The Tempered Discrete Linnik distribution

Modeling overdispersion with the normalized tempered stable distribution

A multivariate distribution which generalizes the Dirichlet distribution is introduced and its use for modeling overdispersion in count data is discussed. The distribution is constructed by normalizing a vector of independent tempered stable random variables. General formulae for all moments and cross-moments of the distribution are derived and they are found to have similar forms to those for ...

The Normal Tempered Stable Distribution for synthetic CDO pricing

A general recursive formula for the discrete stable and Linnik distributions and a family of extensions

The purpose of this paper is to present a general method to compute recursively the probability mass function of the discrete stable, discrete Linnik and discrete Mittag-Le­ er distribution. The recursive computation method is based on the representation of these distributions as compound distributions and on the Panjer algorithm (see Panjer (1981), Klugman et al. (1998) or Rolski et al. (1999)...

Infinite Variation Tempered Stable Ornstein-Uhlenbeck Processes with Discrete Observations

We investigate transition law between consecutive observations of Ornstein-Uhlenbeck processes of infinite variation with tempered stable stationary distribution. Thanks to the Markov autoregressive structure, the transition law can be written in the exact sense as a convolution of three random components; a compound Poisson distribution and two independent tempered stable distributions, one wi...

A Modified Tempered Stable Distribution with Volatility Clustering

We first introduce a new variant of the tempered stable distribution, named the modified tempered stable(MTS) distribution and we use it to develop the GARCH option pricing model with MTS innovations. This model allows one to describe some stylized phenomena observed in financial markets such as volatility clustering, skewness, and heavy tails of the return distribution.