Calvet / Fisher Multifractal Volatility

Theory, Forecasting, and Pricing
1. Auflage 2008
ISBN: 978-0-08-055996-4
Verlag: Elsevier Science & Techn.
Format: PDF
Kopierschutz: 1 - PDF Watermark

E-Book, Englisch, 272 Seiten, Web PDF

Calvet and Fisher present a powerful, new technique for volatility forecasting that draws on insights from the use of multifractals in the natural sciences and mathematics and provides a unified treatment of the use of multifractal techniques in finance. A large existing literature (e.g., Engle, 1982; Rossi, 1995) models volatility as an average of past shocks, possibly with a noise component. This approach often has difficulty capturing sharp discontinuities and large changes in financial volatility. Their research has shown the advantages of modelling volatility as subject to abrupt regime changes of heterogeneous durations. Using the intuition that some economic phenomena are long-lasting while others are more transient, they permit regimes to have varying degrees of persistence. By drawing on insights from the use of multifractals in the natural sciences and mathematics, they show how to construct high-dimensional regime-switching models that are easy to estimate, and substantially outperform some of the best traditional forecasting models such as GARCH. The goal of their book is to popularize the approach by presenting these exciting new developments to a wider audience. They emphasize both theoretical and empirical applications, beginning with a style that is easily accessible and intuitive in early chapters, and extending to the most rigorous continuous-time and equilibrium pricing formulations in final chapters.
· Presents a powerful new technique for forecasting volatility
· Leads the reader intuitively from existing volatility techniques to the frontier of research in this field by top scholars at major universities.
· The first comprehensive book on multifractal techniques in finance, a cutting-edge field of research

Autoren/Hrsg.

Calvet, Laurent E.

Fisher, Adlai J.

