• Corpus ID: 237420894

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

  title={On the dependence between a Wiener process and its running maxima and running minima processes},
  author={Karol Dkabrowski and Piotr Jaworski},
We study a triple of stochastic processes: a Wiener process Wt, t ≥ 0, its running maxima process Mt = sup{Ws : s ∈ [0, t]} and its running minima process mt = inf{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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