Leonenko, Nikolai N.  ORCID: https://orcid.org/0000-0003-1932-4091, Pepelyshev, Andrey ORCID: https://orcid.org/0000-0001-5634-5559 and Saidan, Bader
2026.
Exotic options in fractal activity time models with the student distribution of log-returns.
Presented at: Exploring the World of Mathematical Structures Workshop,
Västerås, Sweden,
14-16 May 2024.
Published in: Silvestrov, Sergei and Malyarenko, Anatoliy eds.
Mathematical Structures I—Stochastic and Analytic Structures with Applications.
Cham:
pp. 297-316.
10.1007/978-3-032-21365-5_10
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Official URL: https://doi.org/10.1007/978-3-032-21365-5_10
Abstract
We consider the fractal activity time geometric Brownian motion (FATGBM) model introduced by Heyde and Leonenko (Adv. Appl. Probab. 37(2):342–365 2005 [13]). We concentrate on the FATGBM model with Student marginals because log-returns for real data are well fitted by the location-scale Student distribution. We derive option pricing formulae for several derivatives including digital options, power options and barrier options. Numerical simulation confirms the derived formulae.
| Item Type: | Conference or Workshop Item - published (Paper) |
|---|---|
| Date Type: | Publication |
| Status: | Published |
| Schools: | Schools > Computational & Mathematical Sciences Schools > Mathematics |
| Additional Information: | RRS policy applied |
| ISBN: | 9783032213648 |
| ISSN: | 2194-1009 |
| Date of First Compliant Deposit: | 9 November 2026 |
| Last Modified: | 09 Nov 2026 11:30 |
| URI: | https://orca.cardiff.ac.uk/id/eprint/190749 |
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