Inhaltsverzeichnis

1;Front Cover;1
2;Multifractal Volatility;4
3;Copyright Page;5
4;Table of Contents;6
5;Acknowledgments;10
6;Foreword;12
7;Credits and Copyright Exceptions;15
8;Chapter 1. Introduction;16
8.1;1.1 Empirical Properties of Financial Returns;16
8.2;1.2 Modeling Multifrequency Volatility;19
8.3;1.3 Pricing Multifrequency Risk;21
8.4;1.4 Contributions to Multifractal Literature;22
8.5;1.5 Organization of the Book;23
9;Part 1: Discrete Time;26
9.1;Chapter 2. Background: Discrete-Time Volatility Modeling;28
9.1.1;2.1 Autoregressive Volatility Modeling;28
9.1.2;2.2 Markov-Switching Models;31
9.2;Chapter 3. The Markov-Switching Multifractal (MSM) in Discrete Time;34
9.2.1;3.1 The MSM Model of Stochastic Volatility;35
9.2.1.1;3.1.1 Definition;35
9.2.1.2;3.1.2 Basic Properties;37
9.2.1.3;3.1.3 Low-Frequency Components and Long Memory;37
9.2.2;3.2 Maximum Likelihood Estimation;40
9.2.2.1;3.2.1 Updating the State Vector;40
9.2.2.2;3.2.2 Closed-Form Likelihood;41
9.2.3;3.3 Empirical Results;41
9.2.3.1;3.3.1 Currency Data;42
9.2.3.2;3.3.2 ML Estimation Results;42
9.2.3.3;3.3.3 Model Selection;47
9.2.4;3.4 Comparison with Alternative Models;49
9.2.4.1;3.4.1 In-Sample Comparison;50
9.2.4.2;3.4.2 Out-of-Sample Forecasts;50
9.2.4.3;3.4.3 Comparison with FIGARCH;57
9.2.5;3.5 Discussion;61
9.3;Chapter 4. Multivariate MSM;64
9.3.1;4.1 Comovement of Univariate Volatility Components;65
9.3.1.1;4.1.1 Comovement of Exchange Rate Volatility;65
9.3.1.2;4.1.2 Currency Volatility and Macroeconomic Indicators;70
9.3.2;4.2 A Bivariate Multifrequency Model;75
9.3.2.1;4.2.1 The Stochastic Volatility Specification;75
9.3.2.2;4.2.2 Properties;77
9.3.3;4.3 Inference;78
9.3.3.1;4.3.1 Closed-Form Likelihood;78
9.3.3.2;4.3.2 Particle Filter;78
9.3.3.3;4.3.3 Simulated Likelihood;79
9.3.3.4;4.3.4 Two-Step Estimation;81
9.3.4;4.4 Empirical Results;82
9.3.4.1;4.4.1 Bivariate MSM Estimates;82
9.3.4.2;4.4.2 Specification Tests;86
9.3.4.3;4.4.3 Out-of-Sample Diagnostics;88
9.3.4.4;4.4.4 Value-at-Risk;90
9.3.5;4.5 Discussion;92
10;Part 2: Continuous Time;94
10.1;Chapter 5. Background: Continuous-Time Volatility Modeling, Fractal Processes, and Multifractal Measures;96
10.1.1;5.1 Continuous-Time Models of Asset Prices;97
10.1.1.1;5.1.1 Brownian Motion, Time Deformation, and Jump-Diffusions;97
10.1.1.2;5.1.2 Self-Similar (Fractal) Processes;98
10.1.2;5.2 Multifractal Measures;99
10.1.2.1;5.2.1 The Binomial Measure;100
10.1.2.2;5.2.2 Random Multiplicative Cascades;101
10.1.2.3;5.2.3 Local Scales and the Multifractal Spectrum;104
10.1.2.4;5.2.4 The Spectrum of Multiplicative Measures;106
10.2;Chapter 6. Multifractal Diffusions Through Time Deformation and the MMAR;110
10.2.1;6.1 Multifractal Processes;110
10.2.2;6.2 Multifractal Time Deformation;111
10.2.3;6.3 The Multifractal Model of Asset Returns;113
10.2.3.1;6.3.1 Unconditional Distribution of Returns;113
10.2.3.2;6.3.2 Long Memory in Volatility;114
10.2.3.3;6.3.3 Sample Paths;115
10.2.4;6.4 An Extension with Autocorrelated Returns;116
10.2.5;6.5 Connection with Related Work;117
10.2.6;6.6 Discussion;118
10.3;Chapter 7. Continuous-Time MSM;120
10.3.1;7.1 MSM with Finitely Many Components;121
10.3.2;7.2 MSM with Countably Many Components;122
10.3.2.1;7.2.1 Limiting Time Deformation;122
10.3.2.2;7.2.2 Multifractal Price Diffusion;125
10.3.2.3;7.2.3 Connection between Discrete-Time and Continuous-Time Versions of MSM;126
10.3.3;7.3 MSM with Dependent Arrivals;129
10.3.4;7.4 Connection with Related Work;130
10.3.5;7.5 Discussion;134
10.4;Chapter 8. Power Variation;136
10.4.1;8.1 Power Variation in Currency Markets;136
10.4.1.1;8.1.1 Data;136
10.4.1.2;8.1.2 Methodology;138
10.4.1.3;8.1.3 Main Empirical Results;138
