English

Clark-Ocone formula for the maximum of processes with the stochastic intensity and its application

Probability 2025-05-27 v1

Abstract

Pricing of the lookback options using the Clark-Ocone formula for the underlying assets driven by stochastic L\'evy processes requires computing the Malliavin derivatives of their maximum or minimum on the Wiener-Poisson space and their distributions. In this work, we will find a generalization of the explicit representation of the Clark-Ocone formula on the maximum of two types of L\'evy processes with stochastic intensity: Cox processes with CIR-modeled intensities, and the Hawkes processes.

Keywords

Cite

@article{arxiv.2505.18370,
  title  = {Clark-Ocone formula for the maximum of processes with the stochastic intensity and its application},
  author = {Mahdieh Tahmasebi},
  journal= {arXiv preprint arXiv:2505.18370},
  year   = {2025}
}