Statistical Inference For Stochastic Volatility Models
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Statistical Inference For Stochastic Volatility Models
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Author : Md. Nazmul Ahsan
language : en
Publisher:
Release Date : 2021
Statistical Inference For Stochastic Volatility Models written by Md. Nazmul Ahsan and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2021 with categories.
"Although stochastic volatility (SV) models have many appealing features, estimation and inference on SV models are challenging problems due to the inherent difficulty of evaluating the likelihood function. The existing methods are either computationally costly and/or inefficient. This thesis studies and contributes to the SV literature from the estimation, inference, and volatility forecasting viewpoints. It consists of three essays, which include both theoretical and empirical contributions. On the whole, the thesis develops easily applicable statistical methods for stochastic volatility models.The first essay proposes computationally simple moment-based estimators for the first-order SV model. In addition to confirming the enormous computational advantage of the proposed estimators, the results show that the proposed estimators match (or exceed) alternative estimators in terms of precision – including Bayesian estimators proposed in this context, which have the best performance among alternative estimators. Using this simple estimator, we study three crucial test problems (no persistence, no latent specification of volatility, and no stochastic volatility hypothesis), and evaluate these null hypotheses in three ways: asymptotic critical values, a parametric bootstrap procedure, and a maximized Monte Carlo procedure. The proposed methods are applied to daily observations on the returns for three major stock prices [Coca-Cola, Walmart, Ford], and the Standard and Poor’s Composite Price Index. The results show the presence of stochastic volatility with strong persistence.The second essay studies the problem of estimating higher-order stochastic volatility [SV(p)] models. The estimation of SV(p) models is even more challenging and rarely considered in the literature. We propose several estimators for higher-order stochastic volatility models. Among these, the simple winsorized ARMA-based estimator is uniformly superior in terms of bias and RMSE to other estimators, including the Bayesian MCMC estimator. The proposed estimators are applied to stock return data, and the usefulness of the proposed estimators is assessed in two ways. First, using daily returns on the S&P 500 index from 1928 to 2016, we find that higher-order SV models – in particular an SV(3) model – are preferable to an SV(1), from the viewpoints of model fit and both asymptotic and finite-sample tests. Second, using different volatility proxies (squared return and realized volatility), we find that higher-order SV models are preferable for out-of-sample volatility forecasting, whether a high volatility period (such as financial crisis) is included in the estimation sample or the forecasted sample. Our results highlight the usefulness of higher-order SV models for volatility forecasting.In the final essay, we introduce a novel class of generalized stochastic volatility (GSV) models which utilize high-frequency (HF) information (realized volatility (RV) measures). GSV models can accommodate nonstationary volatility process, various distributional assumptions, and exogenous regressors in the latent volatility equation. Instrumental variable methods are employed to provide a unified framework for the analysis (estimation and inference) of GSV models. We consider the parameter inference problem in GSV models with nonstationary volatility and develop identification-robust methods for joint hypotheses involving the volatility persistence parameter and the autocorrelation parameter of the composite error (or the noise ratio). For distributional theory, three different sets of assumptions are considered. In simulations, the proposed tests outperform the usual asymptotic test regarding size and exhibit excellent power. We apply our inference methods to IBM price and option data andidentify several empirical relationships"--
Discrete Time Stochastic Volatility Models And Mcmc Based Statistical Inference
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Author : Nikolaus Hautsch
language : en
Publisher:
Release Date : 2008
Discrete Time Stochastic Volatility Models And Mcmc Based Statistical Inference written by Nikolaus Hautsch 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.
Garch Models
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Author : Christian Francq
language : en
Publisher: John Wiley & Sons
Release Date : 2019-03-21
Garch Models written by Christian Francq 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 2019-03-21 with Mathematics categories.
Provides a comprehensive and updated study of GARCH models and their applications in finance, covering new developments in the discipline This book provides a comprehensive and systematic approach to understanding GARCH time series models and their applications whilst presenting the most advanced results concerning the theory and practical aspects of GARCH. The probability structure of standard GARCH models is studied in detail as well as statistical inference such as identification, estimation, and tests. The book also provides new coverage of several extensions such as multivariate models, looks at financial applications, and explores the very validation of the models used. GARCH Models: Structure, Statistical Inference and Financial Applications, 2nd Edition features a new chapter on Parameter-Driven Volatility Models, which covers Stochastic Volatility Models and Markov Switching Volatility Models. A second new chapter titled Alternative Models for the Conditional Variance contains a section on Stochastic Recurrence Equations and additional material on EGARCH, Log-GARCH, GAS, MIDAS, and intraday volatility models, among others. The book is also updated with a more complete discussion of multivariate GARCH; a new section on Cholesky GARCH; a larger emphasis on the inference of multivariate GARCH models; a new set of corrected problems available online; and an up-to-date list of references. Features up-to-date coverage of the current research in the probability, statistics, and econometric theory of GARCH models Covers significant developments in the field, especially in multivariate models Contains completely renewed chapters with new topics and results Handles both theoretical and applied aspects Applies to researchers in different fields (time series, econometrics, finance) Includes numerous illustrations and applications to real financial series Presents a large collection of exercises with corrections Supplemented by a supporting website featuring R codes, Fortran programs, data sets and Problems with corrections GARCH Models, 2nd Edition is an authoritative, state-of-the-art reference that is ideal for graduate students, researchers, and practitioners in business and finance seeking to broaden their skills of understanding of econometric time series models.
