Large Volatility Matrix Inference Based On High Frequency Financial Data
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Large Volatility Matrix Inference Based On High Frequency Financial Data
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Author :
language : en
Publisher:
Release Date : 2013
Large Volatility Matrix Inference Based On High Frequency Financial Data written by and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2013 with categories.
Financial practices often need to estimate an integrated volatility matrix of a large number of assets using noisy high-frequency financial data. This estimation problem is a challenging one for four reasons: (1) high-frequency financial data are discrete observations of the underlying assets' price processes; (2) due to market micro-structure noise, high-frequency data are observed with measurement errors; (3) different assets are traded at different time points, which is the so-called non-synchronization phenomenon in high-frequency financial data; (4) the number of assets may be comparable to or even exceed the observations, and hence many existing estimators of small size volatility matrices become inconsistent when the size of the matrix is close to or larger than the sample size. In this dissertation, we focus on large volatility matrix inference for high-frequency financial data, which can be summarized in three aspects. On the methodological aspect, we propose a new threshold MSRVM estimator of large volatility matrix. This estimator can deal with all the four challenges, and is consistent when both sample size and matrix size go to infinity. On the theoretical aspect, we study the optimal convergence rate for the volatility matrix estimation, by building the asymptotic theory for the proposed estimator and deriving a minimax lower bound for this estimation problem. The proposed threshold MSRVM estimator has a risk matching with the lower bound up to a constant factor, and hence it achieves an optimal convergence rate. As for the applications, we develop a novel approach to predict the volatility matrix. The approach extends the applicability of classical low-frequency models such as matrix factor models and vector autoregressive models to the high-frequency data. With this approach, we pool together the strengths of both classical low-frequency models and new high-frequency estimation methodologies. Furthermore, numerical studies are conducted to test the finite sample performance of the proposed estimators, to support the established asymptotic theories.
A Comparative Study On Large Multivariate Volatility Matrix Modeling For High Frequency Financial Data
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Author : Dongchen Jiang
language : en
Publisher:
Release Date : 2015
A Comparative Study On Large Multivariate Volatility Matrix Modeling For High Frequency Financial Data written by Dongchen Jiang 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.
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.
High Frequency Financial Econometrics
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Author : Yacine Aït-Sahalia
language : en
Publisher: Princeton University Press
Release Date : 2014-07-21
High Frequency Financial Econometrics written by Yacine Aït-Sahalia and has been published by Princeton University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2014-07-21 with Business & Economics categories.
A comprehensive introduction to the statistical and econometric methods for analyzing high-frequency financial data High-frequency trading is an algorithm-based computerized trading practice that allows firms to trade stocks in milliseconds. Over the last fifteen years, the use of statistical and econometric methods for analyzing high-frequency financial data has grown exponentially. This growth has been driven by the increasing availability of such data, the technological advancements that make high-frequency trading strategies possible, and the need of practitioners to analyze these data. This comprehensive book introduces readers to these emerging methods and tools of analysis. Yacine Aït-Sahalia and Jean Jacod cover the mathematical foundations of stochastic processes, describe the primary characteristics of high-frequency financial data, and present the asymptotic concepts that their analysis relies on. Aït-Sahalia and Jacod also deal with estimation of the volatility portion of the model, including methods that are robust to market microstructure noise, and address estimation and testing questions involving the jump part of the model. As they demonstrate, the practical importance and relevance of jumps in financial data are universally recognized, but only recently have econometric methods become available to rigorously analyze jump processes. Aït-Sahalia and Jacod approach high-frequency econometrics with a distinct focus on the financial side of matters while maintaining technical rigor, which makes this book invaluable to researchers and practitioners alike.
Nonparametric Estimation Of Large Spot Volatility Matrices For High Frequency Financial Data
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Author : Ruijun Bu
language : en
Publisher:
Release Date : 2022
Nonparametric Estimation Of Large Spot Volatility Matrices For High Frequency Financial Data written by Ruijun Bu and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2022 with categories.
Factor Garch Ito Models For High Frequency Data With Application To Large Volatility Matrix Prediction
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Author : Donggyu Kim
language : en
Publisher:
Release Date : 2017
Factor Garch Ito Models For High Frequency Data With Application To Large Volatility Matrix Prediction written by Donggyu Kim 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.
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.
Inference From High Frequency Data
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Author :
language : en
Publisher:
Release Date : 2015
Inference From High Frequency Data written by 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.
Big Data
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Author : Kuan-Ching Li
language : en
Publisher: CRC Press
Release Date : 2015-09-15
Big Data written by Kuan-Ching Li and has been published by CRC Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2015-09-15 with Computers categories.
As today’s organizations are capturing exponentially larger amounts of data than ever, now is the time for organizations to rethink how they digest that data. Through advanced algorithms and analytics techniques, organizations can harness this data, discover hidden patterns, and use the newly acquired knowledge to achieve competitive advantages. Presenting the contributions of leading experts in their respective fields, Big Data: Algorithms, Analytics, and Applications bridges the gap between the vastness of Big Data and the appropriate computational methods for scientific and social discovery. It covers fundamental issues about Big Data, including efficient algorithmic methods to process data, better analytical strategies to digest data, and representative applications in diverse fields, such as medicine, science, and engineering. The book is organized into five main sections: Big Data Management—considers the research issues related to the management of Big Data, including indexing and scalability aspects Big Data Processing—addresses the problem of processing Big Data across a wide range of resource-intensive computational settings Big Data Stream Techniques and Algorithms—explores research issues regarding the management and mining of Big Data in streaming environments Big Data Privacy—focuses on models, techniques, and algorithms for preserving Big Data privacy Big Data Applications—illustrates practical applications of Big Data across several domains, including finance, multimedia tools, biometrics, and satellite Big Data processing Overall, the book reports on state-of-the-art studies and achievements in algorithms, analytics, and applications of Big Data. It provides readers with the basis for further efforts in this challenging scientific field that will play a leading role in next-generation database, data warehousing, data mining, and cloud computing research. It also explores related applications in diverse sectors, covering technologies for media/data communication, elastic media/data storage, cross-network media/data fusion, and SaaS.
Discretization Of Processes
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Author : Jean Jacod
language : en
Publisher: Springer Science & Business Media
Release Date : 2011-10-22
Discretization Of Processes written by Jean Jacod 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 2011-10-22 with Mathematics categories.
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.
Essays On Estimation And Inference For Volatility With High Frequency Data
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Author : Ilze Kalnina
language : en
Publisher:
Release Date : 2009
Essays On Estimation And Inference For Volatility With High Frequency Data written by Ilze Kalnina and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2009 with Academic theses categories.
High Frequency Data Frequency Domain Inference And Volatility Forecasting
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Author : Jonathan H. Wright
language : en
Publisher:
Release Date : 1999
High Frequency Data Frequency Domain Inference And Volatility Forecasting written by Jonathan H. Wright and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1999 with Rate of return categories.
While it is clear that the volatility of asset returns is serially correlated, there is no general agreement as to the most appropriate parametric model for characterizing this temporal dependence. In this paper, we propose a simple way of modeling financial market volatility using high frequency data. The method avoids using a tight parametric model, by instead simply fitting a long autoregression to log-squared, squared or absolute high frequency returns. This can either be estimated by the usual time domain method, or alternatively the autoregressive coefficients can be backed out from the smoothed periodogram estimate of the spectrum of log-squared, squared or absolute returns. We show how this approach can be used to construct volatility forecasts, which compare favorably with some leading alternatives in an out-of-sample forecasting exercise.