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Author: Jianqing Fan
Publisher:
ISBN:
Category :
Languages : en
Pages : 36
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Book Description
The wide availability of high-frequency data for many financial instruments stimulates a upsurge interest in statistical research on the estimation of volatility. Jump-diffusion processes observed with market microstructure noise are frequently used to model high-frequency financial data. Yet, existing methods are developed for either noisy data from a continuous diffusion price model or data from a jump-diffusion price model without noise. We propose methods to cope with both jumps in the price and market microstructure noise in the observed data. They allow us to estimate both integrated volatility and jump variation from the data sampled from jump-diffusion price processes, contaminated with the market microstructure noise. Our approach is to first remove jumps from the data and then apply a noise-resistent method to estimated the integrated volatility. The asymptotic analysis and the simulation study reveal that the proposed wavelet methods can successfully remove the jumps in the price processes and the integrated volatility can be estimated as well as the case with no presence of jumps in the price processes. In addition, they have outstanding statistical efficiency. The methods are illustrated by applications to two high-frequency exchange rate data sets.
Author: Jianqing Fan
Publisher:
ISBN:
Category :
Languages : en
Pages : 36
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Book Description
The wide availability of high-frequency data for many financial instruments stimulates a upsurge interest in statistical research on the estimation of volatility. Jump-diffusion processes observed with market microstructure noise are frequently used to model high-frequency financial data. Yet, existing methods are developed for either noisy data from a continuous diffusion price model or data from a jump-diffusion price model without noise. We propose methods to cope with both jumps in the price and market microstructure noise in the observed data. They allow us to estimate both integrated volatility and jump variation from the data sampled from jump-diffusion price processes, contaminated with the market microstructure noise. Our approach is to first remove jumps from the data and then apply a noise-resistent method to estimated the integrated volatility. The asymptotic analysis and the simulation study reveal that the proposed wavelet methods can successfully remove the jumps in the price processes and the integrated volatility can be estimated as well as the case with no presence of jumps in the price processes. In addition, they have outstanding statistical efficiency. The methods are illustrated by applications to two high-frequency exchange rate data sets.
Author: Ionut Florescu
Publisher: John Wiley & Sons
ISBN: 1118593324
Category : Business & Economics
Languages : en
Pages : 414
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Book Description
Reflecting the fast pace and ever-evolving nature of the financial industry, the Handbook of High-Frequency Trading and Modeling in Finance details how high-frequency analysis presents new systematic approaches to implementing quantitative activities with high-frequency financial data. Introducing new and established mathematical foundations necessary to analyze realistic market models and scenarios, the handbook begins with a presentation of the dynamics and complexity of futures and derivatives markets as well as a portfolio optimization problem using quantum computers. Subsequently, the handbook addresses estimating complex model parameters using high-frequency data. Finally, the handbook focuses on the links between models used in financial markets and models used in other research areas such as geophysics, fossil records, and earthquake studies. The Handbook of High-Frequency Trading and Modeling in Finance also features: • Contributions by well-known experts within the academic, industrial, and regulatory fields • A well-structured outline on the various data analysis methodologies used to identify new trading opportunities • Newly emerging quantitative tools that address growing concerns relating to high-frequency data such as stochastic volatility and volatility tracking; stochastic jump processes for limit-order books and broader market indicators; and options markets • Practical applications using real-world data to help readers better understand the presented material The Handbook of High-Frequency Trading and Modeling in Finance is an excellent reference for professionals in the fields of business, applied statistics, econometrics, and financial engineering. The handbook is also a good supplement for graduate and MBA-level courses on quantitative finance, volatility, and financial econometrics. Ionut Florescu, PhD, is Research Associate Professor in Financial Engineering and Director of the Hanlon Financial Systems Laboratory at Stevens Institute of Technology. His research interests include stochastic volatility, stochastic partial differential equations, Monte Carlo Methods, and numerical methods for stochastic processes. Dr. Florescu is the author of Probability and Stochastic Processes, the coauthor of Handbook of Probability, and the coeditor of Handbook of Modeling High-Frequency Data in Finance, all published by Wiley. Maria C. Mariani, PhD, is Shigeko K. Chan Distinguished Professor in Mathematical Sciences and Chair of the Department of Mathematical Sciences at The University of Texas at El Paso. Her research interests include mathematical finance, applied mathematics, geophysics, nonlinear and stochastic partial differential equations and numerical methods. Dr. Mariani is the coeditor of Handbook of Modeling High-Frequency Data in Finance, also published by Wiley. H. Eugene Stanley, PhD, is William Fairfield Warren Distinguished Professor at Boston University. Stanley is one of the key founders of the new interdisciplinary field of econophysics, and has an ISI Hirsch index H=128 based on more than 1200 papers. In 2004 he was elected to the National Academy of Sciences. Frederi G. Viens, PhD, is Professor of Statistics and Mathematics and Director of the Computational Finance Program at Purdue University. He holds more than two dozen local, regional, and national awards and he travels extensively on a world-wide basis to deliver lectures on his research interests, which range from quantitative finance to climate science and agricultural economics. A Fellow of the Institute of Mathematics Statistics, Dr. Viens is the coeditor of Handbook of Modeling High-Frequency Data in Finance, also published by Wiley.
