Download or read book Estimation of the Stochastic Leverage Effect Using the Fourier Transform Method written by Imma Curato and published by . This book was released on 2018 with total page 44 pages. Available in PDF, EPUB and Kindle. Book excerpt: We define a non-parametric estimator of the integrated leverage effect as the covariance between the logarithmic asset price and its volatility. In Curato and Sanfelici (2015), a consistent estimator of the leverage effect has been introduced through a pre-estimate of the Fourier coefficients of the volatility. This is a novel approach compared to the ones present in the literature which use a pre-estimate of the spot volatility path. In this paper, we show the asymptotic normality of the Fourier estimator for non-equidistant observations. Moreover, its finite sample properties are analyzed in a simulation study also in the presence of microstructure noise.
Download or read book Fourier Malliavin Volatility Estimation written by Maria Elvira Mancino and published by Springer. This book was released on 2017-03-01 with total page 139 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume is a user-friendly presentation of the main theoretical properties of the Fourier-Malliavin volatility estimation, allowing the readers to experience the potential of the approach and its application in various financial settings. Readers are given examples and instruments to implement this methodology in various financial settings and applications of real-life data. A detailed bibliographic reference is included to permit an in-depth study.
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 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 Stochastic Processes and Applications to Mathematical Finance written by Jiro Akahori and published by World Scientific. This book was released on 2006 with total page 228 pages. Available in PDF, EPUB and Kindle. Book excerpt: Based around recent lectures given at the prestigious Ritsumeikan conference, the tutorial and expository articles contained in this volume are an essential guide for practitioners and graduates alike who use stochastic calculus in finance.Among the eminent contributors are Paul Malliavin and Shinzo Watanabe, pioneers of Malliavin Calculus. The coverage also includes a valuable review of current research on credit risks in a mathematically sophisticated way contrasting with existing economics-oriented articles.
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 Estimation for Mean reverting Stochastic Volatility Models with a Leverage Effect written by Agnès Grimaud and published by . This book was released on 2006 with total page 16 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Econometric Analysis of Stochastic Dominance written by Yoon-Jae Whang and published by Cambridge University Press. This book was released on 2019-01-31 with total page 279 pages. Available in PDF, EPUB and Kindle. Book excerpt: Provides a comprehensive analysis of stochastic dominance through coverage of concepts, methods of estimation, inferential tools, and applications.
Download or read book Stochastic Conditional Duration Models with Leverage Effect for Financial Transaction Data written by Dingan Feng and published by . This book was released on 2010 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt: This article proposes stochastic conditional duration (SCD) models with quot;leverage effectquot; for financial transaction data, which extends both the autoregressive conditional duration (ACD) model (Engle and Russell, 1998, Econometrica, 66, 1127-1162) and the existing SCD model (Bauwens and Veredas, 2004, Journal of Econometrics, 119, 381-412). The proposed models belong to a class of linear nongaussian state-space models, where the observation equation for the duration process takes an additive form of a latent process and a noise term. The latent process is driven by an autoregressive component to characterize the transition property and a term associated with the observed duration. The inclusion of such a term allows the model to capture the asymmetric behavior or quot;leverage effectquot; of the expected duration. The Monte Carlo maximum-likelihood (MCML) method is employed for consistent and efficient parameter estimation with applications to the transaction data of IBM and other stocks. Our analysis suggests that trade intensity is correlated with stock return volatility and modeling the duration process with quot;leverage effectquot; can enhance the forecasting performance of intraday volatility.
Download or read book Corrections to Dynamic Volatility Matrix Estimation by Fourier Transform Method with Applications written by 張藝馨 and published by . This book was released on 2011 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Stochastic Volatility and Time Deformation written by Joann Jasiak and published by . This book was released on 2012 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt: In this paper, we study stochastic volatility models with time deformation. Such processes relate to the early work by Mandelbrot and Taylor (1967), Clark (1973), Tauchen and Pitts (1983), among others. In our setup, the latent process of stochastic volatility evolves in an operational time which differs from calendar time. The time deformation can be determined by past volume of trade, past returns, possibly with an asymmetric leverage effect, and other variables setting the pace of information arrival. The econometric specification exploits the state-space approach for stochastic volatility models proposed by Harvey, Ruiz and Shephard (1994) as well as the matching moment estimation procedure using SNP densities of stock returns and trading volume estimated by Gallant, Rossi and Tauchen (1992). Daily data on returns and trading volume of the NYSE are used in the empirical application. Supporting evidence for a time deformation representation is found and its impact on the behavior of returns and volume is analyzed. We find that increases in volume accelerate operational time, resulting in volatility being less persistent and subject to shocks with a higher innovation variance. Downward price movements have similar effects while upward price movements increase the persistence in volatility and decrease the dispersion of shocks by slowing down market time. We present the basic model as well as several extensions; in particular, we formulate and estimate a bivariate return-volume stochastic volatility model with time deformation. The latter is examined through bivariate impulse response profiles following the example of Gallant, Rossi and Tauchen (1993).
