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Maximum Likelihood Estimation Of Parametric Tempered Stable Distributions On The Real Line With Applications To Finance
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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 Statistical Tools for Finance and Insurance by : Pavel Cizek
Download or read book Statistical Tools for Finance and Insurance written by Pavel Cizek and published by Springer Science & Business Media. This book was released on 2011-03-18 with total page 410 pages. Available in PDF, EPUB and Kindle. Book excerpt: Statistical Tools for Finance and Insurance presents ready-to-use solutions, theoretical developments and method construction for many practical problems in quantitative finance and insurance. Written by practitioners and leading academics in the field, this book offers a unique combination of topics from which every market analyst and risk manager will benefit. Features of the significantly enlarged and revised second edition: Offers insight into new methods and the applicability of the stochastic technology Provides the tools, instruments and (online) algorithms for recent techniques in quantitative finance and modern treatments in insurance calculations Covers topics such as - expected shortfall for heavy tailed and mixture distributions* - pricing of variance swaps* - volatility smile calibration in FX markets - pricing of catastrophe bonds and temperature derivatives* - building loss models and ruin probability approximation - insurance pricing with GLM* - equity linked retirement plans*(new topics in the second edition marked with*) Presents extensive examples
Book Synopsis Quantile-Based Inference for Tempered Stable Distributions by : Hasan Fallahgoul
Download or read book Quantile-Based Inference for Tempered Stable Distributions written by Hasan Fallahgoul and published by . This book was released on 2016 with total page 25 pages. Available in PDF, EPUB and Kindle. Book excerpt: If the closed-form formula for the probability density function is not available, implementing the maximum likelihood estimation is challenging. We introduce a simple, fast, and accurate way for the estimation of numerous distributions that belong to the class of tempered stable probability distributions. Estimation is based on the Method of Simulated Quantiles (Dominicy and Veredas (2013)). MSQ consists of matching empirical and theoretical functions of quantiles that are informative about the parameters of interest. In the Monte Carlo study we show that MSQ is significantly faster than Maximum Likelihood and the estimates are almost as precise as MLE. A Value at Risk study using 13 years of daily returns from 21 world-wide market indexes shows that MSQ estimates provide as good risk assessments as with MLE.
Book Synopsis Parameter Estimation for Stable Distributions by : Gaoyuan Tian
Download or read book Parameter Estimation for Stable Distributions written by Gaoyuan Tian and published by . This book was released on 2016 with total page 94 pages. Available in PDF, EPUB and Kindle. Book excerpt: Stable distributions are important family of parametric distributions widely used in signal processing as well as in mathematical finance. Estimation of the parameters of this model, is not quite straightforward due to the fact that there is no closed-form expression for their probability density function. Besides the computationally intensive maximum likelihood method where the density has to be evaluated numerically, there are some existing adhoc methods such as the quantile method, and a regression based method. These are introduced in Chapter 2. In this thesis, we introduce two new approaches: One, a spacing based estimation method introduced in Chapter 3 and two, an indirect inference method considered in Chapter 4. Simulation studies show that both these methods are very robust and efficient and do as well or better than the existing methods in most cases. Finally in Chapter 5, we use indirect inference approach to estimate the best fitting income distribution based on limited information that is often available.
Book Synopsis Extreme Value Distributions by : Samuel Kotz
Download or read book Extreme Value Distributions written by Samuel Kotz and published by World Scientific. This book was released on 2000 with total page 195 pages. Available in PDF, EPUB and Kindle. Book excerpt: This important book provides an up-to-date comprehensive and down-to-earth survey of the theory and practice of extreme value distributions OCo one of the most prominent success stories of modern applied probability and statistics. Originated by E J Gumbel in the early forties as a tool for predicting floods, extreme value distributions evolved during the last 50 years into a coherent theory with applications in practically all fields of human endeavor where maximal or minimal values (the so-called extremes) are of relevance. The book is of usefulness both for a beginner with a limited probabilistic background and to expert in the field. Sample Chapter(s). Chapter 1.1: Historical Survey (139 KB). Chapter 1.2: The Three Types of Extreme Value Distributions (146 KB). Chapter 1.3: Limiting Distributions and Domain of Attraction (210 KB). Chapter 1.4: Distribution Function and Moments of Type 1 Distribution (160 KB). Chapter 1.5: Order Statistics, Record Values and Characterizations (175 KB). Contents: Univariate Extreme Value Distributions; Generalized Extreme Value Distributions; Multivariate Extreme Value Distributions. Readership: Applied probabilists, applied statisticians, environmental scientists, climatologists, industrial engineers and management experts."