Author: Yacine Aït-Sahalia
Publisher: Princeton University Press
ISBN: 0691161437
Category : Business & Economics
Languages : en
Pages : 683
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Book Description
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.
Author: Xin Zhang
Publisher:
ISBN:
Category :
Languages : en
Pages : 90
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Book Description
This dissertation work focuses on developing statistical methods for volatility estimation and prediction with high frequency financial data. We consider two kinds of volatility: integrated volatility and jump variation. In the first part, we introduce the methods for integrated volatility estimation with the presence of microstructure noise. We will first talk about the optimal sampling frequency for integrated volatility estimation since subsampling is very popular in practice. Then we will discuss about those methods based on subsampling. Two-scale estimator is developed using the subsampling idea while taking advantage of all of the data. An extension to the multi-scale further improves the efficiency of the estimation. In the second part, we propose a heterogenous autoregressive model for the integrated volatility estimators based on subsampling. An empirical approach is to estimate integrated volatility using high frequency data and then fit the estimates to a low frequency heterogeneous autoregressive volatility model for prediction. We provide some theoretical justifications for the empirical approach by showing that these estimators approximately obey a heterogenous autoregressive model for some appropriate underlying price and volatility processes. In the third part, we propose a method for jump variation estimation using wavelet techniques. Previously, jumps are not assumed in the model. In this part, we will concentrate on jump variation estimation and there- fore, we will be able to estimate the integrated volatility and jump variation individually. We show that by choosing a threshold, we will be able to detect the jump location, and by using the realized volatility processes instead of the original price process, we will be able to improve the convergence rate of estimation. We include both numerical and empirical results of this method.
Author: Donggyu Kim
Publisher:
ISBN:
Category :
Languages : en
Pages : 0
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Book Description
In this dissertation, we study two topics, the volatility analysis based on the high-frequency financial data and quantum state tomography. In Part I, we study the volatility analysis based on the high-frequency financial data. We first investigate how to estimate large volatility matrices effectively and efficiently. For example, we introduce threshold rules to regularize kernel realized volatility, pre-averaging realized volatility, and multi-scale realized volatility. Their convergence rates are derived under sparsity on the large integrated volatility matrix. To account for the sparse structure well, we employ the factor-based Itô processes and under the proposed factor-based model, we develop an estimation scheme called "blocking and regularizing". Also, we establish a minimax lower bound for the eigenspace estimation problem and propose sparse principal subspace estimation methods by using the multi-scale realized volatility matrix estimator or the pre-averaging realized volatility matrix estimator. Finally, we introduce a unified model, which can accommodate both continuous-time Itô processes used to model high-frequency stock prices and GARCH processes employed to model low-frequency stock prices, by embedding a discrete-time GARCH volatility in its continuous-time instantaneous volatility. We adopt realized volatility estimators based on high-frequency financial data and the quasi-likelihood function for the low-frequency GARCH structure to develop parameter estimation methods for the combined high-frequency and low-frequency data. In Part II, we study the quantum state tomography with Pauli measurements. In the quantum science, the dimension of the quantum density matrix usually grows exponentially with the size of the quantum system, and thus it is important to develop effective and efficient estimation methods for the large quantum density matrices. We study large density matrix estimation methods and obtain the minimax lower bound under some sparse structures, for example, (i) the coefficients of the density matrix with respect to the Pauli basis are sparse; (ii) the rank is low; (iii) the eigenvectors are sparse. Their performances may depend on the sparse structure, and so it is essential to choose appropriate estimation methods according to the sparse structure. In light of this, we study how to conduct hypothesis tests for the sparse structure. Specifically, we propose hypothesis test procedures and develop central limit theorems for each test statistics. A simulation study is conducted to check the finite sample performances of proposed estimation methods and hypothesis tests.
