Sequential Sampling for CGMY Processes via Decomposition of their Time Changes

TL;DR

This paper introduces a new sequential sampling method for CGMY processes that decomposes the process into two independent components, enabling efficient and accurate simulation, especially useful for financial modeling.

Contribution

The paper proposes a novel decomposition-based sampling method for CGMY processes, improving efficiency and accuracy over existing techniques.

Findings

The method effectively samples the finite generalized gamma convolution component.

The second component can be made arbitrarily small, enhancing approximation accuracy.

Simulation results outperform existing methods on real market data.

Abstract

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.