Skew Ornstein–Uhlenbeck processes and their financial applications

In this paper, we investigate a special class of skew diffusions: skew Ornstein–Uhlenbeck (abbr. OU) processes, whose scale and speed densities are both piecewise functions. The existence and uniqueness of solutions regarding the related stochastic differential equations (abbr. SDEs) with local time are established, as well as the construction through time changes. Afterwards, we concentrate on three computing issues including the explicit expressions of transition densities, the cumulative distributions and Laplace transforms of the first hitting times for skew OU processes. With the hypothesis on asset dynamics, two financial instances in the field of credit risk are illustrated at the end of this paper.