Handbook of Heavy-Tailed Distributions in Asset Management and Risk Management
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.Contents:PrefaceAbout the AuthorsPart I Preliminaries:IntroductionRandom VariablesStochastic Processes with JumpsPart II Theory and Methodology:The Generalized Hyperbolic DistributionThe Class of Stable DistributionsTempered Stable DistributionsMultivariate Time-Changed Brownian MotionMultivariate Time-Changed Brownian Motion: The Expectation–Maximization Estimation MethodExtreme Value TheoryPart III Applications:A Portfolio Selection Analysis with Non-Gaussian ModelsImplied Volatility Smile with Non-Gaussian ProcessesApplication of Extreme Value Theory to Estimate Tail Thickness for Asset Return DistributionsHow to Run the Matlab CodeLicenseAuthor IndexSubject Index Readership: For those who want to understand the main concepts regarding heavy-tailed distributions and Lévy processes using probability or statistics.Heavy Tail Distributions;Fat Tail Distributions;Lévy Processes;Tempered Stable Distributions;Multivariate Time-changed Brownian Motion;Extreme Value Theory;Risk Management0Key Features:The book differs from competing titles because it is not intended as a theoretical treatise on probability or statistics, but as a tool to understand the main concepts regarding heavy-tailed distributions and Lévy processes as applied to real-world problems in financeThe book seeks to fill the gap between theoretical models and the numerical analysis needed to turn them into a useful computer code for practical applications
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