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Estimation And Approximation Of Tempered Stable Distribution
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Book Synopsis Estimation and Approximation of Tempered Stable Distribution by : Peipei Shi
Download or read book Estimation and Approximation of Tempered Stable Distribution written by Peipei Shi and published by . This book was released on 2010 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt: Tempered stable random variables have a LePage like series representation, which was first introduced by Rosi¶nski. In this dissertation, we study the accuracy of the Rosi¶nski representation as determined by the convergence rates of the series. We also study estimators of parameters of certain tempered stable distributions and construct their confidence intervals. Finally, we present several simulation results for the Gamma-tempered random variable.
Book Synopsis Maximum Likelihood Estimation of Parametric Tempered Stable Distributions on the Real Line with Applications to Finance by : Michael Grabchak
Download or read book Maximum Likelihood Estimation of Parametric Tempered Stable Distributions on the Real Line with Applications to Finance written by Michael Grabchak and published by . This book was released on 2008 with total page 254 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis Financial Models with Levy Processes and Volatility Clustering by : Svetlozar T. Rachev
Download or read book Financial Models with Levy Processes and Volatility Clustering written by Svetlozar T. Rachev and published by John Wiley & Sons. This book was released on 2011-02-08 with total page 316 pages. Available in PDF, EPUB and Kindle. Book excerpt: An in-depth guide to understanding probability distributions and financial modeling for the purposes of investment management In Financial Models with Lévy Processes and Volatility Clustering, the expert author team provides a framework to model the behavior of stock returns in both a univariate and a multivariate setting, providing you with practical applications to option pricing and portfolio management. They also explain the reasons for working with non-normal distribution in financial modeling and the best methodologies for employing it. The book's framework includes the basics of probability distributions and explains the alpha-stable distribution and the tempered stable distribution. The authors also explore discrete time option pricing models, beginning with the classical normal model with volatility clustering to more recent models that consider both volatility clustering and heavy tails. Reviews the basics of probability distributions Analyzes a continuous time option pricing model (the so-called exponential Lévy model) Defines a discrete time model with volatility clustering and how to price options using Monte Carlo methods Studies two multivariate settings that are suitable to explain joint extreme events Financial Models with Lévy Processes and Volatility Clustering is a thorough guide to classical probability distribution methods and brand new methodologies for financial modeling.
Book Synopsis Tempered Stable Distributions by : Michael Grabchak
Download or read book Tempered Stable Distributions written by Michael Grabchak and published by . This book was released on 2011 with total page 176 pages. Available in PDF, EPUB and Kindle. Book excerpt: It has been observed that data often appears to be well approximated by infinite variance stable distributions in some central region, but the tails of the distribution are actually lighter. Tempered stable distributions, which were introduced in [Ros07], are a rich class of models that attempt to capture this type of behavior. We will define certain generalizations of these models, which allow for more flexible structure. We will then derive a number of important results about them. In particular, we will give necessary and sufficient conditions for when they have regularly varying tails. We will also classify the possible weak limits of sequences of tempered stable distributions, and give necessary and sufficient conditions for convergence. These two properties will help us to categorize the long and short time behavior of their corresponding Lévy processes. We also attempt to explain why such models appear in applications. The use of stable distributions is justified by the central limit theorem, which says that stable distributions are the only possible limits of scaled and shifted sums of iid random variables. While this does not apply to tempered stable distributions, we will show that they may provide a good approximation to such sums for large, but not too large, aggregation levels. We base this explanation on the prelimit theorems of [KRS99] and [KRS00]. We then generalize them to d-dimensions.
Book Synopsis One-dimensional Stable Distributions by : V. M. Zolotarev
Download or read book One-dimensional Stable Distributions written by V. M. Zolotarev and published by American Mathematical Soc.. This book was released on 1986-06-30 with total page 298 pages. Available in PDF, EPUB and Kindle. Book excerpt: This is the first book specifically devoted to a systematic exposition of the essential facts known about the properties of stable distributions. In addition to its main focus on the analytic properties of stable laws, the book also includes examples of the occurrence of stable distributions in applied problems and a chapter on the problem of statistical estimation of the parameters determining stable laws. A valuable feature of the book is the author's use of several formally different ways of expressing characteristic functions corresponding to these laws.