Book Synopsis Rapid Maximum Likelihood Estimation of Stable Distribution Parameters by : Timothy Masters
Download or read book Rapid Maximum Likelihood Estimation of Stable Distribution Parameters written by Timothy Masters and published by . This book was released on 1977 with total page 64 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis Parametric Distributional Flexibility and Conditional Variance Models with an Application to Hourly Exchange Rates by : Ms.Jenny N. Lye
Download or read book Parametric Distributional Flexibility and Conditional Variance Models with an Application to Hourly Exchange Rates written by Ms.Jenny N. Lye and published by International Monetary Fund. This book was released on 1998-03-01 with total page 40 pages. Available in PDF, EPUB and Kindle. Book excerpt: This paper builds on the ARCH approach for modeling distributions with time-varying conditional variance by using the generalized Student t distribution. The distribution offers flexibility in modeling both leptokurtosis and asymmetry (characteristics seen in high-frequency financial time series data), nests the standard normal and Student t distributions, and is related to the Gram Charlier and mixture distributions. An empirical ARCH model based on this distribution is formulated and estimated using hourly exchange rate returns for four currencies. The generalized Student t is found to better model the empirical conditional and unconditional distributions than other distributional specifications.
Book Synopsis Handbook of Heavy Tailed Distributions in Finance by : S.T Rachev
Download or read book Handbook of Heavy Tailed Distributions in Finance written by S.T Rachev and published by Elsevier. This book was released on 2003-03-05 with total page 707 pages. Available in PDF, EPUB and Kindle. Book excerpt: The Handbooks in Finance are intended to be a definitive source for comprehensive and accessible information in the field of finance. Each individual volume in the series should present an accurate self-contained survey of a sub-field of finance, suitable for use by finance and economics professors and lecturers, professional researchers, graduate students and as a teaching supplement. The goal is to have a broad group of outstanding volumes in various areas of finance. The Handbook of Heavy Tailed Distributions in Finance is the first handbook to be published in this series.This volume presents current research focusing on heavy tailed distributions in finance. The contributions cover methodological issues, i.e., probabilistic, statistical and econometric modelling under non- Gaussian assumptions, as well as the applications of the stable and other non -Gaussian models in finance and risk management.
Download or read book Lognormal Distributions written by Crow and published by Routledge. This book was released on 2018-05-02 with total page 408 pages. Available in PDF, EPUB and Kindle. Book excerpt: Presenting the first comprehensive review of the subject's theory and applications inmore than 15 years, this outstanding reference encompasses the most-up-to-date advancesin lognormal distributions in thorough, detailed contributions by specialists in statistics,business and economics , industry, biology , ecology, geology, and meteorology.Lognormal Distributions describes the theory and methods of point and intervalestimation as well as the testing of hypotheses clearly and precisely from a modemviewpoint-not only for the basic two-parameter lognormal distribution but also for itsgeneralizations, including three parameters, truncated distributions, delta-lognormaldistributions, and two or more dimensions.Featuring over 600 references plus author and subject indexes, this volume rev iews thesubject's history .. . gives explicit formulas for minimum variance unbiased estimates ofparameters and their variances ... provides optimal tests of hypotheses and confidenceinterval procedures for various functions of the parameters in the two-parameter model. .. and discusses practical methods of analysis for truncated, censored, or groupedsamples.
