  We present a new and easy-to-implement sequential sampling method for CGMY
processes with either finite or infinite variation, exploiting the time change
representation of the CGMY model and a decomposition of its time change. We
find that the time change can be decomposed into two independent components.
While the first component is a \emph{finite} \emph{generalized gamma
convolution} process whose increments can be sampled by either the exact double
CFTP ("coupling from the past") method or an approximation scheme with high
speed and accuracy, the second component can easily be made arbitrarily small
in the $L^1$ sense. Simulation results show that the proposed method is
advantageous over two existing methods under a model calibrated to historical
option price data.
