Download or read book Estimating and Forecasting Generalized Fractional Long Memory Stochastic Volatility Models written by Shelton Peiris and published by . This book was released on 2016 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt:

Download or read book Realized Stochastic Volatility Models with Generalized Gegenbauer Long Memory written by Manabu Asai and published by . This book was released on 2017 with total page 27 pages. Available in PDF, EPUB and Kindle. Book excerpt: In recent years fractionally differenced processes have received a great deal of attention due to their flexibility in financial applications with long memory. In this paper, we develop a new realized stochastic volatility (RSV) model with general Gegenbauer long memory (GGLM), which encompasses a new RSV model with seasonal long memory (SLM). The RSV model uses the information from returns and realized volatility measures simultaneously. The long memory structure of both models can describe unbounded peaks apart from the origin in the power spectrum. For estimating the RSV-GGLM model, we suggest estimating the location parameters for the peaks of the power spectrum in the first step, and the remaining parameters based on the Whittle likelihood in the second step. We conduct Monte Carlo experiments for investigating the finite sample properties of the estimators, with a quasi-likelihood ratio test of RSV-SLM model against the RSV-GGLM model. We apply the RSV-GGLM and RSV-SLM model to three stock market indices. The estimation and forecasting results indicate the adequacy of considering general long memory.

Download or read book Parameter Estimation in Stochastic Volatility Models written by Jaya P. N. Bishwal and published by Springer Nature. This book was released on 2022-08-06 with total page 634 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.

Download or read book Modeling and Forecasting Long Range Dependence in Volatility written by Nan Qu and published by . This book was released on 2010 with total page 364 pages. Available in PDF, EPUB and Kindle. Book excerpt: This thesis conducts three exercises on volatility modeling of financial assets. We are essentially interested in the estimation and forecasting of daily volatility, a measure of the strength of price movements over daily intervals. Two of the exercises are in the realm of high frequency data: modeling and forecasting realized volatility which is constructed from intra-day returns. The other exercise is concerned with discrete stochastic volatility modeling using daily returns. The main focus of each exercise is to represent the high degree of volatility persistence, which is an important stylized fact of daily volatility.In the first exercise, daily realized volatility of the Yen/USD exchange rate is modeled through an autoregressive and moving-average fractionally integrated (ARFIMA) process. We differ from previous studies by averaging across a set of ARFIMA and ARMA models with different orders of autoregressive and moving-average polynomials. The vehicle used to execute this averaging exercise is Bayesian model averaging, through which part of the uncertainty introduced by model selection is integrated out. We examine the practical usefulness of our method by conducting a rolling-sample estimation, and the results indicate the weighted average forecast out-performs that of a single model at long-term horizons by providing smaller mean squared forecast errors.The second exercise is concerned with Bayesian estimation of a long memory stochastic volatility (SV) model. We use a high-order moving-average process to approximate the fractional integration specified for the latent log volatility. As such, the long memory SV model can be expressed in a state-space form, which facilitates the implementation of Markov chain Monte Carlo (MCMC) simulation when parameters and latent volatility are estimated. We update the set of memory parameter and volatility of volatility parameter in one block in the MCMC algorithm, by using the hessian matrix. A Monte Carlo study indicates in general, when the posterior mean is treated as a point estimator of parameters, our Bayesian method compares well with classical methods. Furthermore, the Bayesian estimator tends to outperform the popular frequency quasi maximum likelihood estimator, according to the root mean square error criterion, with small and medium sample size. An empirical analysis of the daily Yen/USD exchange rate spanning 26 years is conducted, and the degree of persistency in volatility is found to be consistent with that from the first exercise when high frequency data are used.In the third exercise, we look at the long memory property from a different angle. There has been a large literature using specifications other than fractional integration to mimic the long memory property in time series analysis, although there are few applications to realized volatility. In this exercise, regime switching models are fitted to daily realized volatility of the JPY/USD exchange rate from 1996 to 2009. Both in-sample fit and out-of-sample forecasting are used to compare across the three types of models, including ARFIMA, regime switching and sum of short memory processes. An extensive recursive estimation over one year suggests that regime switching is superior in capturing the dynamics of the time series examined, and generating more accurate out-of-sample forecasts.

Download or read book Forecasting Realised Volatility Using a Long Memory Stochastic Volatility Model written by and published by . This book was released on 2003 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt:

Download or read book Stochastic Volatility and Realized Stochastic Volatility Models written by Makoto Takahashi and published by Springer Nature. This book was released on 2023-04-18 with total page 120 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.

