Australia and New Zealand Industrial and Applied Mathematics Annual Conference (ANZIAM2012) location:Warrnambool, Australia date:29 January - 2 February 2012
Monte Carlo (MC) and quasi-Monte Carlo (QMC) methods are often used in pricing complex financial 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 and 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 will present an extension to their method for valuing options that have a barrier feature on an underlying asset, incorporating and extending an idea from Staum and 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 accurate results. Our extension aims to reduce the required number of paths.