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Table of Contents
Preface; Contents; 1 Introduction; 1.1 Implied and Historical Volatility; 1.2 High-Frequency Data; 1.3 Fourier Analysis for Volatility Measurement; 2 A First Glance at Fourier Method; 2.1 Main Convolution Formula; 2.2 Specific Features of the Fourier Approach; 3 Estimation of Integrated Volatility; 3.1 Univariate Estimator; 3.1.1 Asymptotic Results; 3.1.2 Finite Sample Properties; 3.2 Feasibility; 3.2.1 Fourier Estimator of Quarticity; 3.3 Multivariate Estimator; 3.3.1 Asymptotic Results; 3.3.2 Asyncronicity Issues; 3.3.3 Comparison Study; 3.3.4 Positive Definiteness
4 Estimation of Instantaneous Volatility4.1 Univariate Estimator; 4.1.1 Asymptotic Results; 4.1.2 Finite Sample Properties; 4.2 Multivariate Estimator; 4.2.1 Asymptotic Results; 4.2.2 Bandwidth and Scale Selection; 4.3 Fourier Method in the Presence of Jumps; 5 High Frequency Analysis: Market Microstructure Noise Issues; 5.1 What Is the Noise Effect on Fourier Estimator?; 5.2 The Case of Integrated Volatility; 5.2.1 Starting from the Additive MA(1) Model; 5.2.2 Moving to Alternative Microstructure Noise Models; 5.2.3 Comparison with Other Estimators; 5.2.4 An Empirical Application
5.3 The Case of Integrated Covariance5.3.1 Comparison with Other Estimators; 5.3.2 An Empirical Application; 5.3.3 Asymptotic Results; 5.4 The Case of Spot Volatility; 6 Getting Inside the Latent Volatility; 6.1 Market Data Considerations; 6.2 Factor Identification for Stochastic Volatility Models; 6.2.1 Volatility of Volatility; 6.2.2 Leverage; 6.2.3 Empirical Analysis; 6.3 Volatility Feedback Effects; 6.3.1 An Empirical Application: Market Stability; 6.4 Volatility Forecasting Performance; 6.4.1 Monte Carlo Analysis; 6.4.1.1 In-sample Forecast; 6.4.1.2 Out-of-Sample Forecast
6.4.2 An Empirical Application6.5 Further Readings; A Mathematical Essentials; A.1 Stochastic Processes; A.1.1 Diffusion Processes; A.1.2 Itô Energy Identity; A.1.3 Itô Formula; A.2 Fourier Analysis; A.2.1 Fejér's Convergence Theorem; A.2.2 Product Formula; A.2.3 Nyquist Frequency; B Codes for the Fourier Estimator; B.1 Integrated Volatility; B.2 Estimated Bias and MSE; B.3 Integrated Covariance; B.4 Spot Volatility; B.5 Using Fast Fourier Transform Algorithm; B.6 Volatility of Volatility; References; Index
4 Estimation of Instantaneous Volatility4.1 Univariate Estimator; 4.1.1 Asymptotic Results; 4.1.2 Finite Sample Properties; 4.2 Multivariate Estimator; 4.2.1 Asymptotic Results; 4.2.2 Bandwidth and Scale Selection; 4.3 Fourier Method in the Presence of Jumps; 5 High Frequency Analysis: Market Microstructure Noise Issues; 5.1 What Is the Noise Effect on Fourier Estimator?; 5.2 The Case of Integrated Volatility; 5.2.1 Starting from the Additive MA(1) Model; 5.2.2 Moving to Alternative Microstructure Noise Models; 5.2.3 Comparison with Other Estimators; 5.2.4 An Empirical Application
5.3 The Case of Integrated Covariance5.3.1 Comparison with Other Estimators; 5.3.2 An Empirical Application; 5.3.3 Asymptotic Results; 5.4 The Case of Spot Volatility; 6 Getting Inside the Latent Volatility; 6.1 Market Data Considerations; 6.2 Factor Identification for Stochastic Volatility Models; 6.2.1 Volatility of Volatility; 6.2.2 Leverage; 6.2.3 Empirical Analysis; 6.3 Volatility Feedback Effects; 6.3.1 An Empirical Application: Market Stability; 6.4 Volatility Forecasting Performance; 6.4.1 Monte Carlo Analysis; 6.4.1.1 In-sample Forecast; 6.4.1.2 Out-of-Sample Forecast
6.4.2 An Empirical Application6.5 Further Readings; A Mathematical Essentials; A.1 Stochastic Processes; A.1.1 Diffusion Processes; A.1.2 Itô Energy Identity; A.1.3 Itô Formula; A.2 Fourier Analysis; A.2.1 Fejér's Convergence Theorem; A.2.2 Product Formula; A.2.3 Nyquist Frequency; B Codes for the Fourier Estimator; B.1 Integrated Volatility; B.2 Estimated Bias and MSE; B.3 Integrated Covariance; B.4 Spot Volatility; B.5 Using Fast Fourier Transform Algorithm; B.6 Volatility of Volatility; References; Index