Tempered stable distributions and finite variation Ornstein-Uhlenbeck\n processes

2020/11/18 by Nicola Cufaro Petroni, Petroni, Nicola Cufaro, Piergiacomo Sabino +1
Economics, Econometrics and Finance · Mathematics · #60G51 60G51 #60G55 #65C05 #Computational Finance (q-fin.CP) #FOS: Economics and business #FOS: Mathematics #Financial Risk and Volatility Modeling #Probability (math.PR) #Stochastic processes and financial applications #Stochastic processes and statistical mechanics

paper · pdf · doi:10.48550/arxiv.2011.09147

openalex publication_date 2020/11/18 · openalex created_date 2021/09/13 · openalex updated_date 2026/07/28

Abstract

Constructing Levy-driven Ornstein-Uhlenbeck processes is a task closely\nrelated to the notion of self-decomposability. In particular, their transition\nlaws are linked to the properties of what will be hereafter called the\n\a-reminder of their self-decomposable stationary laws. In the present\nstudy we fully characterize the L 'evy triplet of these a-reminder s and we\nprovide a general framework to deduce the transition laws of the finite\nvariation Ornstein-Uhlenbeck processes associated with tempered stable\ndistributions. We focus finally on the subclass of the exponentially-modulated\ntempered stable laws and we derive the algorithms for an exact generation of\nthe skeleton of Ornstein-Uhlenbeck processes related to such distributions,\nwith the further advantage of adopting a procedure computationally more\nefficient than those already available in the existing literature.\n

Citations

• The Variance Gamma (V.G.) Model for Share Market Returns
• Exact simulation of Ornstein–Uhlenbeck tempered stable processes

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