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E-grāmata: Handbook of Volatility Models and Their Applications

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The main purpose of this handbook is to illustrate the mathematically fundamental implementation of various volatility models in the banking and financial industries, both at home and abroad, through use of real-world, time-sensitive applications. Conceived and written by over two-dozen experts in the field, the focus is to cohesively demonstrate how volatile certain statistical decision-making techniques can be when solving a range of financial problems. By using examples derived from consulting projects, current research and course instruction, each chapter in the book offers a systematic understanding of the recent advances in volatility modeling related to real-world situations. Every effort is made to present a balanced treatment between theory and practice, as well as to showcase how accuracy and efficiency in implementing various methods can be used as indispensable tools in assessing volatility rates. Unique to the book is in-depth coverage of GARCH-family models, contagion, and model comparisons between different volatility models. To by-pass tedious computation, software illustrations are presented in an assortment of packages, ranging from R, C++, EXCEL-VBA, Minitab, to JMP/SAS-- 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 marketsOther Models and Methods presents alternative approaches, such as multiplicative error models, nonparametric and semi-parametric models, and copula-based models of (co)volatilitiesRealized Volatility explores issues of the measurement of volatility by realized variances and covariances, guiding readers on how to successfully model and forecast these measuresHandbook 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.

Recenzijas

"Conceived and written by over two-dozen experts in the fi eld, the book cohesively demonstrates how 'volatile' certain statistical decision-making techniques can be when solving a range of financial problems." (Zentralblatt MATH 2016)

Preface xvii
Contributors xix
1 Volatility Models
1(48)
1.1 Introduction
1(1)
1.2 GARCH
1(24)
1.2.1 Univariate GARCH
1(2)
1.2.1.1 Structure of GARCH Models
3(2)
1.2.1.2 Early GARCH Models
5(2)
1.2.1.3 Probability Distributions for zt
7(2)
1.2.1.4 New GARCH Models
9(6)
1.2.1.5 Explanation of Volatility Clustering
15(1)
1.2.1.6 Literature and Software
16(1)
1.2.1.7 Applications of Univariate GARCH
16(2)
1.2.2 Multivariate GARCH
18(1)
1.2.2.1 Structure of MGARCH Models
19(1)
1.2.2.2 Conditional Correlations
19(4)
1.2.2.3 Factor Models
23(2)
1.3 Stochastic Volatility
25(8)
1.3.1 Leverage Effect
26(1)
1.3.2 Estimation
27(1)
1.3.3 Multivariate SV Models
28(2)
1.3.4 Model Selection
30(1)
1.3.5 Empirical Example: S&P 500
31(1)
1.3.6 Literature
32(1)
1.4 Realized Volatility
33(16)
1.4.1 Realized Variance
33(7)
1.4.1.1 Empirical Application
40(4)
1.4.2 Realized Covariance
44(1)
1.4.2.1 Realized Quadratic Covariation
44(1)
1.4.2.2 Realized Bipower Covariation
44(1)
Acknowledgments
45(4)
PART ONE Autoregressive Conditional Heteroskedasticity and Stochastic Volatility
2 Nonlinear Models for Autoregressive Conditional Heteroskedasticity
49(22)
2.1 Introduction
49(1)
2.2 The Standard GARCH Model
50(1)
2.3 Predecessors to Nonlinear GARCH Models
51(1)
2.4 Nonlinear ARCH and GARCH Models
52(8)
2.4.1 Engle's Nonlinear GARCH Model
52(1)
2.4.2 Nonlinear ARCH Model
53(1)
2.4.3 Asymmetric Power GARCH Model
53(1)
