We derive the joint density of a Skew Brownian motion, its last visit to the origin, its local and occupation times. The result allows to obtain explicit analytical formulas for pricing European options under both a two valued local volatility model and a displaced diffusion model with constrained volatility.

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This note concerns distributions of Skew Brownian motion with dry friction and its occupation time. These distributions were obtained in [2] by using the Laplace transform and joint characteristic functions. We provide an alternative approach to deriving these distributions. Our approach is based on using the results for Skew Brownian motion obtained in [3].

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