Download or read book Large Volatility Matrix Analysis Using Global and National Factor Models written by Sung Hoon Choi and published by . This book was released on 2022 with total page 0 pages. Available in PDF, EPUB and Kindle. Book excerpt: Several large volatility matrix inference procedures have been developed, based on the latent factor model. They often assumed that there are a few of common factors, which can account for volatility dynamics. However, several studies have demonstrated the presence of local factors. In particular, when analyzing the global stock market, we often observe that nation-specific factors explain their own country's volatility dynamics. To account for this, we propose the Double Principal Orthogonal complEment Thresholding (Double-POET) method, based on multi-level factor models, and also establish its asymptotic properties. Furthermore, we demonstrate the drawback of using the regular principal orthogonal component thresholding (POET) when the local factor structure exists. We also describe the blessing of dimensionality using Double-POET for local covariance matrix estimation. Finally, we investigate the performance of the Double-POET estimator in an out-of-sample portfolio allocation study using international stocks from 20 financial markets.
Download or read book Factor GARCH ITO Models for High Frequency Data with Application to Large Volatility Matrix Prediction written by Donggyu Kim and published by . This book was released on 2017 with total page 41 pages. Available in PDF, EPUB and Kindle. Book excerpt: Several novel large volatility matrix estimation methods have been developed based on the high-frequency financial data. They often employ the approximate factor model that leads to a low-rank plus sparse structure for the integrated volatility matrix and facilitates estimation of large volatility matrices. However, for predicting future volatility matrices, these nonparametric estimators do not have a dynamic structure to implement. In this paper, we introduce a novel Ito diffusion process based on the approximate factor models and call it a factor GARCH-Ito model. We then investigate its properties and propose a quasi-maximum likelihood estimation method for the parameter of the factor GARCH-Ito model. We also apply it to estimating conditional expected large volatility matrices and establish their asymptotic properties. Simulation studies are conducted to validate the finite sample performance of the proposed estimation methods. The proposed method is also illustrated by using data from the constituents of the S&P 500 index and an application to constructing the minimum variance portfolio with gross exposure constraints.
Download or read book Robust High Dimensional Volatility Matrix Estimation for High Frequency Factor Model written by Jianqing Fan and published by . This book was released on 2017 with total page 42 pages. Available in PDF, EPUB and Kindle. Book excerpt: High-frequency financial data allow us to estimate large volatility matrices with relatively short time horizon. Many novel statistical methods have been introduced to address large volatility matrix estimation problems from a high-dimensional Ito process with microstructural noise contamination. Their asymptotic theories require sub-Gaussian or some finite high-order moments assumptions for observed log-returns. These assumptions are at odd with the heavy tail phenomenon that is pandemic in financial stock returns and new procedures are needed to mitigate the influence of heavy tails. In this paper, we introduce the Huber loss function with a diverging threshold to develop a robust realized volatility estimation. We show that it has the sub-Gaussian concentration around the volatility with only finite fourth moments of observed log-returns. With the proposed robust estimator as input, we further regularize it by using the principal orthogonal component thresholding (POET) procedure to estimate the large volatility matrix that admits an approximate factor structure. We establish the asymptotic theories for such low-rank plus sparse matrices. The simulation study is conducted to check the finite sample performance of the proposed estimation methods.
Download or read book Discretization of Processes written by Jean Jacod and published by Springer Science & Business Media. This book was released on 2011-10-22 with total page 596 pages. Available in PDF, EPUB and Kindle. Book excerpt: In applications, and especially in mathematical finance, random time-dependent events are often modeled as stochastic processes. Assumptions are made about the structure of such processes, and serious researchers will want to justify those assumptions through the use of data. As statisticians are wont to say, “In God we trust; all others must bring data.” This book establishes the theory of how to go about estimating not just scalar parameters about a proposed model, but also the underlying structure of the model itself. Classic statistical tools are used: the law of large numbers, and the central limit theorem. Researchers have recently developed creative and original methods to use these tools in sophisticated (but highly technical) ways to reveal new details about the underlying structure. For the first time in book form, the authors present these latest techniques, based on research from the last 10 years. They include new findings. This book will be of special interest to researchers, combining the theory of mathematical finance with its investigation using market data, and it will also prove to be useful in a broad range of applications, such as to mathematical biology, chemical engineering, and physics.
