Mixed Tempered Stable distribution

TL;DR

The paper introduces the Mixed Tempered Stable distribution, a flexible new model for univariate returns that encompasses well-known distributions and outperforms existing models in financial data fitting.

Contribution

It presents a novel parametric distribution that generalizes existing models and demonstrates its effectiveness in modeling financial return data.

Findings

Provides a flexible distribution fitting various density shapes.

Outperforms competing distributions in financial time series modeling.

Includes well-known distributions as special cases.

Abstract

In this paper we introduce a new parametric distribution, the Mixed Tempered Stable. It has the same structure of the Normal Variance Mean Mixtures but the normality assumption leaves place to a semi-heavy tailed distribution. We show that, by choosing appropriately the parameters of the distribution and under the concrete specification of the mixing random variable, it is possible to obtain some well-known distributions as special cases. We employ the Mixed Tempered Stable distribution which has many attractive features for modeling univariate returns. Our results suggest that it is enough flexible to accomodate different density shapes. Furthermore, the analysis applied to statistical time series shows that our approach provides a better fit than competing distributions that are common in the practice of finance.