Word of advice, "A correction note on the first passage time of an Ornstein-Ulhenbeck process to a boundary"has an error in the expression for the passage time density if your boundary <> 0. If you try to plug it into excel and do a fast numerical integration you will be lucky if it integrates to 1...See:"A clarification note about hitting times densities for Ornstein-Uhlenbeck processes" (2002) by Anja Göing-Jaeschke and Marc Yor (publicly available from
www.MaPhySto.dk)The abstract says it all:In this note, we point out that the formula given in the correction note by Leblanc et al. [5] for the distribution of the first hitting time of b by an Ornstein-Uhlenbeck process starting from a is only true in case b=0. The catch, there is always a catch..., is that Göing-Jaeschke and Yor do not derive the hitting time density for an arbitrary boundary, but only for the 0 case. At first this might be ok, but normally what we need in finance is the hitting time density for the Vasicek type which requires a time and position change to fit the setup of Göing-Jaeschke and Yor, rendering the boundary b<>0. If anyone should have the expression for the density for a general Vasicek type process for a nonzero boundary I would be delighted to see it!