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 A Comparative Study on Large Multivariate Volatility Matrix Modeling for High frequency Financial Data written by Dongchen Jiang and published by . This book was released on 2015 with total page 80 pages. Available in PDF, EPUB and Kindle. Book excerpt: Abstract: Modeling and forecasting the volatilities of high-frequency data observed on the prices of financial assets are vibrant research areas in econometrics and statistics. However, most of the available methods are not directly applicable when the number of assets involved is large, due to the lack of accuracy in estimating high-dimensional matrices. This paper compared two methodologies of vast volatility matrix estimation for high-frequency data. One is to estimate the Average Realized Volatility Matrix and to regularize it by banding and thresholding. In this method, first we select grids as pre-sampling frequencies, construct a realized volatility matrix using previous tick method according to each pre-sampling frequency and then take the average of the constructed realized volatility matrices as the stage one estimator, which we call the ARVM estimator. Then we regularize the ARVM estimator to yield good consistent estimators of the large integrated volatility matrix. We consider two regularizations: thresholding and banding. The other is Dynamic Conditional Correlation (DCC) which can be estimated for two stage, where in the rst stage univariate GARCH models are estimated for each residual series, and in the second stage, the residuals are used to estimate the parameters of the dynamic correlation. Asymptotic theory for the two proposed methodologies shows that the estimator are consistent. In numerical studies, the proposed two methodologies are applied to simulated data set and real high-frequency prices from top 100 S & P 500 stocks according to the trading volume over a period of 3 months, 64 trading days in 2013. From the perfomances of estimators, the conclusion is that TARVM estimator performs better than DCC volatility matrix. And its largest eigenvalues are more stable than those of DCC model so that it is more approriable in eigen-based anaylsis.
Download or read book Factor Overnight GARCH It Models written by Donggyu Kim and published by . This book was released on 2023 with total page 0 pages. Available in PDF, EPUB and Kindle. Book excerpt: This paper introduces a unified factor overnight GARCH-Itô Models model for large volatility matrix estimation and prediction. To account for whole-day market dynamics, the proposed model has two different instantaneous factor volatility processes for the open-to-close and close-to-open periods, while each embeds the discrete-time multivariate GARCH model structure. To estimate latent factor volatility, we assume the low rank plus sparse structure and employ non-parametric estimation procedures.Then, based on the connection between the discrete-time model structure and the continuous-time diffusion process, we propose a weighted least squares estimation procedure with the non-parametric factor volatility estimator and establish its asymptotic theorems.
Download or read book The Oxford Handbook of Economic Forecasting written by Michael P. Clements and published by OUP USA. This book was released on 2011-07-08 with total page 732 pages. Available in PDF, EPUB and Kindle. Book excerpt: Greater data availability has been coupled with developments in statistical theory and economic theory to allow more elaborate and complicated models to be entertained. These include factor models, DSGE models, restricted vector autoregressions, and non-linear models.
Download or read book Spectral Analysis of Large Dimensional Random Matrices written by Zhidong Bai and published by Springer Science & Business Media. This book was released on 2009-12-10 with total page 560 pages. Available in PDF, EPUB and Kindle. Book excerpt: The aim of the book is to introduce basic concepts, main results, and widely applied mathematical tools in the spectral analysis of large dimensional random matrices. The core of the book focuses on results established under moment conditions on random variables using probabilistic methods, and is thus easily applicable to statistics and other areas of science. The book introduces fundamental results, most of them investigated by the authors, such as the semicircular law of Wigner matrices, the Marcenko-Pastur law, the limiting spectral distribution of the multivariate F matrix, limits of extreme eigenvalues, spectrum separation theorems, convergence rates of empirical distributions, central limit theorems of linear spectral statistics, and the partial solution of the famous circular law. While deriving the main results, the book simultaneously emphasizes the ideas and methodologies of the fundamental mathematical tools, among them being: truncation techniques, matrix identities, moment convergence theorems, and the Stieltjes transform. Its treatment is especially fitting to the needs of mathematics and statistics graduate students and beginning researchers, having a basic knowledge of matrix theory and an understanding of probability theory at the graduate level, who desire to learn the concepts and tools in solving problems in this area. It can also serve as a detailed handbook on results of large dimensional random matrices for practical users. This second edition includes two additional chapters, one on the authors' results on the limiting behavior of eigenvectors of sample covariance matrices, another on applications to wireless communications and finance. While attempting to bring this edition up-to-date on recent work, it also provides summaries of other areas which are typically considered part of the general field of random matrix theory.
Download or read book Structured Volatility Matrix Estimation for Non Synchronized High Frequency Financial Data written by Jianqing Fan and published by . This book was released on 2017 with total page 35 pages. Available in PDF, EPUB and Kindle. Book excerpt: Recently several large volatility matrix estimation procedures have been developed for factor-based Ito processes whose integrated volatility matrix consists of low-rank and sparse matrices. Their performance depends on the accuracy of input volatility matrix estimators. When estimating co-volatilities based on high-frequency data, one of the crucial challenges is non-synchronization for illiquid assets, which makes their co-volatility estimators inaccurate. In this paper, we study how to estimate the large integrated volatility matrix without using co-volatilities of illiquid assets. Specifically, we pretend that the co-volatilities for illiquid assets are missing, and estimate the low-rank matrix using a matrix completion scheme with a structured missing pattern. To further regularize the sparse volatility matrix, we employ the principal orthogonal complement thresholding method (POET). We also investigate the asymptotic properties of the proposed estimation procedure and demonstrate its advantages over using co-volatilities of illiquid assets. The advantages of our methods are also verified by an extensive simulation study and illustrated by high-frequency financial data for constituents of the S&P 500 index.
