Asymmetrically tempered stable distributions with applications to finance

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, Levy 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 Levy models for them. To demonstrate the advantages of the exponential Levy ACMTS and AMCTS models, we estimate parameters for the S&P 500 Index.