Option pricing by simulation

Abstract

The valuation of path dependent and multivariate options require efficient numerical methods, as their prices are not available in closed form. Monte Carlo simulation is one of the widely used techniques. Although simulation is a highly exible and general method, its e ciency for speci c problems depends on exploiting the special features of that problem via variance reduction techniques. The aim in variance reduction is to reduce the variance of the estimator in order to increase the e ciency. This study proposes new variance reduction methods for path dependent and multivariate options under the assumption of geometric Brownian motion. These methods are based on new control variates. Furthermore, a general control variate framework is suggested for L evy process models. Its application is presented for pricing path dependent options. The options considered in this thesis are European basket, Asian, lookback and barrier options. The method suggested for basket and Asian options combines the use of control variates and conditional Monte Carlo. The new control variate algorithms for lookback and barrier options use the continuously monitored options as external control variates for their discrete counterparts. The general control variate framework for L evy process models contains special and general control variates, which are path functionals of the original L evy process and a coupled Brownian motion. The method is based on fast numerical inversion of the cumulative distribution functions.