Tempered Stable Distributions

Michele Leonardo Bianchi, Stoyan V Stoyanov, Gian Luca Tassinari, Frank Fabozzi () and Sergio M Focardi

Chapter 6 in Handbook of Heavy-Tailed Distributions in Asset Management and Risk Management, 2019, pp 225-275 from World Scientific Publishing Co. Pte. Ltd.

Abstract: The main topics covered in this chapter are:the history of the tempered stable distribution and why this distribution has been applied in finance;the main properties and formulas of tempered stable laws;the evaluation of the characteristic function in a non-trivial case (i.e., for the rapidly decreasing tempered stable law);probability density and cumulative distribution function evaluation when only the characteristic function is available in closed form while the density function is not;how to generate sample draws from a tempered stable distribution;how to estimate the parameters of a tempered stable distribution from a sample;how to evaluate well-known risk measures for a tempered stable stock market model.

Keywords: Heavy Tail Distributions; Fat Tail Distributions; Lévy Processes; Tempered Stable Distributions; Multivariate Time-changed Brownian Motion; Extreme Value Theory; Risk Management (search for similar items in EconPapers)
JEL-codes: C02 G32 (search for similar items in EconPapers)
Date: 2019
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