Journal of Computational Finance

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Representing the CGMY and Meixner Lévy processes as time changed Brownian motions

Dilip B. Madan, Marc Yor

ABSTRACT

We describe the Carr–Geman–Madan–Yor (CGMY) and Meixner processes as time changed Brownian motions. The CGMY uses a time change that is 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 by Asmussen and Rosinski (2001).

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