Download or read book Modelling and Simulation of Stochastic Volatility in Finance written by Christian Kahl and published by Universal-Publishers. This book was released on 2008 with total page 219 pages. Available in PDF, EPUB and Kindle. Book excerpt: The famous Black-Scholes model was the starting point of a new financial industry and has been a very important pillar of all options trading since. One of its core assumptions is that the volatility of the underlying asset is constant. It was realised early that one has to specify a dynamic on the volatility itself to get closer to market behaviour. There are mainly two aspects making this fact apparent. Considering historical evolution of volatility by analysing time series data one observes erratic behaviour over time. Secondly, backing out implied volatility from daily traded plain vanilla options, the volatility changes with strike. The most common realisations of this phenomenon are the implied volatility smile or skew. The natural question arises how to extend the Black-Scholes model appropriately. Within this book the concept of stochastic volatility is analysed and discussed with special regard to the numerical problems occurring either in calibrating the model to the market implied volatility surface or in the numerical simulation of the two-dimensional system of stochastic differential equations required to price non-vanilla financial derivatives. We introduce a new stochastic volatility model, the so-called Hyp-Hyp model, and use Watanabe's calculus to find an analytical approximation to the model implied volatility. Further, the class of affine diffusion models, such as Heston, is analysed in view of using the characteristic function and Fourier inversion techniques to value European derivatives.
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 Alternative Formulations of the Leverage Effect in a Stochastic Volatility Model with Asymmetric Heavy Tailed Errors written by Philippe J. Deschamps and published by . This book was released on 2016 with total page 41 pages. Available in PDF, EPUB and Kindle. Book excerpt: This paper investigates three formulations of the leverage effect in a stochastic volatility model with a skewed and heavy-tailed observation distribution. The first formulation is the conventional one, where the observation and evolution errors are correlated. The second is a hierarchical one, where log-volatility depends on the past log-return multiplied by a time-varying latent coefficient. In the third formulation, this coefficient is replaced by a constant. The three models are compared with each other and with a GARCH formulation, using Bayes factors. MCMC estimation relies on a parametric proposal density estimated from the output of a particle smoother. The results, obtained with recent S&P500 and Swiss Market Index data, suggest that the last two leverage formulations strongly dominate the conventional one. The performance of the MCMC method is consistent across models and sample sizes, and its implementation only requires a very modest (and constant) number of filter and smoother particles.
Download or read book Empirical Evidence of the Leverage Effect in a Stochastic Volatility Model written by Dinghai Xu and published by . This book was released on 2010 with total page 26 pages. Available in PDF, EPUB and Kindle. Book excerpt:
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 Stochastic Models for Prices Dynamics in Energy and Commodity Markets written by Fred Espen Benth and published by Springer Nature. This book was released on 2023-11-16 with total page 250 pages. Available in PDF, EPUB and Kindle. Book excerpt: This monograph presents a theory for random field models in time and space, viewed as stochastic processes with values in a Hilbert space, to model the stochastic dynamics of forward and futures prices in energy, power, and commodity markets. In this book, the well-known Heath–Jarrow–Morton approach from interest rate theory is adopted and extended into an infinite-dimensional framework, allowing for flexible modeling of price stochasticity across time and along the term structure curve. Various models are introduced based on stochastic partial differential equations with infinite-dimensional Lévy processes as noise drivers, emphasizing random fields described by low-dimensional parametric covariance functions instead of classical high-dimensional factor models. The Filipović space, a separable Hilbert space of Sobolev type, is found to be a convenient state space for the dynamics of forward and futures term structures. The monograph provides a classification of important operators in this space, covering covariance operators and the stochastic modeling of volatility term structures, including the Samuelson effect. Fourier methods are employed to price many derivatives of interest in energy, power, and commodity markets, and sensitivity 'delta' expressions can be derived. Additionally, the monograph covers forward curve smoothing, the connection between forwards with fixed delivery and delivery period, as well as the classical theory of forward and futures pricing. This monograph will appeal to researchers and graduate students interested in mathematical finance and stochastic analysis applied in the challenging markets of energy, power, and commodities. Practitioners seeking sophisticated yet flexible and analytically tractable risk models will also find it valuable.
