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

09/05/2021

∙

by   Karol Dąbrowski, et al.

∙

0

∙

share

We study a triple of stochastic processes: a Wiener process W_t, t ≥ 0, its running maxima process M_t=sup{W_s: s ∈ [0,t]} and its running minima process m_t=inf{W_s: s ∈ [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.