CGMY and Meixner Subordinators are Absolutely Continuous with respect to One Sided Stable Subordinators

TL;DR

This paper demonstrates that CGMY and Meixner processes can be represented as time-changed Brownian motions with time changes absolutely continuous relative to specific one-sided stable subordinators, facilitating simulation.

Contribution

It establishes the absolute continuity of CGMY and Meixner subordinators with respect to one-sided stable subordinators and describes their simulation via jump filtering.

Findings

CGMY and Meixner processes are time-changed Brownian motions.

The time changes are absolutely continuous with respect to specific stable subordinators.

Simulation can be performed by generating stable subordinators and filtering jumps.

Abstract

We describe the CGMY and Meixner processes as time changed Brownian motions. The CGMY uses a time change absolutely continuous with respect to the one-sided stable $(Y/2)$ subordinator while the Meixner time change is absolutely continuous with respect to the one sided stable $(1/2)$ subordinator$.$ The required time changes may be generated by simulating the requisite one-sided stable subordinator and throwing away some of the jumps as described in Rosinski (2001).