10.4.1.4;8.1.4 Comparison of MSM vs. Alternative Specifications;144
10.4.1.5;8.1.5 Global Tests of Fit;151
10.4.2;8.2 Power Variation in Equity Markets;152
10.4.3;8.3 Additional Moments;154
10.4.4;8.4 Discussion;156
11;Part III: Equilibrium Pricing;158
11.1;Chapter 9. Multifrequency News and Stock Returns;160
11.1.1;9.1 An Asset Pricing Model with Regime-Switching Dividends;162
11.1.1.1;9.1.1 Preferences, Consumption, and Dividends;163
11.1.1.2;9.1.2 Asset Pricing under Complete Information;164
11.1.2;9.2 Volatility Feedback with Multifrequency Shocks;166
11.1.2.1;9.2.1 Multifrequency Dividend News;166
11.1.2.2;9.2.2 Equilibrium Stock Returns;167
11.1.3;9.3 Empirical Results with Fully Informed Investors;168
11.1.3.1;9.3.1 Excess Return Data;168
11.1.3.2;9.3.2 Maximum Likelihood Estimation and Volatility Feedback;169
11.1.3.3;9.3.3 Comparison with Campbell and Hentschel (1992);174
11.1.3.4;9.3.4 Conditional Inference;175
11.1.3.5;9.3.5 Return Decomposition;177
11.1.3.6;9.3.6 Alternative Calibrations;179
11.1.4;9.4 Learning about Volatility and Endogenous Skewness;180
11.1.4.1;9.4.1 Investor Information and Stock Returns;183
11.1.4.2;9.4.2 Learning Model Results;184
11.1.5;9.5 Preference Implications and Extension to Multifrequency Consumption Risk;187
11.1.6;9.6 Discussion;191
11.2;Chapter 10. Multifrequency Jump-Diffusions;192
11.2.1;10.1 An Equilibrium Model with Endogenous Price Jumps;193
11.2.1.1;10.1.1 Preferences, Information, and Income;193
11.2.1.2;10.1.2 Financial Markets and Equilibrium;194
11.2.1.3;10.1.3 Equilibrium Dynamics under Isoelastic Utility;196
11.2.2;10.2 A Multifrequency Jump-Diffusion for Equilibrium Stock Prices;198
11.2.2.1;10.2.1 Dividends with Multifrequency Volatility;198
11.2.2.2;10.2.2 Multifrequency Economies;198
11.2.2.3;10.2.3 The Equilibrium Stock Price;199
11.2.3;10.3 Price Dynamics with an Infinity of Frequencies;200
11.2.4;10.4 Recursive Utility and Priced Jumps;204
11.2.5;10.5 Discussion;206
11.3;Chapter 11. Conclusion;208
11.4;A. Appendices;212
11.4.1;A.1 Appendix to Chapter 3;212
11.4.1.1;A.1.1 Proof of Proposition 1;212
11.4.1.2;A.1.2 HAC-Adjusted Vuong Test;215
11.4.2;A.2 Appendix to Chapter 4;216
11.4.2.1;A.2.1 Distribution of the Arrival Vector;216
11.4.2.2;A.2.2 Ergodic Distribution of Volatility Components;216
11.4.2.3;A.2.3 Particle Filter;217
11.4.2.4;A.2.4 Two-Step Estimation;218
11.4.2.5;A.2.5 Value-at-Risk Forecasts;219
11.4.2.6;A.2.6 Extension to Many Assets;219
11.4.3;A.3 Appendix to Chapter 5;222
11.4.3.1;A.3.1 Properties of D;222
11.4.3.2;A.3.2 Interpretation of f(a) as a Fractal Dimension;222
11.4.3.3;A.3.3 Heuristic Proof of Proposition 3;223
11.4.4;A.4 Appendix to Chapter 6;224
11.4.4.1;A.4.1 Concavity of the Scaling Function t (q);224
11.4.4.2;A.4.2 Proof of Proposition 5;224
11.4.4.3;A.4.3 Proof of Proposition 7;225
11.4.4.4;A.4.4 Proof of Proposition 8;225
11.4.5;A.5 Appendix to Chapter 7;226
11.4.5.1;A.5.1 Multivariate Version of Continuous-Time MSM;226
11.4.5.2;A.5.2 Proof of Proposition 9;227
11.4.5.3;A.5.3 Proof of Proposition 10;229
11.4.5.4;A.5.4 Proof of Corollary 1;231
11.4.5.5;A.5.5 Proof of Proposition 11;231
11.4.5.6;A.5.6 MSM with Dependent Arrivals;233
11.4.5.7;A.5.7 Autocovariogram of Log Volatility in MSM;234
11.4.5.8;A.5.8 Limiting MRW Process;234
11.4.6;A.6 Appendix to Chapter 9;235
11.4.6.1;A.6.1 Full-Information Economies;235
11.4.6.2;A.6.2 Learning Economies;238
11.4.6.3;A.6.3 Multifrequency Consumption Risk;239
11.4.7;A.7 Appendix to Chapter 10;239
11.4.7.1;A.7.1 Proof of Proposition 13;239
11.4.7.2;A.7.2 Multivariate Extensions;240
11.4.7.3;A.7.3 Proof of Proposition 14;241
11.4.7.4;A.7.4 Proof of Proposition 15;242
11.5;References;244
11.6;Index;266