Modelling the Dependence between a Wiener Process and Its Running Maxima and Running Minima Processes.

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 formula for the corresponding copula and show that it is supported on the hemicube, a convex hexahedron with seven vertices. As an application, we draw out an analytical formula for pricing of a double barrier option. [ABSTRACT FROM AUTHOR]