Book Synopsis Tempered Stable Distributions by : Michael Grabchak
Download or read book Tempered Stable Distributions written by Michael Grabchak and published by Springer. This book was released on 2016-01-26 with total page 127 pages. Available in PDF, EPUB and Kindle. Book excerpt: This brief is concerned with tempered stable distributions and their associated Levy processes. It is a good text for researchers interested in learning about tempered stable distributions. A tempered stable distribution is one which takes a stable distribution and modifies its tails to make them lighter. The motivation for this class comes from the fact that infinite variance stable distributions appear to provide a good fit to data in a variety of situations, but the extremely heavy tails of these models are not realistic for most real world applications. The idea of using distributions that modify the tails of stable models to make them lighter seems to have originated in the influential paper of Mantegna and Stanley (1994). Since then, these distributions have been extended and generalized in a variety of ways. They have been applied to a wide variety of areas including mathematical finance, biostatistics,computer science, and physics.
Book Synopsis Unobserved Components and Time Series Econometrics by : Siem Jan Koopman
Download or read book Unobserved Components and Time Series Econometrics written by Siem Jan Koopman and published by Oxford University Press. This book was released on 2015 with total page 389 pages. Available in PDF, EPUB and Kindle. Book excerpt: Presents original and up-to-date studies in unobserved components (UC) time series models from both theoretical and methodological perspectives.
Book Synopsis Advances in Heavy Tailed Risk Modeling by : Gareth W. Peters
Download or read book Advances in Heavy Tailed Risk Modeling written by Gareth W. Peters and published by John Wiley & Sons. This book was released on 2015-05-21 with total page 667 pages. Available in PDF, EPUB and Kindle. Book excerpt: ADVANCES IN HEAVY TAILED RISK MODELING A cutting-edge guide for the theories, applications, and statistical methodologies essential to heavy tailed risk modeling Focusing on the quantitative aspects of heavy tailed loss processes in operational risk and relevant insurance analytics, Advances in Heavy Tailed Risk Modeling: A Handbook of Operational Risk presents comprehensive coverage of the latest research on the theories and applications in risk measurement and modeling techniques. Featuring a unique balance of mathematical and statistical perspectives, the handbook begins by introducing the motivation for heavy tailed risk processes. A companion with Fundamental Aspects of Operational Risk and Insurance Analytics: A Handbook of Operational Risk, the handbook provides a complete framework for all aspects of operational risk management and includes: Clear coverage on advanced topics such as splice loss models, extreme value theory, heavy tailed closed form loss distribution approach models, flexible heavy tailed risk models, risk measures, and higher order asymptotic approximations of risk measures for capital estimation An exploration of the characterization and estimation of risk and insurance modeling, which includes sub-exponential models, alpha-stable models, and tempered alpha stable models An extended discussion of the core concepts of risk measurement and capital estimation as well as the details on numerical approaches to evaluation of heavy tailed loss process model capital estimates Numerous detailed examples of real-world methods and practices of operational risk modeling used by both financial and non-financial institutions Advances in Heavy Tailed Risk Modeling: A Handbook of Operational Risk is an excellent reference for risk management practitioners, quantitative analysts, financial engineers, and risk managers. The handbook is also useful for graduate-level courses on heavy tailed processes, advanced risk management, and actuarial science.