2.4.4 Smooth Transition GARCH Model
54(2)
2.4.5 Double Threshold ARCH Model
56(1)
2.4.6 Neural Network ARCH and GARCH Models
57(1)
2.4.7 Time-Varying GARCH
58(1)
2.4.8 Families of GARCH Models and their Probabilistic Properties
59(1)
2.5 Testing Standard GARCH Against Nonlinear GARCH
60(3)
2.5.1 Size and Sign Bias Tests
60(1)
2.5.2 Testing GARCH Against Smooth Transition GARCH
61(1)
2.5.3 Testing GARCH Against Artificial Neural Network GARCH
62(1)
2.6 Estimation of Parameters in Nonlinear GARCH Models
63(1)
2.6.1 Smooth Transition GARCH
63(1)
2.6.2 Neural Network GARCH
64(1)
2.7 Forecasting with Nonlinear GARCH Models
64(3)
2.7.1 Smooth Transition GARCH
64(2)
2.7.2 Asymmetric Power GARCH
66(1)
2.8 Models Based on Multiplicative Decomposition of the Variance
67(1)
2.9 Conclusion
68(3)
Acknowledgments
69(2)
3 Mixture and Regime-Switching GARCH Models
71(32)
3.1 Introduction
71(2)
3.2 Regime-Switching GARCH Models for Asset Returns
73(8)
3.2.1 The Regime-Switching Framework
73(2)
3.2.2 Modeling the Mixing Weights
75(3)
3.2.3 Regime-Switching GARCH Specifications
78(3)
3.3 Stationarity and Moment Structure
81(8)
3.3.1 Stationarity
83(4)
3.3.2 Moment Structure
87(2)
3.4 Regime Inference, Likelihood Function, and Volatility Forecasting
89(8)
3.4.1 Determining the Number of Regimes
92(1)
3.4.2 Volatility Forecasts
92(1)
3.4.3 Application of MS-GARCH Models to Stock Return Indices
93(4)
3.5 Application of Mixture GARCH Models to Density Prediction and Value-at-Risk Estimation
97(5)
3.5.1 Value-at-Risk
97(1)
3.5.2 Data and Models
98(1)
3.5.3 Empirical Results
99(3)
3.6 Conclusion
102(1)
Acknowledgments
102(1)
4 Forecasting High Dimensional Covariance Matrices
103(24)
4.1 Introduction
103(1)
4.2 Notation
104(1)
4.3 Rolling Window Forecasts
104(5)
4.3.1 Sample Covariance
105(1)
4.3.2 Observable Factor Covariance
105(1)
4.3.3 Statistical Factor Covariance
106(1)
4.3.4 Equicorrelation
107(1)
4.3.5 Shrinkage Estimators
108(1)
4.4 Dynamic Models
109(8)
4.4.1 Covariance Targeting Scalar VEC
109(1)
4.4.2 Flexible Multivariate GARCH
110(1)
4.4.3 Conditional Correlation GARCH Models
111(2)
4.4.4 Orthogonal GARCH
113(1)
4.4.5 RiskMetrics
114(2)
4.4.6 Alternative Estimators for Multivariate GARCH Models
116(1)
4.5 High Frequency Based Forecasts
117(6)
4.5.1 Realized Covariance
118(1)
4.5.2 Mixed-Frequency Factor Model Covariance
119(1)
4.5.3 Regularization and Blocking Covariance
119(4)
4.6 Forecast Evaluation
123(2)
4.6.1 Portfolio Constraints
124(1)
4.7 Conclusion
125(2)
Acknowledgments
125(2)
5 Mean, Volatility, and Skewness Spillovers in Equity Markets
127(20)
5.1 Introduction
127(2)
5.2 Data and Summary Statistics
129(9)
5.2.1 Data
129(3)
5.2.2 Time-Varying Skewness (Univariate Analysis)
132(3)
5.2.3 Spillover Models
135(3)
5.3 Empirical Results
138(6)
5.3.1 Parameter Estimates
138(1)
5.3.2 Spillover Effects in Variance and Skewness
139(1)
5.3.2.1 Variance Ratios
139(2)
5.3.2.2 Pattern and Size of Skewness Spillovers
141(3)
5.4 Conclusion
144(3)
Acknowledgments
145(2)
6 Relating Stochastic Volatility Estimation Methods
147(28)
6.1 Introduction
147(2)
6.2 Theory and Methodology
149(11)
6.2.1 Quasi-Maximum Likelihood Estimation
150(1)
6.2.2 Gaussian Mixture Sampling
151(1)
6.2.3 Simulated Method of Moments
152(1)
6.2.4 Methods Based on Importance Sampling
153(1)
6.2.4.1 Approximating in the Basic IS Approach
154(1)
6.2.4.2 Improving on IS with IIS
155(1)
6.2.4.3 Alternative Efficiency Gains with EIS
156(2)
6.2.5 Alternative Sampling Methods: SSS and MMS
158(2)
6.3 Comparison of Methods
160(5)
