Mixed Tempered Stable Distribution

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.

A New Tempered Stable Distribution and Its Application to Finance

In this paper, we will discuss a parametric approach to risk-neutral density extraction from option prices based on the knowledge of the estimated historical density. A flexible distribution is needed in order to find an equivalent change of measure and, at the same time, take into account the historical estimates. To this end, we introduce a new tempered stable distribution we refer to as the ...

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

Tempered Fractional Stable Motion

Tempered fractional stable motion adds an exponential tempering to the power-law kernel in a linear fractional stable motion, or a shift to the power-law filter in a harmonizable fractional stable motion. Increments from a stationary time series that can exhibit semi-long-range dependence. This paper develops the basic theory of tempered fractional stable processes, including dependence structu...