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We study a triple of stochastic processes: a Wiener process $W_t$, $t \geq0$, its running maxima process $M_t=\sup \{W_s: s \in [0,t]\}$ and its runningminima process $m_t=\inf \{W_s: s \in [0,t]\}$. We derive the analyticalformulas for the joint distribution function and the corresponding copula. Asan application we draw out an analytical formula for pricing double barrieroptions.

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