Download or read book Time Series with Long Memory written by Peter M. Robinson and published by Advanced Texts in Econometrics. This book was released on 2003 with total page 396 pages. Available in PDF, EPUB and Kindle. Book excerpt: Long memory time series are characterized by a strong dependence between distant events.

Download or read book Estimation and identification in long memory stochastic volatility models written by Ana Perez Espartero and published by . This book was released on 2000 with total page 0 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Download or read book Realized Stochastic Volatility with General Asymmetry and Long Memory written by Manabu Asai and published by . This book was released on 2017 with total page 38 pages. Available in PDF, EPUB and Kindle. Book excerpt: The paper develops a novel realized stochastic volatility model of asset returns and realized volatility that incorporates general asymmetry and long memory (hereafter the RSV-GALM model). The contribution of the paper ties in with Robert Basmann's seminal work in terms of the estimation of highly non-linear model specifications (“Causality tests and observationally equivalent representations of econometric models”, Journal of Econometrics, 1988), especially for specifying causal effects from returns to future volatility. This paper discusses asymptotic results of a Whittle likelihood estimator for the RSV-GALM model and a test for general asymmetry, and analyses the finite sample properties. The paper also develops an approach to obtain volatility estimates and out-of-sample forecasts. Using high frequency data for three US financial assets, the new model is estimated and evaluated. The paper compares the forecasting performance of the new model with a realized conditional volatility model.

Download or read book Handbook of Volatility Models and Their Applications written by Luc Bauwens and published by John Wiley & Sons. This book was released on 2012-04-17 with total page 566 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.

Download or read book Discrete time Volatility Forecasting with Persistent Leverage Effect and the Link with Continuous time Volatility Modeling written by Fulvio Corsi and published by . This book was released on 2010 with total page 34 pages. Available in PDF, EPUB and Kindle. Book excerpt: We first propose a reduced-form model in discrete time for Samp;P500 volatility showing that the forecasting performance of a volatility model can be significantly improved by introducing a persistent leverage effect with a long-range dependence similar to that of volatility itself. We also find a strongly significant positive impact of lagged jumps on volatility, which however is absorbed more quickly. We then estimate continuous-time stochastic volatility models which are able to reproduce the statistical features captured by the reduced-form model. We show that a single-factor model driven by a fractional Brownian motion is unable to reproduce the volatility dynamics observed in the data, while a multi-factor Markovian model is able to reproduce the persistence of both volatility and leverage effect. The impact of jumps can instead be associated with a common jump component in price and volatility. These findings cast serious doubts on the need of modeling volatility with a genuine long memory component, while reinforcing the view of volatility being generated by the superposition of multiple factors.

Download or read book On Estimation Diagnostic Testing and Smoothing of Long Memory Stochastic Volatility Models written by Kai Li and published by . This book was released on 2000 with total page 35 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Download or read book Volatility and Correlation written by Riccardo Rebonato and published by John Wiley & Sons. This book was released on 2005-07-08 with total page 864 pages. Available in PDF, EPUB and Kindle. Book excerpt: In Volatility and Correlation 2nd edition: The Perfect Hedger and the Fox, Rebonato looks at derivatives pricing from the angle of volatility and correlation. With both practical and theoretical applications, this is a thorough update of the highly successful Volatility & Correlation – with over 80% new or fully reworked material and is a must have both for practitioners and for students. The new and updated material includes a critical examination of the ‘perfect-replication’ approach to derivatives pricing, with special attention given to exotic options; a thorough analysis of the role of quadratic variation in derivatives pricing and hedging; a discussion of the informational efficiency of markets in commonly-used calibration and hedging practices. Treatment of new models including Variance Gamma, displaced diffusion, stochastic volatility for interest-rate smiles and equity/FX options. The book is split into four parts. Part I deals with a Black world without smiles, sets out the author’s ‘philosophical’ approach and covers deterministic volatility. Part II looks at smiles in equity and FX worlds. It begins with a review of relevant empirical information about smiles, and provides coverage of local-stochastic-volatility, general-stochastic-volatility, jump-diffusion and Variance-Gamma processes. Part II concludes with an important chapter that discusses if and to what extent one can dispense with an explicit specification of a model, and can directly prescribe the dynamics of the smile surface. Part III focusses on interest rates when the volatility is deterministic. Part IV extends this setting in order to account for smiles in a financially motivated and computationally tractable manner. In this final part the author deals with CEV processes, with diffusive stochastic volatility and with Markov-chain processes. Praise for the First Edition: “In this book, Dr Rebonato brings his penetrating eye to bear on option pricing and hedging.... The book is a must-read for those who already know the basics of options and are looking for an edge in applying the more sophisticated approaches that have recently been developed.” —Professor Ian Cooper, London Business School “Volatility and correlation are at the very core of all option pricing and hedging. In this book, Riccardo Rebonato presents the subject in his characteristically elegant and simple fashion...A rare combination of intellectual insight and practical common sense.” —Anthony Neuberger, London Business School

