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Title: Parametric estimation of tempered stable laws Authors:  Till Massing - University of Duisburg-Essen (Germany) [presenting]
Abstract: Tempered stable distributions are frequently used models in financial applications (e.g., for option pricing) in which the tails of stable distributions are too heavy. Unfortunately, given the non-explicit form of the probability density function, estimation relies on numerical algorithms such as the fast Fourier transform, which typically are time-consuming. We compare several parametric estimation methods, such as the maximum likelihood method and different generalized methods of moment approaches. We conduct extensive simulation studies to analyze finite sample properties measured by the empirical bias and precision and compare computational costs. Additionally, we study large sample properties and derive theoretical results for consistency, asymptotic normality, and asymptotic efficiency for our estimators. We cover various relevant subclasses of tempered stable distributions, including the classical tempered stable distribution and the tempered stable subordinator. Moreover, we discuss the normal tempered stable distribution, which arises by subordinating a Brownian motion with a tempered stable subordinator. Our financial application to energy spot prices illustrates the benefits of tempered stable models. The implemented routines will be published in an R package.