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Exact simulation of truncated Lévy subordinator
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Dassios, Angelos, Lim, Jia Wei and Qu, Yan (2020) Exact simulation of truncated Lévy subordinator. Transactions on Modeling and Computer Simulation, 30 (3). 17. doi:10.1145/3368088 ISSN 1049-3301.
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Official URL: https://doi.org/10.1145/3368088
Abstract
A truncated Lévy subordinator is a Lévy subordinator in R+ with Lévy measure restricted from above by a certain level b. In this paper, we study the path and distribution properties of this type of processes in detail and set up an exact simulation framework based on a marked renewal process. In particular, we focus on a typical specification of truncated Lévy subordinator, namely the truncated stable process. We establish an exact simulation algorithm for the truncated stable process, which is very accurate and efficient. Compared to the existing algorithm suggested in Chi (2012), our algorithm outperforms over all parameter settings. Using a distribution decomposition technique, we also develop an exact simulation algorithm for the truncated tempered stable process and other related processes. We illustrate an application of our algorithm as a valuation tool for stochastic hyperbolic discounting, and numerical analysis are provided to demonstrate the accuracy and effectiveness of our methods. We also show that variations of the result can also be used to sample two-sided truncated Lévy processes, two-sided Lévy processes via subordinating Brownian motions, and truncated Lévy driven Ornstein-Uhlenbeck processes.
Item Type: | Journal Article | ||||||
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Subjects: | H Social Sciences > HA Statistics Q Science > QA Mathematics |
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Divisions: | Faculty of Science, Engineering and Medicine > Science > Statistics | ||||||
Library of Congress Subject Headings (LCSH): | Monte Carlo method, Probabilities, Lévy processes | ||||||
Journal or Publication Title: | Transactions on Modeling and Computer Simulation | ||||||
Publisher: | ACM | ||||||
ISSN: | 1049-3301 | ||||||
Official Date: | May 2020 | ||||||
Dates: |
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Volume: | 30 | ||||||
Number: | 3 | ||||||
Article Number: | 17 | ||||||
DOI: | 10.1145/3368088 | ||||||
Status: | Peer Reviewed | ||||||
Publication Status: | Published | ||||||
Reuse Statement (publisher, data, author rights): | Full cite © ACM 2020. This is the author's version of the work. It is posted here for your personal use. Not for redistribution. The definitive Version of Record was published in Transactions on Modeling and Computer Simulation, http://dx.doi.org/10.1145//3368088 | ||||||
Access rights to Published version: | Restricted or Subscription Access | ||||||
Date of first compliant deposit: | 16 October 2019 | ||||||
Date of first compliant Open Access: | 24 February 2021 | ||||||
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