6.3.1 Setup of Data-Generating Process and Estimation Procedures
160(1)
6.3.2 Parameter Estimates for the Simulation
161(2)
6.3.3 Precision of IS
163(1)
6.3.4 Precision of Bayesian Methods
164(1)
6.4 Estimating Volatility Models in Practice
165(7)
6.4.1 Describing Return Data of Goldman Sachs and IBM Stock
165(2)
6.4.2 Estimating SV Models
167(1)
6.4.3 Extracting Underlying Volatility
168(1)
6.4.4 Relating the Returns in a Bivariate Model
169(3)
6.5 Conclusion
172(3)
7 Multivariate Stochastic Volatility Models
175(24)
7.1 Introduction
175(1)
7.2 MSV Model
176(7)
7.2.1 Model
176(1)
7.2.1.1 Likelihood Function
177(1)
7.2.1.2 Prior Distribution
178(1)
7.2.1.3 Posterior Distribution
179(1)
7.2.2 Bayesian Estimation
179(1)
7.2.2.1 Generation of α
179(2)
7.2.2.2 Generation of θ
181(1)
7.2.2.3 Generation of Σ
181(1)
7.2.3 Multivariate-t Errors
181(1)
7.2.3.1 Generation of ν
182(1)
7.2.3.2 Generation of λ
183(1)
7.3 Factor MSV Model
183(5)
7.3.1 Model
183(1)
7.3.1.1 Likelihood Function
184(1)
7.3.1.2 Prior and Posterior Distributions
185(1)
7.3.2 Bayesian Estimation
185(1)
7.3.2.1 Generation of α, θ, and Σ
186(1)
7.3.2.2 Generation of f
187(1)
7.3.2.3 Generation of λ
187(1)
7.3.2.4 Generation of β
188(1)
7.3.2.5 Generation of ν
188(1)
7.4 Applications to Stock Indices Returns
188(7)
7.4.1 S&P 500 Sector Indices
188(1)
7.4.2 MSV Model with Multivariate t Errors
189(1)
7.4.2.1 Prior Distributions
189(1)
7.4.2.2 Estimation Results
189(3)
7.4.3 Factor MSV Model
192(1)
7.4.3.1 Prior Distributions
192(1)
7.4.3.2 Estimation Results
192(3)
7.5 Conclusion
195(1)
7.6 Appendix: Sampling α in the MSV Model
195(4)
7.6.1 Single-Move Sampler
195(1)
7.6.2 Multi-move Sampler
196(3)
8 Model Selection and Testing of Conditional and Stochastic Volatility Models
199(26)
8.1 Introduction
199(3)
8.1.1 Model Specifications
200(2)
8.2 Model Selection and Testing
202(9)
8.2.1 In-Sample Comparisons
202(4)
8.2.2 Out-of-Sample Comparisons
206(1)
8.2.2.1 Direct Model Evaluation
206(3)
8.2.2.2 Indirect Model Evaluation
209(2)
8.3 Empirical Example
211(10)
8.4 Conclusion
221(4)
PART TWO Other Models and Methods
9 Multiplicative Error Models
225(24)
9.1 Introduction
225(1)
9.2 Theory and Methodology
226(9)
9.2.1 Model Formulation
226(1)
9.2.1.1 Specifications for μt
227(3)
9.2.1.2 Specifications for εt
230(1)
9.2.2 Inference
230(1)
9.2.2.1 Maximum Likelihood Inference
230(3)
9.2.2.2 Generalized Method of Moments Inference
233(2)
9.3 MEMs for Realized Volatility
235(7)
9.4 MEM Extensions
242(5)
9.4.1 Component Multiplicative Error Model
242(1)
9.4.2 Vector Multiplicative Error Model
243(4)
9.5 Conclusion
247(2)
10 Locally Stationary Volatility Modeling
249(20)
10.1 Introduction
249(2)
10.2 Empirical Evidences
251(5)
10.2.1 Structural Breaks, Nonstationarity, and Persistence
251(2)
10.2.2 Testing Stationarity
253(3)
10.3 Locally Stationary Processes and their Time-Varying Autocovariance Function
256(4)
10.4 Locally Stationary Volatility Models
260(6)
10.4.1 Multiplicative Models
260(1)
10.4.2 Time-Varying ARCH Processes
261(3)
10.4.3 Adaptive Approaches
264(2)
10.5 Multivariate Models for Locally Stationary Volatility
266(1)
10.5.1 Multiplicative Models
266(1)
10.5.2 Adaptive Approaches
267(1)
10.6 Conclusions
267(2)
Acknowledgments
268(1)
11 Nonparametric and Semiparametric Volatility Models: Specification, Estimation, and Testing
269(24)
11.1 Introduction
269(2)
11.2 Nonparametric and Semiparametric Univariate Volatility Models
271(13)
11.2.1 Stationary Volatility Models
271(1)
11.2.1.1 The Simplest Nonparametric Volatility Model
271(2)
