebastien Laurent, PhD, is Associate Professor of Econometrics in the Department of Quantitative Economics at Maastricht University (The Netherlands). Dr. Laurent's current areas of research interest include financial econometrics and computational econometrics.