Handbook of Volatility Models and Their Applications

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