11.2.1.2 Additive Nonparametric Volatility Model
273(3)
11.2.1.3 Functional-Coefficient Volatility Model
276(1)
11.2.1.4 Single-Index Volatility Model
277(1)
11.2.1.5 Stationary Semiparametric ARCH (∞) Models
278(1)
11.2.1.6 Semiparametric Combined Estimator of Volatility
279(1)
11.2.1.7 Semiparametric Inference in GARCH-in-Mean Models
280(1)
11.2.2 Nonstationary Univariate Volatility Models
281(1)
11.2.3 Specification of the Error Density
282(1)
11.2.4 Nonparametric Volatility Density Estimation
283(1)
11.3 Nonparametric and Semiparametric Multivariate Volatility Models
284(4)
11.3.1 Modeling the Conditional Covariance Matrix under Stationarity
285(1)
11.3.1.1 Hafner, van Dijk, and Franses' Semiparametric Estimator
285(1)
11.3.1.2 Long, Su, and Ullah's Semiparametric Estimator
286(1)
11.3.1.3 Test for the Correct Specification of Parametric Conditional Covariance Models
286(1)
11.3.2 Specification of the Error Density
287(1)
11.4 Empirical Analysis
288(3)
11.5 Conclusion
291(2)
Acknowledgments
291(2)
12 Copula-Based Volatility Models
293(26)
12.1 Introduction
293(1)
12.2 Definition and Properties of Copulas
294(6)
12.2.1 Sklar's Theorem
295(1)
12.2.2 Conditional Copula
296(1)
12.2.3 Some Commonly Used Bivariate Copulas
296(2)
12.2.4 Copula-Based Dependence Measures
298(2)
12.3 Estimation
300(4)
12.3.1 Exact Maximum Likelihood
300(1)
12.3.2 IFM
301(1)
12.3.3 Bivariate Static Copula Models
301(3)
12.4 Dynamic Copulas
304(4)
12.4.1 Early Approaches
305(1)
12.4.2 Dynamics Based on the DCC Model
305(2)
12.4.3 Alternative Methods
307(1)
12.5 Value-at-Risk
308(2)
12.6 Multivariate Static Copulas
310(5)
12.6.1 Multivariate Archimedean Copulas
310(3)
12.6.2 Vines
313(2)
12.7 Conclusion
315(4)
PART THREE Realized Volatility
13 Realized Volatility: Theory and Applications
319(28)
13.1 Introduction
319(1)
13.2 Modeling Framework
320(3)
13.2.1 Efficient Price
320(2)
13.2.2 Measurement Error
322(1)
13.3 Issues in Handling Intraday Transaction Databases
323(6)
13.3.1 Which Price to Use?
324(2)
13.3.2 High Frequency Data Preprocessing
326(1)
13.3.3 How to and How Often to Sample?
326(3)
13.4 Realized Variance and Covariance
329(8)
13.4.1 Univariate Volatility Estimators
329(1)
13.4.1.1 Measurement Error
330(3)
13.4.2 Multivariate Volatility Estimators
333(3)
13.4.2.1 Measurement Error
336(1)
13.5 Modeling and Forecasting
337(3)
13.5.1 Time Series Models of (co) Volatility
337(2)
13.5.2 Forecast Comparison
339(1)
13.6 Asset Pricing
340(4)
13.6.1 Distribution of Returns Conditional on the Volatility Measure
340(1)
13.6.2 Application to Factor Pricing Model
341(1)
13.6.3 Effects of Algorithmic Trading
342(1)
13.6.4 Application to Option Pricing
342(2)
13.7 Estimating Continuous Time Models
344(3)
14 Likelihood-Based Volatility Estimators in the Presence of Market Microstructure Noise
347(16)
14.1 Introduction
347(2)
14.2 Volatility Estimation
349(7)
14.2.1 Constant Volatility and Gaussian Noise Case: MLE
349(2)
14.2.2 Robustness to Non-Gaussian Noise
351(1)
14.2.3 Implementing Maximum Likelihood
351(1)
14.2.4 Robustness to Stochastic Volatility: QMLE
352(3)
14.2.5 Comparison with Other Estimators
355(1)
14.2.6 Random Sampling and Non-i.i.d. Noise
356(1)
14.3 Covariance Estimation
356(3)
14.4 Empirical Application: Correlation between Stock and Commodity Futures
359(1)
14.5 Conclusion
360(3)
Acknowledgments
361(2)
15 HAR Modeling for Realized Volatility Forecasting
363(20)
15.1 Introduction
363(2)
15.2 Stylized Facts on Realized Volatility
365(1)
15.3 Heterogeneity and Volatility Persistence
366(4)
