ASYMMETRICALLY TEMPERED STABLE DISTRIBUTIONS WITH
APPLICATIONS TO FINANCE
Abstract: In this paper, we introduce a technique to produce a new family of tempered stable
distributions. We call this family asymmetrically tempered stable distributions. We provide
two examples of this family named asymmetrically classical modified tempered stable
(ACMTS) and asymmetrically modified classical tempered stable (AMCTS) distributions.
Since the tempered stable distributions are infinitely divisible, Lévy processes can be induced
by the ACMTS and AMCTS distributions. The properties of these distributions will be
discussed along with the advantages in applying them to financial modeling. Furthermore, we
develop exponential Lévy models for them. To demonstrate the advantages of the exponential
Lévy ACMTS and AMCTS models, we estimate parameters for the SP 500 Index.
2000 AMS Mathematics Subject Classification: Primary: 60E07; Secondary:
91B84.
Keywords and phrases: Tempered stable distributions, exponential Lé vy model.