Book Synopsis Maximum Likelihood Estimation of Parameters with Constraints in Normal and Multinomial Distributions by : HUITIAN. XUE
Download or read book Maximum Likelihood Estimation of Parameters with Constraints in Normal and Multinomial Distributions written by HUITIAN. XUE and published by . This book was released on 2017-01-26 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt: This dissertation, "Maximum Likelihood Estimation of Parameters With Constraints in Normal and Multinomial Distributions" by Huitian, Xue, 薛惠天, was obtained from The University of Hong Kong (Pokfulam, Hong Kong) and is being sold pursuant to Creative Commons: Attribution 3.0 Hong Kong License. The content of this dissertation has not been altered in any way. We have altered the formatting in order to facilitate the ease of printing and reading of the dissertation. All rights not granted by the above license are retained by the author. Abstract: Motivated by problems in medicine, biology, engineering and economics, con- strained parameter problems arise in a wide variety of applications. Among them the application to the dose-response of a certain drug in development has attracted much interest. To investigate such a relationship, we often need to conduct a dose- response experiment with multiple groups associated with multiple dose levels of the drug. The dose-response relationship can be modeled by a shape-restricted normal regression. We develop an iterative two-step ascent algorithm to estimate normal means and variances subject to simultaneous constraints. Each iteration consists of two parts: an expectation{maximization (EM) algorithm that is utilized in Step 1 to compute the maximum likelihood estimates (MLEs) of the restricted means when variances are given, and a newly developed restricted De Pierro algorithm that is used in Step 2 to find the MLEs of the restricted variances when means are given. These constraints include the simple order, tree order, umbrella order, and so on. A bootstrap approach is provided to calculate standard errors of the restricted MLEs. Applications to the analysis of two real datasets on radioim-munological assay of cortisol and bioassay of peptides are presented to illustrate the proposed methods. Liu (2000) discussed the maximum likelihood estimation and Bayesian estimation in a multinomial model with simplex constraints by formulating this constrained parameter problem into an unconstrained parameter problem in the framework of missing data. To utilize the EM and data augmentation (DA) algorithms, he introduced latent variables {Zil;Yil} (to be defined later). However, the proposed DA algorithm in his paper did not provide the necessary individual conditional distributions of Yil given (the observed data and) the updated parameter estimates. Indeed, the EM algorithm developed in his paper is based on the assumption that{ Yil} are fixed given values. Fortunately, the EM algorithm is invariant under any choice of the value of Yil, so the final result is always correct. We have derived the aforesaid conditional distributions and hence provide a valid DA algorithm. A real data set is used for illustration. DOI: 10.5353/th_b4785001 Subjects: Estimation theory Parameter estimation
Book Synopsis Univariate Stable Distributions by : John P. Nolan
Download or read book Univariate Stable Distributions written by John P. Nolan and published by Springer Nature. This book was released on 2020-09-13 with total page 342 pages. Available in PDF, EPUB and Kindle. Book excerpt: This textbook highlights the many practical uses of stable distributions, exploring the theory, numerical algorithms, and statistical methods used to work with stable laws. Because of the author’s accessible and comprehensive approach, readers will be able to understand and use these methods. Both mathematicians and non-mathematicians will find this a valuable resource for more accurately modelling and predicting large values in a number of real-world scenarios. Beginning with an introductory chapter that explains key ideas about stable laws, readers will be prepared for the more advanced topics that appear later. The following chapters present the theory of stable distributions, a wide range of applications, and statistical methods, with the final chapters focusing on regression, signal processing, and related distributions. Each chapter ends with a number of carefully chosen exercises. Links to free software are included as well, where readers can put these methods into practice. Univariate Stable Distributions is ideal for advanced undergraduate or graduate students in mathematics, as well as many other fields, such as statistics, economics, engineering, physics, and more. It will also appeal to researchers in probability theory who seek an authoritative reference on stable distributions.
Book Synopsis Stable Distributions by : John Nolan
Download or read book Stable Distributions written by John Nolan and published by Birkhauser. This book was released on 2007-03-01 with total page 352 pages. Available in PDF, EPUB and Kindle. Book excerpt: Stable distributions model phenomena in a wide range of applications in real systems. Their intriguing mathematical properties have long been of interest, but the lack of computational tools has prevented their practical application. This book, the first to deal with stable distributions as a practical tool, develops an intuition for stable distributions by giving a complete, self-contained derivation of their properties and describing accurate numerical methods for computing stable laws.
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 Trends in Partial Differential Equations of Mathematical Physics by : José-Francisco Rodrigues
Download or read book Trends in Partial Differential Equations of Mathematical Physics written by José-Francisco Rodrigues and published by Birkhauser. This book was released on 2005-01-01 with total page 282 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book consists of contributions originating from a conference in Obedo, Portugal, which honoured the 70th birthday of V.A. Solonnikov. A broad variety of topics centering on nonlinear problems is presented, particularly Navier-Stokes equations, viscosity problems, diffusion-absorption equations, free boundaries, and Euler equations.
