Stochastic Volatility and Realized Stochastic Volatility Models

✍ Scribed by Makoto Takahashi, Yasuhiro Omori, Toshiaki Watanabe

• Publisher: Springer
• Year: 2023
• Tongue: English
• Leaves: 120
• Series: SpringerBriefs in Statistics: JSS Research Series in Statistics
• Category: Library

✦ Synopsis

This treatise delves into the latest advancements in stochastic volatility models, highlighting the utilization of Markov chain Monte Carlo simulations for estimating model parameters and forecasting the volatility and quantiles of financial asset returns. The modeling of financial time series volatility constitutes a crucial aspect of finance, as it plays a vital role in predicting return distributions and managing risks. Among the various econometric models available, the stochastic volatility model has been a popular choice, particularly in comparison to other models, such as GARCH models, as it has demonstrated superior performance in previous empirical studies in terms of fit, forecasting volatility, and evaluating tail risk measures such as Value-at-Risk and Expected Shortfall.

The book also explores an extension of the basic stochastic volatility model, incorporating a skewed return error distribution and a realized volatility measurement equation. The concept of realized volatility, a newly established estimator of volatility using intraday returns data, is introduced, and a comprehensive description of the resulting realized stochastic volatility model is provided. The text contains a thorough explanation of several efficient sampling algorithms for latent log volatilities, as well as an illustration of parameter estimation and volatility prediction through empirical studies utilizing various asset return data, including the yen/US dollar exchange rate, the Dow Jones Industrial Average, and the Nikkei 225 stock index.

This publication is highly recommended for readers with an interest in the latest developments in stochastic volatility models and realized stochastic volatility models, particularly in regards to financial risk management.

✦ 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