Option Pricing by Willow Tree Method for Generalized Hyperbolic Lévy Processes
In this paper, a new approach is proposed to construct willow tree (WT) for generalized hyperbolic (GH) Lévy processes. There are two advantages of our proposed approach compared to the classical WT methods. Firstly, it avoids the moments matching from Johnson curve in the known WT construction. Sec...
| Main Authors: | , , |
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| Format: | Article |
| Language: | English |
| Published: |
Hindawi Limited
2023-01-01
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| Series: | Journal of Mathematics |
| Online Access: | http://dx.doi.org/10.1155/2023/9996556 |
| _version_ | 1797650868426768384 |
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| author | Hongying Wu Zhiqiang Zhou Caijuan Kang |
| author_facet | Hongying Wu Zhiqiang Zhou Caijuan Kang |
| author_sort | Hongying Wu |
| collection | DOAJ |
| description | In this paper, a new approach is proposed to construct willow tree (WT) for generalized hyperbolic (GH) Lévy processes. There are two advantages of our proposed approach compared to the classical WT methods. Firstly, it avoids the moments matching from Johnson curve in the known WT construction. Secondly, the error of European option pricing is only determined by time partition ∆t under some conditions. Since the moments of Lévy measure are removed from this algorithm, our approach improves the stability and accuracy of WT in option pricing. Numerical experiments support our claims. Moreover, the new approach can be extended to other Lévy processes if their characteristic functions are expressed by explicit forms. |
| first_indexed | 2024-03-11T16:07:51Z |
| format | Article |
| id | doaj.art-f9cf2b41f2f346e284d8a05445335ed6 |
| institution | Directory Open Access Journal |
| issn | 2314-4785 |
| language | English |
| last_indexed | 2024-03-11T16:07:51Z |
| publishDate | 2023-01-01 |
| publisher | Hindawi Limited |
| record_format | Article |
| series | Journal of Mathematics |
| spelling | doaj.art-f9cf2b41f2f346e284d8a05445335ed62023-10-25T00:00:04ZengHindawi LimitedJournal of Mathematics2314-47852023-01-01202310.1155/2023/9996556Option Pricing by Willow Tree Method for Generalized Hyperbolic Lévy ProcessesHongying Wu0Zhiqiang Zhou1Caijuan Kang2School of Mathematics and Information ScienceSchool of Economics and ManagementSchool of Economics and ManagementIn this paper, a new approach is proposed to construct willow tree (WT) for generalized hyperbolic (GH) Lévy processes. There are two advantages of our proposed approach compared to the classical WT methods. Firstly, it avoids the moments matching from Johnson curve in the known WT construction. Secondly, the error of European option pricing is only determined by time partition ∆t under some conditions. Since the moments of Lévy measure are removed from this algorithm, our approach improves the stability and accuracy of WT in option pricing. Numerical experiments support our claims. Moreover, the new approach can be extended to other Lévy processes if their characteristic functions are expressed by explicit forms.http://dx.doi.org/10.1155/2023/9996556 |
| spellingShingle | Hongying Wu Zhiqiang Zhou Caijuan Kang Option Pricing by Willow Tree Method for Generalized Hyperbolic Lévy Processes Journal of Mathematics |
| title | Option Pricing by Willow Tree Method for Generalized Hyperbolic Lévy Processes |
| title_full | Option Pricing by Willow Tree Method for Generalized Hyperbolic Lévy Processes |
| title_fullStr | Option Pricing by Willow Tree Method for Generalized Hyperbolic Lévy Processes |
| title_full_unstemmed | Option Pricing by Willow Tree Method for Generalized Hyperbolic Lévy Processes |
| title_short | Option Pricing by Willow Tree Method for Generalized Hyperbolic Lévy Processes |
| title_sort | option pricing by willow tree method for generalized hyperbolic levy processes |
| url | http://dx.doi.org/10.1155/2023/9996556 |
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