Correlated time-changed L\'evy Processes

TL;DR

This paper extends Carr and Wu's framework for continuous-time option pricing models by allowing adapted, non-stopping time changes, broadening the applicability of their results to more general models.

Contribution

It introduces a generalized approach for correlated time-changed Lévy processes where the time changes are adapted but not necessarily stopping times, expanding the original framework.

Findings

Applicable to all models in CW

Provides analogous results for adapted time changes

Broadens the class of models for option pricing

Abstract

Carr and Wu (2004), henceforth CW, developed a framework that encompasses almost all of the continuous-time models proposed in the option pricing literature. Their main result hinges on the stopping time property of the time changes, but all of the models CW proposed for the time changes do not satisfy this assumption. In this paper, when the time changes are adapted, but not necessarily stopping times, we provide analogous results to CW. We show that our approach can be applied to all models in CW.