Book Synopsis Handbook Of Heavy-tailed Distributions In Asset Management And Risk Management by : Michele Leonardo Bianchi
Download or read book Handbook Of Heavy-tailed Distributions In Asset Management And Risk Management written by Michele Leonardo Bianchi and published by World Scientific. This book was released on 2019-03-08 with total page 598 pages. Available in PDF, EPUB and Kindle. Book excerpt: The study of heavy-tailed distributions allows researchers to represent phenomena that occasionally exhibit very large deviations from the mean. The dynamics underlying these phenomena is an interesting theoretical subject, but the study of their statistical properties is in itself a very useful endeavor from the point of view of managing assets and controlling risk. In this book, the authors are primarily concerned with the statistical properties of heavy-tailed distributions and with the processes that exhibit jumps. A detailed overview with a Matlab implementation of heavy-tailed models applied in asset management and risk managements is presented. The book is not intended as a theoretical treatise on probability or statistics, but as a tool to understand the main concepts regarding heavy-tailed random variables and processes as applied to real-world applications in finance. Accordingly, the authors review approaches and methodologies whose realization will be useful for developing new methods for forecasting of financial variables where extreme events are not treated as anomalies, but as intrinsic parts of the economic process.
Book Synopsis Statistical Methods for Stable Distribution Using the Empirical Characteristic Function by : Xiaonan Zhang
Download or read book Statistical Methods for Stable Distribution Using the Empirical Characteristic Function written by Xiaonan Zhang and published by . This book was released on 2018 with total page 43 pages. Available in PDF, EPUB and Kindle. Book excerpt: Stable distributions are a class of distributions allowing heavy tail and skewness. Most of stable distributions lack closed-form expression for their densities, so that estimating parameters is a challenging problem. When distributions have no closed-form density expression, their characteristic function becomes a useful alternative to define the unique distribution. We use the empirical characteristic function, i.e. the sample analog of the characteristic function, for estimation and goodness-of-fit tests for data. The existing fixed interval empirical characteristic function method works well when the alpha parameter is large but performs poorly for small values of alpha. This study offers a modification based on an adaptive grid to improve the estimation result for small alpha parameter without having a negative effect on the estimation of the other parameters. Goodness-of-fit tests based on the empirical characteristic function are also given and compared to classical tests based on the empirical cumulative distribution function.
Book Synopsis Mathematical and Statistical Methods for Actuarial Sciences and Finance by : Cira Perna
Download or read book Mathematical and Statistical Methods for Actuarial Sciences and Finance written by Cira Perna and published by Springer. This book was released on 2014-07-08 with total page 190 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume aims to collect new ideas presented in the form of 4 page papers dedicated to mathematical and statistical methods in actuarial sciences and finance. The cooperation between mathematicians and statisticians working in insurance and finance is a very fruitful field and provides interesting scientific products in theoretical models and practical applications, as well as in scientific discussion of problems of national and international interest. This work reflects the results discussed at the biennial conference on Mathematical and Statistical Methods for Actuarial Sciences and Finance (MAF), born at the University of Salerno in 2004.
Book Synopsis Parameter Estimation in Stochastic Volatility Models by : Jaya P. N. Bishwal
Download or read book Parameter Estimation in Stochastic Volatility Models written by Jaya P. N. Bishwal and published by Springer Nature. This book was released on 2022-08-06 with total page 634 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book develops alternative methods to estimate the unknown parameters in stochastic volatility models, offering a new approach to test model accuracy. While there is ample research to document stochastic differential equation models driven by Brownian motion based on discrete observations of the underlying diffusion process, these traditional methods often fail to estimate the unknown parameters in the unobserved volatility processes. This text studies the second order rate of weak convergence to normality to obtain refined inference results like confidence interval, as well as nontraditional continuous time stochastic volatility models driven by fractional Levy processes. By incorporating jumps and long memory into the volatility process, these new methods will help better predict option pricing and stock market crash risk. Some simulation algorithms for numerical experiments are provided.
Book Synopsis Estimation of Stable Distributions by Indirect Inference by : René Garcia
Download or read book Estimation of Stable Distributions by Indirect Inference written by René Garcia and published by . This book was released on 2009 with total page 62 pages. Available in PDF, EPUB and Kindle. Book excerpt: This article deals with the estimation of the parameters of an a-stable distribution with indirect inference, using the skewed-t distribution as an auxiliary model. The latter distribution appears as a good candidate since it has the same number of parameters as the a-stable distribution, with each parameter playing a similar role. To improve the properties of the estimator in finite sample, we use constrained indirect inference. In a Monte Carlo study we show that this method delivers estimators with good properties in finite sample. We provide an empirical application to the distribution of jumps in the Samp;P 500 index returns.
