On the dependence between a Wiener process and its running maxima and running minima processes

Karol Dąbrowski; Piotr Jaworski

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arXiv · 2109.02024

On the dependence between a Wiener process and its running maxima and running minima processes

Karol Dąbrowski·Piotr Jaworski

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Abstract

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.

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Karol Dąbrowski, Piotr Jaworski. 2021-09-05. On the dependence between a Wiener process and its running maxima and running minima processes. https://arxiv.org/abs/2109.02024

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