Stochastic Volatility and Realized Stochastic Volatility Models

✍ Scribed by Makoto Takahashi, Yasuhiro Omori, Toshiaki Watanabe

• Publisher: Springer
• Year: 2023
• Tongue: English
• Leaves: 121
• Series: SpringerBriefs in Statistics. JSS Research Series in Statistics
• Category: Library

✦ Table of Contents

Preface
Contents
1 Introduction
1.1 Research Background
1.2 Summary of Topics
References
2 Stochastic Volatility Model
2.1 Introduction
2.2 Single-Move Sampler for the Symmetric SV Model
2.2.1 Generation of θ=(µ, φ,ση2)'
2.2.2 Generation of h
2.3 Mixture Sampler
2.3.1 Reformulation of the Measurement Equation
2.3.2 MCMC Algorithm
2.3.3 Correcting for Misspecification
2.4 Multi-move Sampler
2.5 Auxiliary Particle Filter
2.6 Empirical Study
2.7 Appendix
2.7.1 Simulation Smoother
2.7.2 Augmented Kalman Filter
References
3 Asymmetric Stochastic Volatility Model
3.1 Introduction
3.2 Single-Move Sampler for the Asymmetric SV Model
3.2.1 Generation of (µ,φ,ση2,ρ)
3.2.2 Generation of h
3.3 Mixture Sampler
3.3.1 Reformulation of the Measurement Equation
3.3.2 MCMC Algorithm
3.3.3 Correcting for Misspecification
3.4 Multi-move Sampler
3.5 Auxiliary Particle Filter
3.6 Empirical Study
3.7 Appendix
3.7.1 Simulation Smoother
3.7.2 Augmented Kalman Filter
References
4 Stochastic Volatility Model with Generalized Hyperbolic Skew Student's t Error
4.1 Introduction
4.2 Generalized Hyperbolic Skew Student's t Distribution
4.3 SV Model with GH Skew Student's t Error
4.4 MCMC Estimation
4.4.1 Generation of (µ,φ,ση,ρ)
4.4.2 Generation of (ν, β)
4.4.3 Generation of λ and h
4.5 News Impact Curve: Simulation-Based Method
4.5.1 Simulation Example
4.6 Empirical Study
References
5 Realized Stochastic Volatility Model
5.1 Introduction
5.2 Realized Volatility
5.3 Realized Stochastic Volatility Model
5.4 RSV Model with GH Skewed Student's t Error
5.5 MCMC Estimation
5.5.1 Generation of (µ,φ,ση,ρ, ν, β) and λ
5.5.2 Generation of ξ and σu
5.5.3 Generation of h
5.6 Evaluation of Forecasts
5.6.1 Volatility, VaR, and ES Forecasts
5.6.2 Loss Functions for Volatility
5.6.3 A Joint Loss Function for VaR and ES
5.6.4 Testing Relative Forecast Performance
5.7 EGARCH and Realized EGARCH Models
5.8 Empirical Study
5.8.1 Estimation Results
5.8.2 Prediction Results
References