# Exponential stock models driven by tempered stable processes

## TL;DR

This paper explores exponential stock models driven by tempered stable processes, analyzing their mathematical properties and providing option pricing formulas, with a focus on martingale measures and practical case studies.

## Contribution

It offers a systematic analysis of martingale measures for tempered stable driven models and derives explicit pricing formulas for European options.

## Key findings

- Existence of equivalent martingale measures established.
- Explicit pricing formulas for European call options derived.
- Case study demonstrating model application and effectiveness.

## Abstract

We investigate exponential stock models driven by tempered stable processes, which constitute a rich family of purely discontinuous L\'{e}vy processes. With a view of option pricing, we provide a systematic analysis of the existence of equivalent martingale measures, under which the model remains analytically tractable. This includes the existence of Esscher martingale measures and martingale measures having minimal distance to the physical probability measure. Moreover, we provide pricing formulae for European call options and perform a case study.