Analysis Of High Dimensional Multivariate Stochastic Volatility Models
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Analysis of High Dimensional Multivariate Stochastic Volatility Models
This paper is concerned with the fitting and comparison of high dimensional multivariate time series models with time varying correlations. The models considered here combine features of the classical factor model with those of the univariate stochastic volatility model. Specifically, a set of unobserved time-dependent factors, along with an associated loading matrix, are used to model the contemporaneous correlation while, conditioned on the factors, the noise in each factor and each series is assumed to follow independent three-parameter univariate stochastic volatility processes. A complete analysis of these models, and its special cases, is developed that encompasses estimation, filtering and model choice. The centerpieces of our estimation algorithm (which relies on MCMC methods) is (1) a reduced blocking scheme for sampling the free elements of the loading matrix and the factors and (2) a special method for sampling the parameters of the univariate SV process. The sampling of the loading matrix (containing typically many hundreds of parameters) is done via a highly tuned Metropolis-Hastings step. The resulting algorithm is completely scalable in terms of series and factors and very simulation-efficient. We also provide methods for estimating the log-likelihood function and the filtered values of the time-varying volatilities and correlations. We pay special attention to the problem of comparing one version of the model with another and for determining the number of factors. For this purpose we use MCMC methods to find the marginal likelihood and associated Bayes factors of each fitted model. In sum, these procedures lead to the first unified and practical likelihood based analysis of truly high dimensional models of stochastic volatility. We apply our methods in detail to two datasets. The first is the return vector on 20 exchange rates against the US Dollar. The second is the return vector on 40 common stocks quoted on the New York Stock Exchange.
Parameter Estimation in Stochastic Volatility Models
Author: Jaya P. N. Bishwal
language: en
Publisher: Springer Nature
Release Date: 2022-08-06
This book develops alternative methods to estimate the unknown parameters in stochastic volatility models, offering a new approach to test model accuracy. While there is ample research to document stochastic differential equation models driven by Brownian motion based on discrete observations of the underlying diffusion process, these traditional methods often fail to estimate the unknown parameters in the unobserved volatility processes. This text studies the second order rate of weak convergence to normality to obtain refined inference results like confidence interval, as well as nontraditional continuous time stochastic volatility models driven by fractional Levy processes. By incorporating jumps and long memory into the volatility process, these new methods will help better predict option pricing and stock market crash risk. Some simulation algorithms for numerical experiments are provided.
Handbook of Volatility Models and Their Applications
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 markets Other Models and Methods presents alternative approaches, such as multiplicative error models, nonparametric and semi-parametric models, and copula-based models of (co)volatilities Realized Volatility explores issues of the measurement of volatility by realized variances and covariances, guiding readers on how to successfully model and forecast these measures Handbook 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.