Multivariate Stochastic Volatility Models With Correlated Errors
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Multivariate Stochastic Volatility Models With Correlated Errors
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Author : David X. Chan
language : en
Publisher:
Release Date : 2008
Multivariate Stochastic Volatility Models With Correlated Errors written by David X. Chan and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2008 with categories.
We develop a Bayesian approach for parsimoniously estimating the correlation structure of the errors in a multivariate stochastic volatility model. Since the number of parameters in the joint correlation matrix of the return and volatility errors is potentially very large, we impose a prior that allows the off-diagonal elements of the inverse of the correlation matrix to be identically zero. The model is estimated using a Markov chain simulation method that samples from the posterior distribution of the volatilities and parameters. We illustrate the approach using both simulated and real examples. In the real examples, the method is applied to equities at three levels of aggregation: returns for firms within the same industry, returns for different industries and returns aggregated at the index level. We find pronounced correlation effects only at the highest level of aggregation.
A New Class Of Discrete Time Stochastic Volatility Model With Correlated Errors
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Author : Sujay Mukhoti
language : en
Publisher:
Release Date : 2017
A New Class Of Discrete Time Stochastic Volatility Model With Correlated Errors written by Sujay Mukhoti and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2017 with categories.
In an efficient stock market, the returns and their time-dependent volatility are often jointly modeled by stochastic volatility models (SVMs). Over the last few decades several SVMs have been proposed to adequately capture the defining features of the relationship between the return and its volatility. Among one of the earliest SVM, Taylor (1982) proposed a hierarchical model, where the current return is a function of the current latent volatility, which is further modeled as an auto-regressive process. In an attempt to make the SVMs more appropriate for complex realistic market behavior, a leverage parameter was introduced in the Taylor's SVM, which however led to the violation of the efficient market hypothesis (EMH, a necessary mean-zero condition for the return distribution that prevents arbitrage possibilities). Subsequently, a host of alternative SVMs had been developed and are currently in use. In this paper, we propose mean-corrections for several generalizations of Taylor's SVM that capture the complex market behavior as well as satisfy EMH. We also establish a few theoretical results to characterize the key desirable features of these models, and present comparison with other popular competitors. Furthermore, four real-life examples (Oil price, CITI bank stock price, Euro-USD rate, and S&P 500 index returns) have been used to demonstrate the performance of this new class of SVMs.
Handbook Of Volatility Models And Their Applications
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Author : Luc Bauwens
language : en
Publisher: John Wiley & Sons
Release Date : 2012-03-22
Handbook Of Volatility Models And Their Applications written by Luc Bauwens and has been published by John Wiley & Sons this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012-03-22 with Business & Economics categories.
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.
Box Cox Stochastic Volatility Models With Heavy Tails And Correlated Errors
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Author : Xibin Zhang
language : en
Publisher:
Release Date : 2004
Box Cox Stochastic Volatility Models With Heavy Tails And Correlated Errors written by Xibin Zhang and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2004 with Markov processes categories.
Essays On Multivariate Stochastic Volatility Models
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Author : Sebastian Trojan
language : en
Publisher:
Release Date : 2015
Essays On Multivariate Stochastic Volatility Models written by Sebastian Trojan and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2015 with categories.
The first essay describes a very general stochastic volatility (SV) model specification with leverage, heavy tails, skew and switching regimes, using realized volatility (RV) as an auxiliary time series to improve inference on latent volatility. The information content of the range and of implied volatility using the VIX index is also analyzed. Database is the S & P 500 index. Asymmetry in the observation error is modeled by the generalized hyperbolic skew Student-t distribution, whose heavy and light tail enable substantial skewness. Resulting number of regimes and dynamics differ dependent on the auxiliary volatility proxy and are investigated in-sample for the financial crash period 2008/09 in more detail. An out-of-sample study comparing predictive ability of various model variants for a calm and a volatile period yields insights about the gains on forecasting performance from different volatility proxies. Results indicate that including RV or the VIX pays off mostly in more volatile market conditions, whereas in calmer environments SV specifications using no auxiliary series outperform. The range as volatility proxy provides a superior in-sample fit, but its predictive performance is found to be weak. The second essay presents a high frequency stochastic volatility model. Price duration and associated absolute price change in event time are modeled contemporaneously to fully capture volatility on the tick level, combining the SV and stochastic conditional duration (SCD) model. Estimation is with IBM stock intraday data 2001/10 (decimalization completed), taking a minimum midprice threshold of a half tick. Persistent information flow is extracted, featuring a positively correlated innovation term and negative cross effects in the AR(1) persistence matrix. Additionally, regime switching in both duration and absolute price change is introduced to increase nonlinear capabilities of the model. Thereby, a separate price jump.
Estimating High Dimensional Multivariate Stochastic Volatility Models
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Author : Matteo Pelagatti
language : en
Publisher:
Release Date : 2020
Estimating High Dimensional Multivariate Stochastic Volatility Models written by Matteo Pelagatti and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2020 with categories.
Stochastic Volatility
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Author : Neil Shephard
language : en
Publisher: OUP Oxford
Release Date : 2005-03-10
Stochastic Volatility written by Neil Shephard and has been published by OUP Oxford this book supported file pdf, txt, epub, kindle and other format this book has been release on 2005-03-10 with Business & Economics categories.
Stochastic volatility is the main concept used in the fields of financial economics and mathematical finance to deal with time-varying volatility in financial markets. This book brings together some of the main papers that have influenced the field of the econometrics of stochastic volatility, and shows that the development of this subject has been highly multidisciplinary, with results drawn from financial economics, probability theory, and econometrics, blending to produce methods and models that have aided our understanding of the realistic pricing of options, efficient asset allocation, and accurate risk assessment. A lengthy introduction by the editor connects the papers with the literature.
Analysis Of High Dimensional Multivariate Stochastic Volatility Models
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Author : Siddhartha Chib
language : en
Publisher:
Release Date : 2005
Analysis Of High Dimensional Multivariate Stochastic Volatility Models written by Siddhartha Chib and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2005 with categories.
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.
Real Time Estimation Of Multivariate Stochastic Volatility Models
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Author : Jian Wang
language : en
Publisher:
Release Date : 2017
Real Time Estimation Of Multivariate Stochastic Volatility Models written by Jian Wang and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2017 with categories.
Univariate And Multivariate Stochastic Volatility Models
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Author : Roman Liesenfeld
language : en
Publisher:
Release Date : 2002
Univariate And Multivariate Stochastic Volatility Models written by Roman Liesenfeld and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2002 with categories.
A Maximum Likelihood (ML) approach based upon an Efficient Importance Sampling (EIS) procedure is used to estimate several extensions of the standard Stochastic Volatility (SV) model for daily financial return series. EIS provides a highly generic procedure for a very accurate Monte Carlo evaluation of the marginal likelihood which depends upon high-dimensional interdependent integrals. Extensions of the standard SV model being analyzed only require minor modifications in the ML-EIS procedure. Furthermore, EIS can also be applied for filtering which provides the basis for several diagnostic tests. Our empirical analysis indicates that extensions such as a semi-nonparametric specification of the error term distribution in the return equation dominate the standard SV model. Finally, we also apply the ML-EIS approach to a multivariate factor model with stochastic volatility.