Fractal activity time models for risky asset with dependence and generalized hyperbolic distributions

Leonenko, Nikolai N. ORCID: https://orcid.org/0000-0003-1932-4091, Petherick, Stuart Gary and Sikorskii, A. 2012. Fractal activity time models for risky asset with dependence and generalized hyperbolic distributions. Stochastic Analysis and Applications 30 (3) , pp. 476-492. 10.1080/07362994.2012.668443

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Abstract

Risky asset models with the dependence through fractal activity time are described. The construction of the fractal activity time is implemented via superpositions of Ornstein-Uhlenbeck type processes driven by Lévy noise. The model features both tractable dependence structure and desired marginal distributions of the returns from the generalized hyperbolic class: the Variance Gamma and normal inverse Gaussian. These distributions provide good fit to real financial data. Pricing formulae for the proposed models are derived.

Item Type:	Article
Date Type:	Publication
Status:	Published
Schools:	Mathematics
Subjects:	Q Science > QA Mathematics
Uncontrolled Keywords:	Fractal activity time, Geometric Brownian motion, Lévy noise, Normal inverse Gaussian distribution, Ornstein-Uhlenbeck type processes, Self-similarity, Variance Gamma distribution
Publisher:	Taylor and Francis
ISSN:	0736-2994
Last Modified:	20 Oct 2022 08:46
URI:	https://orca.cardiff.ac.uk/id/eprint/29553

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