Author: Xinyu Song
Publisher:
ISBN:
Category :
Languages : en
Pages : 68
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Book Description
In this dissertation, we present the topic on volatility analysis with combined discrete-time and continuous-time models by employing low-frequency, high-frequency and option data. We first investigate the traditional low-frequency approach for volatility analysis that frequently adopts generalized autoregressive conditional heteroscedastic (GARCH) type models and modern high-frequency approach for volatility estimation that often employs realized volatility type estimators, examples include multi-scale realized volatility estimators, pre-averaging realized volatility estimators and kernel realized volatility estimators. We introduce a new model for volatility analysis by combining low-frequency and high-frequency approaches. The proposed model is an Ito diffusion process where the instantaneous volatility depends on integrated volatility and squared log return. When the model is restricted to integer times, conditional volatility of the process adopts an analogous structure with the one seen in a standard GARCH model and includes one additional innovation: the integrated volatility. The proposed model is named as generalized unified GARCH-Ito model. Parameter estimation is built on the marriage of a quasi-likelihood function obtained based on conditional volatility structure from the proposed model and common realized volatility estimators obtained based on high-frequency financial data. To improve the performance of proposed estimators, we also provide the option of incorporating option data by adopting a joint quasi-likelihood function. We study the asymptotic behaviors of proposed estimators and conduct a simulation study that confirms proposed estimators have good finite sample statistical performance. An empirical study has been carried out to demonstrate the ease of implementation of the proposed model in daily volatility estimation.
Author: Jin-Chuan Duan
Publisher: Springer Science & Business Media
ISBN: 3642172547
Category : Business & Economics
Languages : en
Pages : 791
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Book Description
Any financial asset that is openly traded has a market price. Except for extreme market conditions, market price may be more or less than a “fair” value. Fair value is likely to be some complicated function of the current intrinsic value of tangible or intangible assets underlying the claim and our assessment of the characteristics of the underlying assets with respect to the expected rate of growth, future dividends, volatility, and other relevant market factors. Some of these factors that affect the price can be measured at the time of a transaction with reasonably high accuracy. Most factors, however, relate to expectations about the future and to subjective issues, such as current management, corporate policies and market environment, that could affect the future financial performance of the underlying assets. Models are thus needed to describe the stochastic factors and environment, and their implementations inevitably require computational finance tools.
Author: Hrishikesh D. Vinod
Publisher: North Holland
ISBN: 0128202505
Category :
Languages : en
Pages : 350
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Book Description
Financial, Macro and Micro Econometrics Using R, Volume 42, provides state-of-the-art information on important topics in econometrics, including multivariate GARCH, stochastic frontiers, fractional responses, specification testing and model selection, exogeneity testing, causal analysis and forecasting, GMM models, asset bubbles and crises, corporate investments, classification, forecasting, nonstandard problems, cointegration, financial market jumps and co-jumps, among other topics. Presents chapters authored by distinguished, honored researchers who have received awards from the Journal of Econometrics or the Econometric Society Includes descriptions and links to resources and free open source R Gives readers what they need to jumpstart their understanding on the state-of-the-art
Author: Xiaohua Zheng
Publisher:
ISBN:
Category : Electronic dissertations
Languages : en
Pages : 79
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Book Description
Measuring and modeling financial volatility are key steps for derivative pricing and risk management. In financial markets, there are two kinds of data: low-frequency financial data and high-frequency financial data. Most research has been done based on low-frequency data. In this dissertation we focus on high-frequency data. In theory, the sum of squares of log returns sampled at high frequency estimates their variance. For log price data following a diffusion process without noise, the realized volatility converges to its quadratic variation. When log price data contain market microstructure noise, the realized volatility explodes as the sampling interval converges to 0. In this dissertation, we generalize the fundamental Ito isometry and analyze the speed with which stochastic processes approach to their quadratic variations. We determine the difference between realized volatility and quadratic variation under mean square constraints for Brownian motion and general case. We improve the estimation for quadratic variation. The estimators found by us converge to quadratic variation at a higher rate.
Author: Lan Zhang
Publisher:
ISBN:
Category :
Languages : en
Pages : 25
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Book Description
With the availability of high frequency financial data, nonparametric estimation of volatility of an asset return process becomes feasible. A major problem is how to estimate the volatility consistently and efficiently, when the observed asset returns contain error or noise, for example, in the form of microstructure noise. The former (consistency) has been addressed heavily in the recent literature, however, the resulting estimator is not quite efficient. In Zhang, Mykland, Ait-Sahalia (2003), the best estimator converges to the true volatility only at the rate of n wedge{-1/6}. In this paper, we propose an estimator, the Multi-scale Realized Volatility (MSRV), which converges to the true volatility at the rate of n wedge{-1/4}, which is the best attainable. We have shown a central limit theorem for the MSRV estimator, which permits setting intervals for the true integrated volatility on the basis of MSRV.
