Monte Carlo Option Pricing for Tempered Stable (CGMY) Processes

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Pricing discretely monitored Asian options under Levy processes (2008, methodology): “Unfortunately, this bias is difficult to quantify but, to the best of our knowledge, no exact simulation method for the increments of this process is known, although a possible alternative is proposed by Poirot and Tankov (2007) .”
On the jump activity index for semimartingales (2012, unknown): “The trajectories of the CGMY process could be approximately simulated by the time-changed-Brownian-motion algorithm, where the change of time is via the β/2 stable subordinator which is also a Lévy process with the Lévy density: fss(x) = KI(x > 0)/x1+β/2 for some constant K; see Poirot and Tankov (2”
Tempered stable and tempered infinitely divisible GARCH models (2010, methodology): “CTS distributed random numbers can be generated using the subordination method developed by Poirot and Tankov (2006).”
Jump-adapted discretization schemes for Lévy-driven SDEs (2010, methodology): “No easy algorithm is available for simulating the increments of this process (cf [15, 18]), however, it is straightforward to simulate random variables with density ν(x)1|x|>ε ∫ |x|>ε ν(x)dx using the rejection method [6, example 6.”