Download or read book Bias Reduced Estimation of Long Memory Stochastic Volatility written by Per Skaarup Frederiksen and published by . This book was released on 2008 with total page 17 pages. Available in PDF, EPUB and Kindle. Book excerpt: We propose to use a variant of the local polynomial Whittle estimator to estimate the memory parameter in volatility for long memory stochastic volatility models with potential nonstationarity in the volatility process. We show that the estimator is asymptotically normal and capable of obtaining bias reduction as well as a rate of convergence arbitrarily close to the parametric rate, n1=2. A Monte Carlo study is conducted to support the theoretical results, and an analysis of daily exchange rates demonstrates the empirical usefulness of the estimators.

Download or read book Estimation of the Long Memory Stochastic Volatility Model Parameters that is Robust to Level Shifts and Deterministic Trends written by Adam McCloskey and published by . This book was released on 2013 with total page 0 pages. Available in PDF, EPUB and Kindle. Book excerpt: I provide conditions under which the trimmed FDQML estimator, advanced by McCloskey (2010) in the context of fully parametric short-memory models, can be used to estimate the long-memory stochastic volatility model parameters in the presence of additive low-frequency contamination in log-squared returns. The types of low-frequency contamination covered include level shifts as well as deterministic trends. I establish consistency and asymptotic normality in the presence or absence of such low-frequency contamination under certain conditions on the growth rate of the trimming parameter. I also provide theoretical guidance on the choice of trimming parameter by heuristically obtaining its asymptotic MSE-optimal rate under certain types of low-frequency contamination. A simulation study examines the finite sample properties of the robust estimator, showing substantial gains from its use in the presence of level shifts. The finite sample analysis also explores how different levels of trimming affect the parameter estimates in the presence and absence of low-frequency contamination and long-memory.

Download or read book Handbook of Quantitative Finance and Risk Management written by Cheng-Few Lee and published by Springer Science & Business Media. This book was released on 2010-06-14 with total page 1700 pages. Available in PDF, EPUB and Kindle. Book excerpt: Quantitative finance is a combination of economics, accounting, statistics, econometrics, mathematics, stochastic process, and computer science and technology. Increasingly, the tools of financial analysis are being applied to assess, monitor, and mitigate risk, especially in the context of globalization, market volatility, and economic crisis. This two-volume handbook, comprised of over 100 chapters, is the most comprehensive resource in the field to date, integrating the most current theory, methodology, policy, and practical applications. Showcasing contributions from an international array of experts, the Handbook of Quantitative Finance and Risk Management is unparalleled in the breadth and depth of its coverage. Volume 1 presents an overview of quantitative finance and risk management research, covering the essential theories, policies, and empirical methodologies used in the field. Chapters provide in-depth discussion of portfolio theory and investment analysis. Volume 2 covers options and option pricing theory and risk management. Volume 3 presents a wide variety of models and analytical tools. Throughout, the handbook offers illustrative case examples, worked equations, and extensive references; additional features include chapter abstracts, keywords, and author and subject indices. From "arbitrage" to "yield spreads," the Handbook of Quantitative Finance and Risk Management will serve as an essential resource for academics, educators, students, policymakers, and practitioners.

Download or read book On the Log Periodogram Regression Estimator of the Memory Parameter in Long Memory Stochastic Volatility Models written by Rohit Deo and published by . This book was released on 2008 with total page 25 pages. Available in PDF, EPUB and Kindle. Book excerpt: We consider semiparametric estimation of the memory parameter in a long memorystochastic volatility model. We study the estimator based on a log periodogramregression as originally proposed by Geweke and Porter-Hudak (1983,Journal of Time Series Analysis 4, 221 238). Expressions for the asymptotic biasand variance of the estimator are obtained, and the asymptotic distribution is shownto be the same as that obtained in recent literature for a Gaussian long memoryseries. The theoretical result does not require omission of a block of frequenciesnear the origin. We show that this ability to use the lowest frequencies is particularlydesirable in the context of the long memory stochastic volatility model.