Monte Carlo Simulation in Valuing Parisian and Parasian Barrier Options

Abstract

Although a number of researchers have grappled with the problem of valuing Parisian and Parasian barrier options, few have used Monte Carlo methods to do so. In this thesis, we first create new Monte Carlo algorithms that use Brownian bridges and various other statistical shortcuts to quickly and accurately value Parisian and Parasian options. We find that with this advanced Monte Carlo simulation, we are able to use fewer points of randomness to obtain a more accurate result. Furthermore, we test the efficacies of various variance reduction techniques in the valuation of a number of cases of Parisian and Parasian barrier options, varying the parameters of the options. As might be expected, the usefulness of these variance reduction techniques differ greatly from case to case. In particular, we find that antithetic variates are not useful at all times, as previous researchers have put forth when studying variance reduction in valuing standard barrier options. We suggest that when valuing both Parisian and Parasian barrier options, the analogous standard barrier option works very well as a control variate; its ease of implementation means that it is a viable variance reduction technique to use in a wide range of valuations.