Inference For A Class Of Stochastic Volatility Models In Presence Of Jumps
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Author : Petra Posedel
language : en
Publisher:
Release Date : 2007
Inference For A Class Of Stochastic Volatility Models In Presence Of Jumps written by Petra Posedel and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2007 with categories.
Statistical Modelling And Regression Structures
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Author : Thomas Kneib
language : en
Publisher: Springer Science & Business Media
Release Date : 2010-01-12
Statistical Modelling And Regression Structures written by Thomas Kneib and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2010-01-12 with Mathematics categories.
The contributions collected in this book have been written by well-known statisticians to acknowledge Ludwig Fahrmeir's far-reaching impact on Statistics as a science, while celebrating his 65th birthday. The contributions cover broad areas of contemporary statistical model building, including semiparametric and geoadditive regression, Bayesian inference in complex regression models, time series modelling, statistical regularization, graphical models and stochastic volatility models.
Inference In Stochastic Volatility Models For Gaussian And T Data
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Author : Nan Zheng
language : en
Publisher:
Release Date : 2013
Inference In Stochastic Volatility Models For Gaussian And T Data written by Nan Zheng and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2013 with Estimation theory categories.
Statistical Inference In Continuous Time Models With Short Range And Or Long Range Dependence
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Author : Isabel Casas Villalba
language : en
Publisher:
Release Date : 2006
Statistical Inference In Continuous Time Models With Short Range And Or Long Range Dependence written by Isabel Casas Villalba and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2006 with Finance categories.
The aim of this thesis is to estimate the volatility function of continuoustime stochastic models. The estimation of the volatility of the following wellknown international stock market indexes is presented as an application: Dow Jones Industrial Average, Standard and Poor’s 500, NIKKEI 225, CAC 40, DAX 30, FTSE 100 and IBEX 35. This estimation is studied from two different perspectives: a) assuming that the volatility of the stock market indexes displays shortrange dependence (SRD), and b) extending the previous model for processes with longrange dependence (LRD), intermediaterange dependence (IRD) or SRD. Under the efficient market hypothesis (EMH), the compatibility of the Vasicek, the CIR, the Anh and Gao, and the CKLS models with the stock market indexes is being tested. Nonparametric techniques are presented to test the affinity of these parametric volatility functions with the volatility observed from the data. Under the assumption of possible statistical patterns in the volatility process, a new estimation procedure based on the Whittle estimation is proposed. This procedure is theoretically and empirically proven. In addition, its application to the stock market indexes provides interesting results.
Stochastic Volatility And Realized Stochastic Volatility Models
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Author : Makoto Takahashi
language : en
Publisher: Springer Nature
Release Date : 2023-04-18
Stochastic Volatility And Realized Stochastic Volatility Models written by Makoto Takahashi and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2023-04-18 with Business & Economics categories.
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.
Indirect Inference Methods For Stochastic Volatility Models Based On Non Gaussian Ornstein Uhlenbeck Processes
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Author : Arvid Raknerud
language : en
Publisher:
Release Date : 2009
Indirect Inference Methods For Stochastic Volatility Models Based On Non Gaussian Ornstein Uhlenbeck Processes written by Arvid Raknerud and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2009 with categories.
Inference In Hidden Markov Models
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Author : Olivier Cappé
language : en
Publisher: Springer Science & Business Media
Release Date : 2006-04-12
Inference In Hidden Markov Models written by Olivier Cappé and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2006-04-12 with Mathematics categories.
This book is a comprehensive treatment of inference for hidden Markov models, including both algorithms and statistical theory. Topics range from filtering and smoothing of the hidden Markov chain to parameter estimation, Bayesian methods and estimation of the number of states. In a unified way the book covers both models with finite state spaces and models with continuous state spaces (also called state-space models) requiring approximate simulation-based algorithms that are also described in detail. Many examples illustrate the algorithms and theory. This book builds on recent developments to present a self-contained view.