Sequential sampling for CGMY processes via decomposition of their time changes

Abstract

We present a new and easy‐to‐implement sequential sampling method for Carr–Geman–Madan–Yor (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 L1 sense. Simulation results show that the proposed method is advantageous over two existing methods under a model calibrated to historical option price data.