Author: Michael GrabchakPublisher:
ISBN:
Category :
Languages : en
Pages : 254
Book Description
Maximum Likelihood Estimation of Parametric Tempered Stable Distributions on the Real Line with Applications to Finance
Author: Michael GrabchakStatistical Tools for Finance and Insurance
Author: Pavel CizekPublisher: Springer Science & Business Media
ISBN: 3642180620
Category : Business & Economics
Languages : en
Pages : 410
Book Description
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
Quantile-Based Inference for Tempered Stable Distributions
Author: Hasan FallahgoulPublisher:
ISBN:
Category :
Languages : en
Pages : 25
Book Description
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.
Parameter Estimation for Stable Distributions
Author: Gaoyuan TianPublisher:
ISBN: 9781339671680
Category :
Languages : en
Pages : 94
Book Description
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.
Extreme Value Distributions
Author: Samuel KotzPublisher: World Scientific
ISBN: 1860944027
Category : Mathematics
Languages : en
Pages : 195
Book Description
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."
Rapid Maximum Likelihood Estimation of Stable Distribution Parameters
Author: Timothy MastersParametric Distributional Flexibility and Conditional Variance Models with an Application to Hourly Exchange Rates
Author: Ms.Jenny N. LyePublisher: International Monetary Fund
ISBN: 1451844778
Category : Business & Economics
Languages : en
Pages : 40
Book Description
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.
Handbook of Heavy Tailed Distributions in Finance
Author: S.T RachevPublisher: Elsevier
ISBN: 0080557732
Category : Business & Economics
Languages : en
Pages : 707
Book Description
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.
Lognormal Distributions
Author: CrowPublisher: Routledge
ISBN: 1351434691
Category : Mathematics
Languages : en
Pages : 408
Book Description
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.
Univariate Stable Distributions
Author: John P. NolanPublisher: Springer Nature
ISBN: 3030529150
Category : Mathematics
Languages : en
Pages : 342
Book Description
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.