hi, interestingly I had to implement this at work and the first approach I used was the “closed form” you mentioned in RISK. By the way, the reason it is called Parisian Option is simply that it was derived by a bunch of academics from Paris: Monique Jeanblanc, M. Chesney, M. YorYou can take a look at the paper "Brownianexcursion and Parisian Barrier options" which can be found at
www.univ-evry.fr/labos/lami/maths/pages ... nc.htmlThe problem is that the solution is a Laplace Transform that needs to be inverted numerically. There are many methods for this however this inversion is very very non-robust and unstable (I emailed Monique Jeanblac and she confirmed) so the method is NOT practically helpful.I then used an explicit version (Trinomial Tree) of the Haber-Schonbucher-Wilmott grid and it seems to be working well. (No flattery intended)A very similar approach was described in Avellaneda and Wu's paper "Pricing Parisian options with a trinomial lattice method" available on
http://www.math.nyu.edu/research/lixin/ (but be careful, unlike Haber-Schonbucher-Wilmott, they suppose for the option to knock-out stock has to be STRICTLY above barrier and also they use a closed-form for the knock-in probability once the stock is above the barrier which unlike Haber-Schonbucher-Wilmott, would not allow you to price American options)