Exponential stock models driven by tempered stable processes
Mathematical Finance
2025-11-21 v1 Probability
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.
Keywords
Cite
@article{arxiv.1907.05142,
title = {Exponential stock models driven by tempered stable processes},
author = {Uwe Küchler and Stefan Tappe},
journal= {arXiv preprint arXiv:1907.05142},
year = {2025}
}
Comments
20 pages