Symmetrization associated with hyperbolic reflection principle
Abstract In this paper, in view of application to pricing of Barrier options under a stochastic volatility model, we study a reflection principle for the hyperbolic Brownian motion, and introduce a hyperbolic version of Imamura-Ishigaki-Okumura’s symmetrization. Some results of numerical experiments...
| Main Authors: | , , |
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| Format: | Article |
| Language: | English |
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SpringerOpen
2018-01-01
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| Series: | Pacific Journal of Mathematics for Industry |
| Subjects: | |
| Online Access: | http://link.springer.com/article/10.1186/s40736-017-0035-2 |
| _version_ | 1818555430503186432 |
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| author | Yuuki Ida Tsuyoshi Kinoshita Tomohiro Matsumoto |
| author_facet | Yuuki Ida Tsuyoshi Kinoshita Tomohiro Matsumoto |
| author_sort | Yuuki Ida |
| collection | DOAJ |
| description | Abstract In this paper, in view of application to pricing of Barrier options under a stochastic volatility model, we study a reflection principle for the hyperbolic Brownian motion, and introduce a hyperbolic version of Imamura-Ishigaki-Okumura’s symmetrization. Some results of numerical experiments, which imply the efficiency of the numerical scheme based on the symmetrization, are given. |
| first_indexed | 2024-12-12T09:53:22Z |
| format | Article |
| id | doaj.art-c5071fe47aa143a490be3b3448d46347 |
| institution | Directory Open Access Journal |
| issn | 2198-4115 |
| language | English |
| last_indexed | 2024-12-12T09:53:22Z |
| publishDate | 2018-01-01 |
| publisher | SpringerOpen |
| record_format | Article |
| series | Pacific Journal of Mathematics for Industry |
| spelling | doaj.art-c5071fe47aa143a490be3b3448d463472022-12-22T00:28:13ZengSpringerOpenPacific Journal of Mathematics for Industry2198-41152018-01-011011810.1186/s40736-017-0035-2Symmetrization associated with hyperbolic reflection principleYuuki Ida0Tsuyoshi Kinoshita1Tomohiro Matsumoto2Department of Mathematics, Ritsumeikan UniversityDepartment of Mathematics, Ritsumeikan UniversityDepartment of Mathematics, Ritsumeikan UniversityAbstract In this paper, in view of application to pricing of Barrier options under a stochastic volatility model, we study a reflection principle for the hyperbolic Brownian motion, and introduce a hyperbolic version of Imamura-Ishigaki-Okumura’s symmetrization. Some results of numerical experiments, which imply the efficiency of the numerical scheme based on the symmetrization, are given.http://link.springer.com/article/10.1186/s40736-017-0035-2Hyperbolic Brownian motionReflection principleSymmetrizationBarrier optionEuler-Maruyama scheme |
| spellingShingle | Yuuki Ida Tsuyoshi Kinoshita Tomohiro Matsumoto Symmetrization associated with hyperbolic reflection principle Pacific Journal of Mathematics for Industry Hyperbolic Brownian motion Reflection principle Symmetrization Barrier option Euler-Maruyama scheme |
| title | Symmetrization associated with hyperbolic reflection principle |
| title_full | Symmetrization associated with hyperbolic reflection principle |
| title_fullStr | Symmetrization associated with hyperbolic reflection principle |
| title_full_unstemmed | Symmetrization associated with hyperbolic reflection principle |
| title_short | Symmetrization associated with hyperbolic reflection principle |
| title_sort | symmetrization associated with hyperbolic reflection principle |
| topic | Hyperbolic Brownian motion Reflection principle Symmetrization Barrier option Euler-Maruyama scheme |
| url | http://link.springer.com/article/10.1186/s40736-017-0035-2 |
| work_keys_str_mv | AT yuukiida symmetrizationassociatedwithhyperbolicreflectionprinciple AT tsuyoshikinoshita symmetrizationassociatedwithhyperbolicreflectionprinciple AT tomohiromatsumoto symmetrizationassociatedwithhyperbolicreflectionprinciple |