CBI-time-changed L\'evy processes
Abstract
We introduce and study the class of CBI-time-changed L\'evy processes (CBITCL), obtained by time-changing a L\'evy process with respect to an integrated continuous-state branching process with immigration (CBI). We characterize CBITCL processes as solutions to a certain stochastic integral equation and relate them to affine stochastic volatility processes. We provide a complete analysis of the time of explosion of exponential moments of CBITCL processes and study their asymptotic behavior. In addition, we show that CBITCL processes are stable with respect to a suitable class of equivalent changes of measure. As illustrated by some examples, CBITCL processes are flexible and tractable processes with a significant potential for applications in finance.
Keywords
Cite
@article{arxiv.2205.12355,
title = {CBI-time-changed L\'evy processes},
author = {Claudio Fontana and Alessandro Gnoatto and Guillaume Szulda},
journal= {arXiv preprint arXiv:2205.12355},
year = {2023}
}