Book Synopsis Parameter Estimation and Uncertainty Quantification in Water Resources Modeling by : Philippe Renard
Download or read book Parameter Estimation and Uncertainty Quantification in Water Resources Modeling written by Philippe Renard and published by Frontiers Media SA. This book was released on 2020-04-22 with total page 177 pages. Available in PDF, EPUB and Kindle. Book excerpt: Numerical models of flow and transport processes are heavily employed in the fields of surface, soil, and groundwater hydrology. They are used to interpret field observations, analyze complex and coupled processes, or to support decision making related to large societal issues such as the water-energy nexus or sustainable water management and food production. Parameter estimation and uncertainty quantification are two key features of modern science-based predictions. When applied to water resources, these tasks must cope with many degrees of freedom and large datasets. Both are challenging and require novel theoretical and computational approaches to handle complex models with large number of unknown parameters.
Book Synopsis Fractional Calculus and Fractional Processes with Applications to Financial Economics by : Hasan Fallahgoul
Download or read book Fractional Calculus and Fractional Processes with Applications to Financial Economics written by Hasan Fallahgoul and published by Academic Press. This book was released on 2016-10-06 with total page 120 pages. Available in PDF, EPUB and Kindle. Book excerpt: Fractional Calculus and Fractional Processes with Applications to Financial Economics presents the theory and application of fractional calculus and fractional processes to financial data. Fractional calculus dates back to 1695 when Gottfried Wilhelm Leibniz first suggested the possibility of fractional derivatives. Research on fractional calculus started in full earnest in the second half of the twentieth century. The fractional paradigm applies not only to calculus, but also to stochastic processes, used in many applications in financial economics such as modelling volatility, interest rates, and modelling high-frequency data. The key features of fractional processes that make them interesting are long-range memory, path-dependence, non-Markovian properties, self-similarity, fractal paths, and anomalous diffusion behaviour. In this book, the authors discuss how fractional calculus and fractional processes are used in financial modelling and finance economic theory. It provides a practical guide that can be useful for students, researchers, and quantitative asset and risk managers interested in applying fractional calculus and fractional processes to asset pricing, financial time-series analysis, stochastic volatility modelling, and portfolio optimization. Provides the necessary background for the book's content as applied to financial economics Analyzes the application of fractional calculus and fractional processes from deterministic and stochastic perspectives
Book Synopsis Parameters Estimation of the Discrete Stable Distribution by : Shu Mei Jiang
Download or read book Parameters Estimation of the Discrete Stable Distribution written by Shu Mei Jiang and published by . This book was released on 2006 with total page 124 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis Option Pricing and Estimation of Financial Models with R by : Stefano M. Iacus
Download or read book Option Pricing and Estimation of Financial Models with R written by Stefano M. Iacus and published by John Wiley & Sons. This book was released on 2011-02-23 with total page 402 pages. Available in PDF, EPUB and Kindle. Book excerpt: Presents inference and simulation of stochastic process in the field of model calibration for financial times series modelled by continuous time processes and numerical option pricing. Introduces the bases of probability theory and goes on to explain how to model financial times series with continuous models, how to calibrate them from discrete data and further covers option pricing with one or more underlying assets based on these models. Analysis and implementation of models goes beyond the standard Black and Scholes framework and includes Markov switching models, Lévy models and other models with jumps (e.g. the telegraph process); Topics other than option pricing include: volatility and covariation estimation, change point analysis, asymptotic expansion and classification of financial time series from a statistical viewpoint. The book features problems with solutions and examples. All the examples and R code are available as an additional R package, therefore all the examples can be reproduced.
