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 finite 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. Our approach is appealing in that its approximation errors have a more transparent interpretation than those of existing methods. The proposed method is compared with several widely used methods via simulations of the pricing of European and path-dependent options.
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