Abstract
Lévy processes are popular models for stock price behavior since they allow to take into account jump risk and reproduce the implied volatility smile. In this paper, we focus on the tempered stable (also known as CGMY) processes, which form a flexible 6-parameter family of Lévy processes with infinite jump intensity. It is shown that under an appropriate equivalent probability measure a tempered stable process becomes a stable process whose increments can be simulated exactly. This provides a fast Monte Carlo algorithm for computing the expectation of any functional of tempered stable process. We use our method to price European options and compare the results to a recent approximate simulation method for tempered stable process by Madan and Yor (CGMY and Meixner Subordinators are absolutely continuous with respect to one sided stable subordinators, 2005).
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Poirot, J., Tankov, P. Monte Carlo Option Pricing for Tempered Stable (CGMY) Processes. Asia-Pacific Finan Markets 13, 327–344 (2006). https://doi.org/10.1007/s10690-007-9048-7
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DOI: https://doi.org/10.1007/s10690-007-9048-7