Fast simulation of tempered stable Ornstein–Uhlenbeck processes

Piergiacomo Sabino () and Nicola Cufaro Petroni ()
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Piergiacomo Sabino: Quantitative Risk Management
Nicola Cufaro Petroni: Università di Bari INFN Sezione di Bari

Computational Statistics, 2022, vol. 37, issue 5, No 17, 2517-2551

Abstract: Abstract Constructing Lévy-driven Ornstein–Uhlenbeck processes is a task closely related to the notion of self-decomposability. In particular, their transition laws are linked to the properties of what will be hereafter called the a-remainder of their self-decomposable stationary laws. In the present study we fully characterize the Lévy triplet of these $$a$$ a -remainders and we provide a general framework to deduce the transition laws of the finite variation Ornstein–Uhlenbeck processes associated with tempered stable distributions. We focus finally on the subclass of the exponentially-modulated tempered stable laws and we derive the algorithms for an exact generation of the skeleton of Ornstein–Uhlenbeck processes related to such distributions, with the further advantage of adopting procedures which are tens of times faster than those already available in the existing literature.

Keywords: Lévy-driven Ornstein–Uhlenbeck processes; Self-decomposable laws; Tempered stable distributions; Simulations (search for similar items in EconPapers)
Date: 2022
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Citations: View citations in EconPapers (4)

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DOI: 10.1007/s00180-022-01205-8

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