Extensions of the LT method for option pricing

Monte Carlo (MC) and quasi-Monte Carlo (QMC) methods are often used in pricing complex derivatives. The merit of QMC is that, theoretically at least, higher convergence rates can be obtained than regular MC. The payoff function is usually high-dimensional and non-smooth, eliminating the advantage of using QMC. Imai & Tan (2006) introduced the LT method which minimizes the effective dimension of the problem by transforming the normal variates using an orthogonal transformation, thereby improving the QMC method. We extended their method for valuing options that have a barrier feature on an underlying asset, incorporating and extending an idea from Staum & Glasserman (2001). These options have a payoff that depends on whether the asset does or does not cross a certain level during the life of the option. If the probability of (not) hitting is large enough, then much more paths have to be sampled for reliable results. Our method greatly reduces the required number of paths and our aim is to extend this method to Levy market models.status: publishe