On the dependence between a Wiener process and its running maxima and running minima processes
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arXiv
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| Hauptverfasser: | , |
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| Format: | Preprint |
| Veröffentlicht: |
2021
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| author | Dąbrowski, Karol Jaworski, Piotr |
| author_facet | Dąbrowski, Karol Jaworski, Piotr |
| contents | We study a triple of stochastic processes: a Wiener process $W_t$, $t \geq 0$, its running maxima process $M_t=\sup \{W_s: s \in [0,t]\}$ and its running minima process $m_t=\inf \{W_s: s \in [0,t]\}$. We derive the analytical formulas for the joint distribution function and the corresponding copula. As an application we draw out an analytical formula for pricing double barrier options. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2109_02024 |
| institution | arXiv |
| publishDate | 2021 |
| record_format | arxiv |
| spellingShingle | On the dependence between a Wiener process and its running maxima and running minima processes Dąbrowski, Karol Jaworski, Piotr Probability Statistics Theory 60G18 (Primary) 60G70, 60E05, 62H05, 62H20, 91G20 (Secondary) We study a triple of stochastic processes: a Wiener process $W_t$, $t \geq 0$, its running maxima process $M_t=\sup \{W_s: s \in [0,t]\}$ and its running minima process $m_t=\inf \{W_s: s \in [0,t]\}$. We derive the analytical formulas for the joint distribution function and the corresponding copula. As an application we draw out an analytical formula for pricing double barrier options. |
| title | On the dependence between a Wiener process and its running maxima and running minima processes |
| topic | Probability Statistics Theory 60G18 (Primary) 60G70, 60E05, 62H05, 62H20, 91G20 (Secondary) |
| url | https://arxiv.org/abs/2109.02024 |