15.3.1 Genuine Long Memory or Superposition of Factors?
369(1)
15.4 HAR Extensions
370(5)
15.4.1 Jump Measures and Their Volatility Impact
370(2)
15.4.2 Leverage Effects
372(1)
15.4.3 General Nonlinear Effects in Volatility
373(2)
15.5 Multivariate Models
375(3)
15.6 Applications
378(3)
15.7 Conclusion
381(2)
16 Forecasting Volatility with MIDAS
383(20)
16.1 Introduction
383(1)
16.2 MIDAS Regression Models and Volatility Forecasting
384(7)
16.2.1 MIDAS Regressions
384(2)
16.2.2 Direct Versus Iterated Volatility Forecasting
386(3)
16.2.3 Variations on the Theme of MIDAS Regressions
389(1)
16.2.4 Microstructure Noise and MIDAS Regressions
390(1)
16.3 Likelihood-Based Methods
391(8)
16.3.1 Risk-Return Trade-Off
391(2)
16.3.2 HYBRID GARCH Models
393(5)
16.3.3 GARCH-MIDAS Models
398(1)
16.4 Multivariate Models
399(2)
16.5 Conclusion
401(2)
17 Jumps
403(44)
17.1 Introduction
403(8)
17.1.1 Some Models Used in Finance and Our Framework
403(4)
17.1.2 Simulated Models Used in This
Chapter
407(2)
17.1.3 Realized Variance and Quadratic Variation
409(1)
17.1.4 Importance of Disentangling
410(1)
17.1.5 Further Notation
411(1)
17.2 How to Disentangle: Estimators of Integrated Variance and Integrated Covariance
411(22)
17.2.1 Bipower Variation
413(3)
17.2.2 Threshold Estimator
416(3)
17.2.3 Threshold Bipower Variation
419(2)
17.2.4 Other Methods
421(1)
17.2.4.1 Realized Quantile
421(1)
17.2.4.2 MinRV and MedRV
422(1)
17.2.4.3 Realized Outlyingness Weighted Variation
422(1)
17.2.4.4 Range Bipower Variation
423(1)
17.2.4.5 Generalization of the Realized Range
424(1)
17.2.4.6 Duration-Based Variation
425(1)
17.2.4.7 Irregularly Spaced Observations
425(1)
17.2.5 Comparative Implementation on Simulated Data
426(1)
17.2.6 Noisy Data
427(5)
17.2.7 Multivariate Assets
432(1)
17.3 Testing for the Presence of Jumps
433(11)
17.3.1 Confidence Intervals
434(1)
17.3.2 Tests Based on IVn -- RVn or on 1 -- IVn/RVn
434(2)
17.3.3 Tests Based on Normalized Returns
436(3)
17.3.4 PV-Based Tests
439(1)
17.3.4.1 Remarks
440(1)
17.3.5 Tests Based on Signature Plots
441(1)
17.3.6 Tests Based on Observation of Option Prices
442(1)
17.3.6.1 Remarks
442(1)
17.3.7 Indirect Test for the Presence of Jumps
443(1)
17.3.7.1 In the Presence of Noise
443(1)
17.3.8 Comparisons
443(1)
17.4 Conclusions
444(3)
Acknowledgments
445(2)
18 Nonparametric Tests for Intraday Jumps: Impact of Periodicity and Microstructure Noise
447(18)
18.1 Introduction
447(2)
18.2 Model
449(1)
18.3 Price Jump Detection Method
450(5)
18.3.1 Estimation of the Noise Variance
451(1)
18.3.2 Robust Estimators of the Integrated Variance
451(1)
18.3.3 Periodicity Estimation
452(2)
18.3.4 Jump Test Statistics
454(1)
18.3.5 Critical Value
454(1)
18.4 Simulation Study
455(5)
18.4.1 Intraday Differences in the Value of the Test Statistics
455(2)
18.4.2 Comparison of Size and Power
457(1)
18.4.3 Simulation Setup
457(1)
18.4.4 Results
458(2)
18.5 Comparison on NYSE Stock Prices
460(2)
18.6 Conclusion
462(3)
19 Volatility Forecasts Evaluation and Comparison
465(22)
19.1 Introduction
465(2)
19.2 Notation
467(1)
19.3 Single Forecast Evaluation
468(3)
19.4 Loss Functions and the Latent Variable Problem
471(3)
19.5 Pairwise Comparison
474(3)
19.6 Multiple Comparison
477(4)
19.7 Consistency of the Ordering and Inference on Forecast Performances
481(4)
19.8 Conclusion
485(2)
Bibliography 487(50)
Index 537
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.
Biežāk uzdotie jautājumi par e-grāmatām Biežāk uzdotie jautājumi par e-grāmatām
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