Book Synopsis Information-Theoretic Methods for Estimating of Complicated Probability Distributions by : Zhi Zong
Download or read book Information-Theoretic Methods for Estimating of Complicated Probability Distributions written by Zhi Zong and published by Elsevier. This book was released on 2006-08-15 with total page 321 pages. Available in PDF, EPUB and Kindle. Book excerpt: Mixing up various disciplines frequently produces something that are profound and far-reaching. Cybernetics is such an often-quoted example. Mix of information theory, statistics and computing technology proves to be very useful, which leads to the recent development of information-theory based methods for estimating complicated probability distributions. Estimating probability distribution of a random variable is the fundamental task for quite some fields besides statistics, such as reliability, probabilistic risk analysis (PSA), machine learning, pattern recognization, image processing, neural networks and quality control. Simple distribution forms such as Gaussian, exponential or Weibull distributions are often employed to represent the distributions of the random variables under consideration, as we are taught in universities. In engineering, physical and social science applications, however, the distributions of many random variables or random vectors are so complicated that they do not fit the simple distribution forms at al. Exact estimation of the probability distribution of a random variable is very important. Take stock market prediction for example. Gaussian distribution is often used to model the fluctuations of stock prices. If such fluctuations are not normally distributed, and we use the normal distribution to represent them, how could we expect our prediction of stock market is correct? Another case well exemplifying the necessity of exact estimation of probability distributions is reliability engineering. Failure of exact estimation of the probability distributions under consideration may lead to disastrous designs. There have been constant efforts to find appropriate methods to determine complicated distributions based on random samples, but this topic has never been systematically discussed in detail in a book or monograph. The present book is intended to fill the gap and documents the latest research in this subject. Determining a complicated distribution is not simply a multiple of the workload we use to determine a simple distribution, but it turns out to be a much harder task. Two important mathematical tools, function approximation and information theory, that are beyond traditional mathematical statistics, are often used. Several methods constructed based on the two mathematical tools for distribution estimation are detailed in this book. These methods have been applied by the author for several years to many cases. They are superior in the following senses: (1) No prior information of the distribution form to be determined is necessary. It can be determined automatically from the sample; (2) The sample size may be large or small; (3) They are particularly suitable for computers. It is the rapid development of computing technology that makes it possible for fast estimation of complicated distributions. The methods provided herein well demonstrate the significant cross influences between information theory and statistics, and showcase the fallacies of traditional statistics that, however, can be overcome by information theory. Key Features: - Density functions automatically determined from samples - Free of assuming density forms - Computation-effective methods suitable for PC- density functions automatically determined from samples- Free of assuming density forms- Computation-effective methods suitable for PC
Book Synopsis Maximum Likelihood Estimation of Discrete Log-Concave Distributions with Applications by : Yanhua Tian
Download or read book Maximum Likelihood Estimation of Discrete Log-Concave Distributions with Applications written by Yanhua Tian and published by . This book was released on 2018 with total page 0 pages. Available in PDF, EPUB and Kindle. Book excerpt: Shape-constrained methods specify a class of distributions instead of a single parametric family. The approach increases the robustness of the estimation without much loss of efficiency. Among these, log-concavity is an appealing shape constraint in distribution modeling, because it falls into the popular unimodal shape-constraint and many parametric models are log-concave. This is, therefore, the focus of our work. First, we propose a maximum likelihood estimator of discrete log-concave distributions in higher dimensions. We define a new class of log-concave distributions in multiple dimensional spaces and study its properties. We show how to compute the maximum likelihood estimator from an independent and identically distributed sample, and establish consistency of the estimator, even if the class has been incorrectly specified. For finite sample sizes, the proposed estimator outperforms a purely nonparametric approach (the empirical distribution), but is able to remain comparable to the correct parametric approach. Furthermore, the new class has a natural relationship with log-concave densities when data has been grouped or discretized. We show how this property can be used in a real data example. Secondly, we apply the discrete log-concave maximum likelihood estimator in one-dimensional space to a clustering problem. Our work mainly focuses on the categorical nominal data. We develop a log-concave mixture model using the discrete log-concave maximum likelihood estimator. We then apply the log-concave mixture model to our clustering algorithm. We compare our proposed clustering algorithm with the other two clustering methods. Comparing results show that our proposed algorithm has a good performance.
Book Synopsis The Relevance of Distributional Assumptions in GARCH Models and Applications to the Evaluation of Financial Risk by : Maria Gloria González Rivera
Download or read book The Relevance of Distributional Assumptions in GARCH Models and Applications to the Evaluation of Financial Risk written by Maria Gloria González Rivera and published by . This book was released on 1991 with total page 300 pages. Available in PDF, EPUB and Kindle. Book excerpt:
