Download or read book The Estimation of Leverage Effect with High Frequency Data written by Christina Dan Wang and published by . This book was released on 2014 with total page 44 pages. Available in PDF, EPUB and Kindle. Book excerpt: Leverage effect has become an extensively studied phenomenon which describes the negative relation between the stock return and its volatility. Although this characteristic of stock returns is well acknowledged, most studies about it are based on cross-sectional calibration with parametric models. Other than that, most previous work are over daily or longer return horizons and usually do not specify the quantitative measure of it. This paper provides nonparametric estimation of a class of stochastic measures of leverage effect for both cases with and without microstructure noise, and studies the statistical properties of the estimators when the log price process is a quite general continuous semimartingale, in the stochastic volatility context and for high frequency data. The consistency and limit distribution of the estimators are derived, and simulation results present the properties accordingly. This estimator also provides the opportunity to study the empirical relation between skewness and leverage effect, which further leads to the prediction of skewness. Furthermore, adopting similar ideas to these in this paper, it is easy to extend the study to other important aspects of the stock returns, e.g. volatility of volatility.

Download or read book The Estimation of Leverage Effect with High Frequency Data written by Dan Christina Wang and published by . This book was released on 2012 with total page 101 pages. Available in PDF, EPUB and Kindle. Book excerpt: The leverage effect has become an extensively studied phenomenon that describes the (usually) negative correlation between stock returns and volatility. All the previous studies have focused on the origin and properties of the leverage effect. Even though most studies of the leverage effect are based on cross-sectional calibration with parametric models, few of them have carefully studied its estimation. However, estimation of the leverage effect is important because sensible inference is possible only when the leverage effect is estimated reliably. In this thesis, we provide the first nonparametric estimation for a class of stochastic measures of the leverage effect. Unlike most previous work conducted over daily or longer return horizons, we study the estimation of the leverage effect with high frequency data. In order to construct estimators with good statistical properties, we introduce a new stochastic leverage effect parameter, which is usually not specified by other studies. The estimators and their statistical properties are provided in cases both with and without microstructure noise, under the stochastic volatility model. In asymptotics, the consistency and limiting distribution of the estimators are derived and corroborated by simulation results. For consistency, a previously unknown bias correction factor is added to the estimators. In finite samples, we provide two modifications of the estimator to improve its performance. In addition, we explore several applications of the estimators. In one application, we apply the estimators in high frequency regression and discover a novel predictor of volatility that depends on an estimator of the leverage effect. A related study reveals that the leverage effect improves estimation of volatility. In another application, we discover the first theoretical connection between skewness and the leverage effect, which yields a new predictor of skewness.

Download or read book The Leverage Effect Puzzle written by Yacine Ait-Sahalia and published by . This book was released on 2011 with total page 0 pages. Available in PDF, EPUB and Kindle. Book excerpt: The leverage effect refers to the generally negative correlation between an asset return and its changes of volatility. A natural estimate consists in using the empirical correlation between the daily returns and the changes of daily volatility estimated from high-frequency data. The puzzle lies in the fact that such an intuitively natural estimate yields nearly zero correlation for most assets tested, despite the many economic reasons for expecting the estimated correlation to be negative. To better understand the sources of the puzzle, we analyze the different asymptotic biases that are involved in high frequency estimation of the leverage effect, including biases due to discretization errors, to smoothing errors in estimating spot volatilities, to estimation error, and to market microstructure noise. This decomposition enables us to propose novel bias correction methods for estimating the leverage effect.

Download or read book High Frequency Financial Econometrics written by Yacine Aït-Sahalia and published by Princeton University Press. This book was released on 2014-07-21 with total page 683 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.

Download or read book Leverage and Volatility Feedback Effects in High Frequency Data written by Tim Bollerslev and published by . This book was released on 2008 with total page 34 pages. Available in PDF, EPUB and Kindle. Book excerpt: We examine the relationship between volatility and past and future returns in high-frequency equity market data. Consistent with a prolonged leverage effect, we find the correlations between absolute high-frequency returns and current and past high-frequency returns to be significantly negative for several days, while the reverse cross-correlations between absolute returns and future returns are generally negligible. Based on a simple aggregation formula, we demonstrate how the high-frequency data may similarly be used in more effectively assessing volatility asymmetries over longer daily return horizons. Motivated by the striking cross-correlation patterns uncovered in the high-frequency data, we investigate the ability of some popular continuous-time stochastic volatility models for explaining the observed asymmetries. Our results clearly highlight the importance of allowing for multiple latent volatility factors at very fine time scales in order to adequately describe and understand the patterns in the data.

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 Estimation of the Discontinuous Leverage Effect written by Markus Bibinger and published by . This book was released on 2019 with total page 0 pages. Available in PDF, EPUB and Kindle. Book excerpt: An extensive empirical literature documents a generally negative correlation, named the “leverage effect,” between asset returns and changes of volatility. It is more challenging to establish such a return-volatility relationship for jumps in high-frequency data. We propose new nonparametric methods to assess and test for a discontinuous leverage effect -- i.e. a relation between contemporaneous jumps in prices and volatility -- in high-frequency data with market microstructure noise. We present local tests and estimators for price jumps and volatility jumps. Five years of transaction data from 320 NASDAQ firms display no negative relation between price and volatility cojumps. We show, however, that there is a strong relation between price-volatility cojumps if one conditions on the sign of price jumps and whether the price jumps are market-wide or idiosyncratic.

Download or read book Nonparametric Estimation of the Leverage Effect written by Ilze Kalnina and published by . This book was released on 2015 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt:

Download or read book Risk Return Relationship in High Frequency Data written by Jihyun Lee and published by . This book was released on 2008 with total page 57 pages. Available in PDF, EPUB and Kindle. Book excerpt: This study investigates the relationship between the return on a stock index and its volatility using high frequency data. Two well-known hypotheses are reexamined: the leverage effect and the volatility feedback effect hypotheses. In an analysis of the five-minute data from the Samp;P500 index, two distinct characteristics of high frequency data were found. First, it was noted that the sign of the relationship between the smallest wavelet scale components for return and volatility differs from those between other scale components. Second, it was found that long memory exists in the daily realized volatility. The study further demonstrates how these findings affect the risk and return relationship.In the regression of changes in volatility on returns, it was found that the leverage effect does not appear in intraday data, in contrast to the results for daily data. It is believed that the difference can be attributed to the different relationships between scale components. By applying wavelet multiresolution analysis, it becomes clear that the leverage effect holds true between return and volatility components with scales equal to or larger than twenty minutes. However, these relationships are obscured in a five-minute data analysis because the smallest scale component accounts for a dominant portion of the variation of return. In testing the volatility feedback hypothesis, a modified model was used to incorporate apparent long memory in the daily realized volatility. This makes both sides of the test model balanced in integration order. No evidence of a volatility feedback effect was found under these stipulations.The results of this study reinforce the horizon dependency of the relationships. Hence, investors should assume different risk-return relationships for each horizon of interest. Additionally, the results show that the introduction of the long memory property to the proposed model is critical in the testing of risk-return relationships.

Download or read book Estimating and Forecasting Volatility Using Leverage Effect written by Christina Dan Wang and published by . This book was released on 2017 with total page 33 pages. Available in PDF, EPUB and Kindle. Book excerpt: This research provides a theoretical foundation for our previous empirical finding that leverage effect has a role in estimating and forecasting volatility. This empirics is also related to earlier econometric studies of news impact curves (Engle and Ng, Chen and Ghysels). Our new theoretical development is based on the concept of projection on stable subspaces of semi-martingales. We show that this projection provides a framework for forecasting (across time periods) that is internally consistent with the semi-martingale model which is used for the intra-day high frequency asymptotics. The paper shows that the approach provides improved estimation and forecasting both theoretically, in simulation, and in data.

Download or read book Handbook of High Frequency Trading written by Greg N. Gregoriou and published by Academic Press. This book was released on 2015-02-05 with total page 495 pages. Available in PDF, EPUB and Kindle. Book excerpt: This comprehensive examination of high frequency trading looks beyond mathematical models, which are the subject of most HFT books, to the mechanics of the marketplace. In 25 chapters, researchers probe the intricate nature of high frequency market dynamics, market structure, back-office processes, and regulation. They look deeply into computing infrastructure, describing data sources, formats, and required processing rates as well as software architecture and current technologies. They also create contexts, explaining the historical rise of automated trading systems, corresponding technological advances in hardware and software, and the evolution of the trading landscape. Developed for students and professionals who want more than discussions on the econometrics of the modelling process, The Handbook of High Frequency Trading explains the entirety of this controversial trading strategy. - Answers all questions about high frequency trading without being limited to mathematical modelling - Illuminates market dynamics, processes, and regulations - Explains how high frequency trading evolved and predicts its future developments

Download or read book Handbook of Financial Time Series written by Torben Gustav Andersen and published by Springer Science & Business Media. This book was released on 2009-04-21 with total page 1045 pages. Available in PDF, EPUB and Kindle. Book excerpt: The Handbook of Financial Time Series gives an up-to-date overview of the field and covers all relevant topics both from a statistical and an econometrical point of view. There are many fine contributions, and a preamble by Nobel Prize winner Robert F. Engle.

Download or read book An Introduction to High Frequency Finance written by Ramazan Gençay and published by Elsevier. This book was released on 2001-05-29 with total page 411 pages. Available in PDF, EPUB and Kindle. Book excerpt: Liquid markets generate hundreds or thousands of ticks (the minimum change in price a security can have, either up or down) every business day. Data vendors such as Reuters transmit more than 275,000 prices per day for foreign exchange spot rates alone. Thus, high-frequency data can be a fundamental object of study, as traders make decisions by observing high-frequency or tick-by-tick data. Yet most studies published in financial literature deal with low frequency, regularly spaced data. For a variety of reasons, high-frequency data are becoming a way for understanding market microstructure. This book discusses the best mathematical models and tools for dealing with such vast amounts of data.This book provides a framework for the analysis, modeling, and inference of high frequency financial time series. With particular emphasis on foreign exchange markets, as well as currency, interest rate, and bond futures markets, this unified view of high frequency time series methods investigates the price formation process and concludes by reviewing techniques for constructing systematic trading models for financial assets.

Download or read book Modeling the Leverage Effect with Copulas and Realized Volatility written by Cathy Ning and published by . This book was released on 2015 with total page 7 pages. Available in PDF, EPUB and Kindle. Book excerpt: In this paper, we propose the use of static and dynamic copulas to study the leverage effect in the S&P 500 index. Copula models can conveniently separate the leverage effect from the marginal distributions of the return and its volatility. Daily volatility is proxied by a measure of realized volatility, which is constructed from high-frequency data. We uncover a significant leverage effect in the S&P 500 index, and this leverage effect is found to be changing over time in a highly persistent manner. Moreover the dynamic copula models are shown to outperform the static counterparts.

Download or read book Estimating the Leverage Effect Using Panel Data With a Large Number of Stock Issues Over Short Run Focus on the Tokyo Stock Exchange written by Yoshitsugu Kitazawa and published by . This book was released on 2017 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt: This paper explores the leverage effect (the negative association between the stock return today and the stock return's volatility tomorrow), by utilizing the exponential ARCH type specification for panel data with a large number of stock issues and a small number of daily time series observations. The leverage effect is significantly estimated in the span from June 22 to 29 in 1998. This is the period right after the joint intervention into the yen-dollar exchange market. Judging from this fact, we may say that the leverage effect is associated with the deregulations in Japanese market incidental to the intervention.

Download or read book Asset Price Dynamics Volatility and Prediction written by Stephen J. Taylor and published by Princeton University Press. This book was released on 2011-02-11 with total page 544 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book shows how current and recent market prices convey information about the probability distributions that govern future prices. Moving beyond purely theoretical models, Stephen Taylor applies methods supported by empirical research of equity and foreign exchange markets to show how daily and more frequent asset prices, and the prices of option contracts, can be used to construct and assess predictions about future prices, their volatility, and their probability distributions. Stephen Taylor provides a comprehensive introduction to the dynamic behavior of asset prices, relying on finance theory and statistical evidence. He uses stochastic processes to define mathematical models for price dynamics, but with less mathematics than in alternative texts. The key topics covered include random walk tests, trading rules, ARCH models, stochastic volatility models, high-frequency datasets, and the information that option prices imply about volatility and distributions. Asset Price Dynamics, Volatility, and Prediction is ideal for students of economics, finance, and mathematics who are studying financial econometrics, and will enable researchers to identify and apply appropriate models and methods. It will likewise be a valuable resource for quantitative analysts, fund managers, risk managers, and investors who seek realistic expectations about future asset prices and the risks to which they are exposed.

Download or read book Estimation of the Continuous and Discontinuous Leverage Effects written by Yacine Ait-Sahalia and published by . This book was released on 2015 with total page 67 pages. Available in PDF, EPUB and Kindle. Book excerpt: This paper examines the leverage effect, or the generally negative covariation between asset returns and their changes in volatility, under a general setup that allows the log-price and volatility processes to be Ito semimartingales. We decompose the leverage effect into continuous and discontinuous parts and develop statistical methods to estimate them. We establish the asymptotic properties of these estimators. We also extend our methods and results to the situation where there is market microstructure noise in the observed returns. We show in Monte Carlo simulations that our estimators have good finite sample performance. When applying our methods to real data, our empirical results provide convincing evidence of the presence of the two leverage effects, especially the discontinuous one.