Download or read book Risk and Asset Allocation written by Attilio Meucci and published by Springer Science & Business Media. This book was released on 2009-05-22 with total page 547 pages. Available in PDF, EPUB and Kindle. Book excerpt: Discusses in the practical and theoretical aspects of one-period asset allocation, i.e. market Modeling, invariants estimation, portfolia evaluation, and portfolio optimization in the prexence of estimation risk The book is software based, many of the exercises simulate in Matlab the solution to practical problems and can be downloaded from the book's web-site
Download or read book Dynamic Factor Models written by Jörg Breitung and published by . This book was released on 2016 with total page 40 pages. Available in PDF, EPUB and Kindle. Book excerpt: Factor models can cope with many variables without running into scarce degrees of freedom.
Download or read book Empirical Asset Pricing written by Wayne Ferson and published by MIT Press. This book was released on 2019-03-12 with total page 497 pages. Available in PDF, EPUB and Kindle. Book excerpt: An introduction to the theory and methods of empirical asset pricing, integrating classical foundations with recent developments. This book offers a comprehensive advanced introduction to asset pricing, the study of models for the prices and returns of various securities. The focus is empirical, emphasizing how the models relate to the data. The book offers a uniquely integrated treatment, combining classical foundations with more recent developments in the literature and relating some of the material to applications in investment management. It covers the theory of empirical asset pricing, the main empirical methods, and a range of applied topics. The book introduces the theory of empirical asset pricing through three main paradigms: mean variance analysis, stochastic discount factors, and beta pricing models. It describes empirical methods, beginning with the generalized method of moments (GMM) and viewing other methods as special cases of GMM; offers a comprehensive review of fund performance evaluation; and presents selected applied topics, including a substantial chapter on predictability in asset markets that covers predicting the level of returns, volatility and higher moments, and predicting cross-sectional differences in returns. Other chapters cover production-based asset pricing, long-run risk models, the Campbell-Shiller approximation, the debate on covariance versus characteristics, and the relation of volatility to the cross-section of stock returns. An extensive reference section captures the current state of the field. The book is intended for use by graduate students in finance and economics; it can also serve as a reference for professionals.
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 Dynamic Factor Models written by Siem Jan Koopman and published by Emerald Group Publishing. This book was released on 2016-01-08 with total page 685 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume explores dynamic factor model specification, asymptotic and finite-sample behavior of parameter estimators, identification, frequentist and Bayesian estimation of the corresponding state space models, and applications.
Download or read book Multifractal Volatility written by Laurent E. Calvet and published by Academic Press. This book was released on 2008-10-13 with total page 273 pages. Available in PDF, EPUB and Kindle. Book excerpt: Calvet and Fisher present a powerful, new technique for volatility forecasting that draws on insights from the use of multifractals in the natural sciences and mathematics and provides a unified treatment of the use of multifractal techniques in finance. A large existing literature (e.g., Engle, 1982; Rossi, 1995) models volatility as an average of past shocks, possibly with a noise component. This approach often has difficulty capturing sharp discontinuities and large changes in financial volatility. Their research has shown the advantages of modelling volatility as subject to abrupt regime changes of heterogeneous durations. Using the intuition that some economic phenomena are long-lasting while others are more transient, they permit regimes to have varying degrees of persistence. By drawing on insights from the use of multifractals in the natural sciences and mathematics, they show how to construct high-dimensional regime-switching models that are easy to estimate, and substantially outperform some of the best traditional forecasting models such as GARCH. The goal of Multifractal Volatility is to popularize the approach by presenting these exciting new developments to a wider audience. They emphasize both theoretical and empirical applications, beginning with a style that is easily accessible and intuitive in early chapters, and extending to the most rigorous continuous-time and equilibrium pricing formulations in final chapters. Presents a powerful new technique for forecasting volatility Leads the reader intuitively from existing volatility techniques to the frontier of research in this field by top scholars at major universities The first comprehensive book on multifractal techniques in finance, a cutting-edge field of research
Download or read book Recent Econometric Techniques for Macroeconomic and Financial Data written by Gilles Dufrénot and published by Springer Nature. This book was released on 2020-11-21 with total page 387 pages. Available in PDF, EPUB and Kindle. Book excerpt: The book provides a comprehensive overview of the latest econometric methods for studying the dynamics of macroeconomic and financial time series. It examines alternative methodological approaches and concepts, including quantile spectra and co-spectra, and explores topics such as non-linear and non-stationary behavior, stochastic volatility models, and the econometrics of commodity markets and globalization. Furthermore, it demonstrates the application of recent techniques in various fields: in the frequency domain, in the analysis of persistent dynamics, in the estimation of state space models and new classes of volatility models. The book is divided into two parts: The first part applies econometrics to the field of macroeconomics, discussing trend/cycle decomposition, growth analysis, monetary policy and international trade. The second part applies econometrics to a wide range of topics in financial economics, including price dynamics in equity, commodity and foreign exchange markets and portfolio analysis. The book is essential reading for scholars, students, and practitioners in government and financial institutions interested in applying recent econometric time series methods to financial and economic data.
