On the dependence between a Wiener process and its running maxima and running minima processes
Abstract
We study a triple of stochastic processes: a Wiener process Wt, t ≥ 0, its running maxima process Mt= \Ws: s ∈ [0,t]\ and its running minima process mt=∈f \Ws: 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.
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