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Sequential sampling for CGMY processes via decomposition of their time changes
Author(s) -
Zhang Chengwei,
Zhang Zhiyuan
Publication year - 2018
Publication title -
naval research logistics (nrl)
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.665
H-Index - 68
eISSN - 1520-6750
pISSN - 0894-069X
DOI - 10.1002/nav.21821
Subject(s) - convolution (computer science) , sampling (signal processing) , representation (politics) , component (thermodynamics) , decomposition , algorithm , mathematics , computer science , coupling (piping) , carr , sampling scheme , process (computing) , mathematical optimization , scheme (mathematics) , statistics , mathematical analysis , artificial intelligence , filter (signal processing) , computer vision , estimator , law , ecology , engineering , biology , operating system , artificial neural network , political science , thermodynamics , mechanical engineering , physics , politics
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 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.