Time-changed Lévy processes and option pricing: a critical comment

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 framework hinges on the stopping time property of the time changes. By ana- lyzing the measurability of the time changes with respect to the underlying filtration, we show that many asset price models using correlated time changes fail to satisfy this assumption.

Keywords: Jumps, Time Changes, Business Time

JEL Classification: G10, G12, G13