CBI-time-changed L\'evy processes

TL;DR

This paper introduces CBITCL processes, a new class of stochastic models obtained by time-changing Le9vy processes with integrated CBI processes, with applications in finance.

Contribution

It characterizes CBITCL processes, analyzes their exponential moments, asymptotic behavior, and stability under measure changes, highlighting their flexibility and tractability.

Findings

Complete analysis of exponential moment explosion times

Asymptotic behavior characterization

Stability under measure changes

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.